From df668a3362c988d87b547118cbd68cd0802d25ab Mon Sep 17 00:00:00 2001 From: =?utf8?q?Andr=C3=A9s=20Mej=C3=ADa?= Date: Wed, 26 Oct 2011 19:25:52 -0500 Subject: [PATCH] Adding ICPC Live Archive --- ICPC Live Archive/3130 - Pipes/in.txt | 7 + ICPC Live Archive/3130 - Pipes/pipes_oh | Bin 0 -> 14472 bytes ICPC Live Archive/3130 - Pipes/pipes_oh.cpp | 110 + ICPC Live Archive/3927 - Ambiguous Codes/3927.cpp | 133 + ICPC Live Archive/3927 - Ambiguous Codes/a.out | Bin 0 -> 41352 bytes .../3927 - Ambiguous Codes/ambiguous.in | 8343 + .../3927 - Ambiguous Codes/ambiguous.sol | 107 + ICPC Live Archive/3927 - Ambiguous Codes/gen.rb | 10 + ICPC Live Archive/3927 - Ambiguous Codes/in.txt | 110 + ICPC Live Archive/3927 - Ambiguous Codes/myout | 107 + ICPC Live Archive/3927 - Ambiguous Codes/rand.in | 102 + .../3927 - Ambiguous Codes/testset_2007/acqua.in | 271155 ++++++++++++++ .../3927 - Ambiguous Codes/testset_2007/acqua.sol | 265545 ++++++++++++++ .../testset_2007/ambiguous.in | 8343 + .../testset_2007/ambiguous.sol | 107 + .../testset_2007/ballroom.in | 4522 + .../testset_2007/ballroom.sol | 59 + .../testset_2007/carplates.in | 10017 + .../testset_2007/carplates.sol | 10016 + .../3927 - 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Ballroom lights/a.out | Bin 0 -> 86956 bytes ICPC Live Archive/3928 - Ballroom lights/ac | Bin 0 -> 72452 bytes .../3928 - Ballroom lights/ballroom.cpp | 277 + .../3928 - Ballroom lights/ballroom.in | 4522 + .../3928 - Ballroom lights/ballroom.sol | 59 + .../3928 - Ballroom lights/critical.in | 7 + .../help/gomox.ar-pap-2010-d9b17e5cb110.zip | Bin 0 -> 1466883 bytes .../.hg_archival.txt | 5 + .../tpa/3nmas1/main.cpp | 53 + .../tpa/bishops/bishops_con_tabla.py | 51 + .../tpa/bishops/main.cpp | 66 + .../tpa/doc/3nmas1.tex | 157 + .../tpa/doc/algorithm.sty | 96 + .../tpa/doc/algorithmic.sty | 194 + .../tpa/doc/bishops.tex | 222 + .../tpa/doc/caratula.sty | 290 + .../tpa/doc/code_color.sty | 20 + .../tpa/doc/figuras/collatz_conjecture.png | Bin 0 -> 38838 bytes .../tpa/doc/figuras/logo_dc.jpg | Bin 0 -> 128041 bytes .../tpa/doc/figuras/logo_uba.jpg | Bin 0 -> 55466 bytes .../tpa/doc/figuras/tablero1.png | Bin 0 -> 451913 bytes .../tpa/doc/figuras/tablero1.svg | 3371 + .../tpa/doc/informe.tex | 112 + .../tpa/doc/intervalos.tex | 187 + .../tpa/doc/main.tex | 165 + .../tpa/doc/subsecuencias.tex | 237 + .../tpa/doc/trans_algorithmic.tex | 15 + .../tpa/minimal-coverage/main.cpp | 83 + .../tpa/subseq/main.cpp | 128 + .../tpa/subseq/test.cpp | 202 + .../tpb/acm/CppApplication_1/main.cpp | 220 + .../tpb/data-flow/main.cpp | 150 + .../gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/acm.tex | 438 + .../tpb/doc/algorithm.sty | 96 + .../tpb/doc/algorithmic.sty | 194 + .../tpb/doc/caratula.sty | 290 + .../tpb/doc/code_color.sty | 20 + .../tpb/doc/data-flow.tex | 283 + .../tpb/doc/figuras/grafo.dot | 56 + .../tpb/doc/figuras/grafo.pdf | Bin 0 -> 39121 bytes .../tpb/doc/figuras/laberinto.fig | 99 + .../tpb/doc/figuras/laberinto.pdf | Bin 0 -> 4853 bytes .../tpb/doc/figuras/logo_dc.jpg | Bin 0 -> 128041 bytes .../tpb/doc/figuras/logo_uba.jpg | Bin 0 -> 55466 bytes .../tpb/doc/informe.tex | 113 + .../tpb/doc/labyrinth.tex | 195 + .../tpb/doc/trains.tex | 454 + .../tpb/doc/trans_algorithmic.tex | 15 + .../tpb/labyrinth/main.cpp | 86 + .../tpb/trains/main.cpp | 207 + .../tpc/billing-tables/main.cpp | 256 + .../tpc/billing-tables/test.py | 158 + .../tpc/doc/algorithm.sty | 96 + .../tpc/doc/algorithmic.sty | 194 + .../tpc/doc/billing-tables.tex | 441 + .../tpc/doc/caratula.sty | 290 + .../tpc/doc/code_color.sty | 20 + .../tpc/doc/figuras/kmp.fig | 57 + .../tpc/doc/figuras/kmp.pdf | Bin 0 -> 6626 bytes .../tpc/doc/figuras/logo_dc.jpg | Bin 0 -> 128041 bytes .../tpc/doc/figuras/logo_uba.jpg | Bin 0 -> 55466 bytes .../tpc/doc/informe.tex | 114 + .../tpc/doc/needle-haystack.tex | 139 + .../tpc/doc/newdistinct.tex | 240 + .../gomox.ar-pap-2010-d9b17e5cb110/tpc/doc/rmq.tex | 285 + .../tpc/doc/trans_algorithmic.tex | 15 + .../tpc/needle-haystack/main.cpp | 83 + .../tpc/needle-haystack/main_alternativo.cpp | 93 + .../tpc/new-distinct-substrings/main.cpp | 132 + .../tpc/new-distinct-substrings/test.txt | 5003 + .../tpc/rmq/main.cpp | 158 + .../tpc/rmq/test.txt | 32231 ++ .../tpc/rmq/uva_problem_11235.txt | 16110 + .../tpd/ballroom/ballroom.cpp | 272 + .../tpd/ballroom/ballroom.py | 459 + .../tpd/ballroom/test.txt | 92 + .../tpd/disgruntled/disgruntled.cpp | 256 + .../tpd/doc/algorithm.sty | 96 + .../tpd/doc/algorithmic.sty | 194 + .../tpd/doc/ballroom.tex | 376 + .../tpd/doc/caratula.sty | 290 + .../tpd/doc/code_color.sty | 20 + .../tpd/doc/disgruntled.tex | 417 + .../tpd/doc/figuras/ballroom.png | Bin 0 -> 42778 bytes .../tpd/doc/figuras/ballroom.svg | 341 + .../tpd/doc/figuras/logo_dc.jpg | Bin 0 -> 128041 bytes .../tpd/doc/figuras/logo_uba.jpg | Bin 0 -> 55466 bytes .../gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/gnu.tex | 229 + .../tpd/doc/informe.tex | 118 + .../tpd/doc/trans_algorithmic.tex | 15 + .../tpd/doc/walk.tex | 270 + .../gomox.ar-pap-2010-d9b17e5cb110/tpd/gnu/gnu.cpp | 128 + .../tpd/walk/walk.cpp | 132 + ICPC Live Archive/3928 - 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(jj;+@j z#~Y*X$5h*|Lc04Hrhfwq+unPu1KZepEP*LE>vAi`vfRuAS#E-YcqFB0Pp90%`sNv! zU-a@OebpXaZiz<}=LL)t=SfBDP}r){p=e!-6j7uu#D^*ipt`5Bcy%zf+KxxG&<<=a zLt*pP47ueRfgGtoazkT%15qck27~PZ+tK3eZqPKw3bfEX(OL7vwX27bvxZf6i7sT9 z=ni&4B7hW$3xFdAz!Cwl!~h7Pla-b!b32mJ)Bs{P3%KS)*vBUf5%vc+86moub@k49X1A`P+`Q-pYZ&vv zWvm4QP2K}W&OcyqNvA|?wMVTOTp)zAb1mk$S}eEN_TKO%02q^lt-0?D6kBo9m0NAi zZYDmi%ZC=pkK3A;e8J{pDH2w$vejDaIQ=0MBv<6z?nK*14%PN?+2WKT)R$ID#tQUj z95MNDyi1c0L*CdQ7lZO1+#fO%MV~MkuMB-vzcM#Z&5mirxFdvnw|=;HgZn@E0xr6^ z=EJSoqK-fwE7IgxUk)n;4)R#y1}C4nhL>&}54WDTFu?fKZW#Lb)Ke^di>2?dw1=hd zvGjeGe!$WwOFv}kS(bjp(ilrWW{(e?_NDfz6*KJ~k-H7q6;K5ma97kJTbD;_9D%LK zu1^>gc5C9CaZO?jD} zptjQGsd4ZpC6Z*Z5XnL?<@?USOKcB%W%#xeFrG!F@u^24Z()zjdOw0#sM?9#`^bG4 zxl_n}1Gz5brXhD6xe3UE7?Qb+T`P1#Q@QFmD747%H@zzCdf8RCWzW~QSh5dwUus@58X#XwOU_TyI z=SBPH4%L2>eKDvmUgGxKj0cxP*qaG0jOTAXB9DqZCh}?5_?#r29uv=#|0MF)ME;V< zpAq>Y@m%~jLOvt%K9T=R*Vn!bWhg@#%20+fl%Wh|C_@>_P=@{= zXv{K7H)EiL! zE=NsC87(WIa_Is}(3@7))lr|zAMkn{)oyh=tt}ueV^I-M9nP)PS+$i`1|9wiu*Mfg z`3vcr-JS}UpNQ(`*0?<-HS)R@Wwdk-{-9}15Z)_ASa?WE>$5EmcQq=G zpu(_fL!r{822hBg;PbmZ>J}8cPz*R79+ZfMl92%BS4lM)PDyc%gFGRvUSH&|B+p4M zPp#YU^^g-1n5Zt&EqPqqIQzEb_SE9;16H+xe4o7<@4;90 z|0v{lR-LaCl8^iqRuHS48?Q0OGDNVTLL z%DRgHvfdRc-ra@Y!K^h_4tm&E-`<2#VKLN@lVWFglHxl+hJvHyg- zw4<$rxWs;vj&fG=JBvr*n3SFTPT~;i@!f5^*v~?Fbn<=iSK+XYOzy9B3fb6adlO|~ z_KxH7-qgT(bwp`VQMD6C&%@-&I#cZ}!yyM=z)J6xV4 zd5MsX_vh~u{>FRKB@*Uh>l$c%np}}4*QUvP)8s=;PHx>jpC+GAv!8BZa$@^= zL7H4_N%h~5rmyDuguE+FA4-$;H2J4#@}p^Z_&)uOgum~N-vHn~FTMkgpV3T$1GmPZ zYsnpi?`KbiCzA`{5~cKkm1~w4t)#Ss@@t>XbSn$*p|sZJcW>EFEB)S}&+Vy%*{o(A%(h@b zRp%C3fTkPF7reZXvJYD*WvY2K4!1|1TMdhh9p`&H{{RU9eC&G~UK9AZz1UJh+05h= zc`fQwrjsF72}+Z55v2oXD{4%1R7`3V+l48xi78K +#include +#include +using namespace std; + +#define D(x) cout << #x " = " << (x) << endl + +#define NONE 0 +#define IN 1 +#define OUT 2 +#define FEDECOST 0xfede +#define MAXSTATES 5798 // pre-calculated +#define GETTYPE(sidx,i) (((sidx)>>(2*(i)))&3) +#define SETTYPE(type,i) (((type)<<(2*(i)))) + +int state[MAXSTATES], newstate[MAXSTATES], map[MAXSTATES]; +short invmap[1<<(2*11)]; + +// calculate a map used to enumerate all valid boundaries +int genmap(int c, int n, int i, int nest, int sidx) +{ + printf("c = %d, n = %d, i = %d, nest = %d, sidx = %x\n", c, n, i, nest, sidx); + if (nest>=0 && i<=c) { + n=genmap(c,n,i+1,nest, sidx|SETTYPE(NONE,i)); + n=genmap(c,n,i+1,nest+1,sidx|SETTYPE(IN,i)); + n=genmap(c,n,i+1,nest-1,sidx|SETTYPE(OUT,i)); + } + else if (nest==0){ + map[n++]=sidx; + printf("mask = %X, nest = 0\n", sidx); + } + assert(n<=MAXSTATES); + return n; +} + +int main(){ + int floors, r, c, x, y, n, i, j, sidx, left, up, right, down, cost, prevcost; + char lrwall[30],udwall[30]; + for( scanf("%d",&floors); floors--;) { + scanf("%d %d\n",&r,&c); + gets(udwall); //dummy-input + n=genmap(c,0,0,0,0); + + for (int i = 0; i < n; ++i){ + int mask = map[i]; + printf("mask = %X\n", mask); + for (int j = 0; j <= c; ++j){ + int what = GETTYPE(mask, j); + switch (what){ + case NONE: + cout << "NONE "; + break; + case IN: + cout << "IN "; + break; + case OUT: + cout << "OUT "; + break; + } + } + cout << endl; + } + + for(i=0; i0 ? state[i] : ((map[i]&3)==NONE) ? state[invmap[map[i]>>2]] : FEDECOST); + if (prevcost>=FEDECOST) + continue; // speed up somewhat + sidx=map[i]; + left=GETTYPE(sidx,x); + up =GETTYPE(sidx,x+1); + for(j=0; jOUT + } + sidx = sidx & ~SETTYPE(15,x) | SETTYPE(down,x) | SETTYPE(right,x+1); + if (cost +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#define foreach(x, v) for (typeof (v).begin() x=(v).begin(); x !=(v).end(); ++x) +#define For(i, a, b) for (int i=(a); i<(b); ++i) +#define D(x) cout << #x " is " << x << endl + +const double EPS = 1e-9; +int cmp(double x, double y = 0, double tol = EPS) { + return (x <= y + tol) ? (x + tol < y) ? -1 : 0 : 1; +} + +const int MAXN = 105, MAXL = 55, oo = 1 << 28; +string words[MAXN]; +int dist[MAXN][MAXL]; +int n; + +long long pack(int index, int behind, int weight) { + return ((long long)weight << 16L) + (behind << 8L) + index; +} + +void unpack(long long state, int &index, int &behind, int &weight) { + index = state & 255L; + state >>= 8L; + behind = state & 255L; + state >>= 8L; + weight = state; +} + +inline bool isPrefix(const string &a, const string &b) { + if (a.size() > b.size()) return false; + for (int i = 0; i < a.size(); ++i) { + if (a[i] != b[i]) return false; + } + return true; +} + + +int search() { + for (int i = 0; i < n; ++i) { + for (int d = 0; d < MAXL; ++d) { + dist[i][d] = oo; + } + } + + priority_queue, greater > q; + for (int i = 0; i < n; ++i) { + for (int j = 0; j < n; ++j) { + if (i == j) continue; + if (isPrefix(words[j], words[i])) { + assert(words[j].size() < words[i].size()); + int diff = words[i].size() - words[j].size(); + dist[i][diff] = words[i].size(); + long long state = pack(i, diff, dist[i][diff]); + q.push(state); + } + } + } + + while (q.size() > 0) { + long long state = q.top(); q.pop(); + int index, behind, weight; + unpack(state, index, behind, weight); + //printf("Popped state (%s, %s) with weight w=%d\n", index, behind, words[index].c_str(), words[index].substr(0, words[index].size() - behind).c_str(), weight); + if (behind == 0) { + return weight; + } + if (weight > dist[index][behind]) continue; + + const string tail = words[index].substr(words[index].size() - behind); + //printf(" Tail is %s\n", tail.c_str()); + assert(tail.size() == behind); + + for (int k = 0; k < n; ++k) { + //printf(" Trying words[k=%d] = %s\n", k, words[k].c_str()); + if (words[k].size() - behind >= 0 and isPrefix(tail, words[k]) ) { + int new_index = k; + int new_behind = words[new_index].size() - behind; + int new_weight = weight + new_behind; + //printf(" Option 1: Can reach state (%s, %s) with weight = w=%d\n", new_index, new_behind, words[new_index].c_str(), words[new_index].substr(0, words[new_index].size() - new_behind).c_str(), new_weight ); + if (new_weight < dist[new_index][new_behind]) { + dist[new_index][new_behind] = new_weight; + q.push( pack(new_index, new_behind, new_weight) ); + //printf(" That's better.\n"); + } + } + + if (behind - words[k].size() >= 0 and isPrefix(words[k], tail) ) { + int new_index = index; + int new_behind = behind - words[k].size(); + int new_weight = weight + 0; + //printf(" Option 2: Can reach state (%s, %s) with weight = w=%d\n", new_index, new_behind, words[new_index].c_str(), words[new_index].substr(0, words[new_index].size() - new_behind).c_str(), new_weight ); + if (new_weight < dist[new_index][new_behind]) { + dist[new_index][new_behind] = new_weight; + q.push( pack(new_index, new_behind, new_weight) ); + //printf(" That's better.\n"); + } + } + } + + } + return -1; +} + +int main(){ + while (cin >> n) { + if (n == 0) break; + for (int i = 0; i < n; 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zsCF85PLH~9VifHZW1!7(4F|)H@3x}x(HcSu1Pz}5hGc$aYD0xEl#UbaD2E5=vkiM@ zNEXuUB-}lrvVTT~I9(GD@s2m!Vkmb>mo(a*N(2q z(1IC|i$IY`YAM$Vi4o(t8v*)e(k;-AwB%bND^an02Jcc;1CLEl|J(u5B*s3|oljLX zH5*U}$qi3|s~@8ar%2!2nV)gv0RT|D$+{QO>Iz*!aHTtXu|eOU%2+pbI82NP@jToH%!z$DTNrsyeKN7I zx*OJ)ra=PAUatCIBx=LF!p%w!PHgz4l6^*W)VME;WKbi234nB_AYZOV3)cbBTpI}t4!oM zms-`li)+Ouahb58i(t*_BvI(6JzlK}F80^<9}UB2sbpo6;}T~3)B21|2G>{ycpHl>2y^&!c3B{Wmv4=lpdFyWp!v}1EoFoCoGi|=kv+r-|A)>cG z#l?^B_XU(3P3l%6y$9Q6XyK4UP~-80=JDa#ixqToZf`ac7+D6ZF9`B6@GW@F0dMi= zVJn=I@cZKcC#LbBTO%iObe5o$shi7qCaDYd_NDt#Y4XhzFiaKpAAB;vs!N2+T~>Kn z(hvrq%H;5k^W7VbXZvP_ykW6_II!f>NY%bY>|PJCC#EIII5$WW)4Quo@k?Tu6-Xfm zLZzC@aCwG~$-Zl8(<9t59Q#w~^fpJJpjEM0WmBd9xD@`W_NgJ_Tbv-G@F+N*06+t1N-a5{Bs1i2enqOk1~vc# z;A-aL>SE?v?;%a4LM(^TatELJA082__k@#z&c5gXn{AU?$M9 zqQsNmSbhz( ze@OhF=Ebtde8jxVe8?QKaOAiSDz7tWB?3nOYgQnjSYWV#zplUVfPc9Ve%=3jApn1AEl{mSwWy#J}ge*va2m-oz+0s!wXU;v!I0iUCge*@YXTUod{ zxVijEvc=q0KkrxM{tJZrHzo!n%70@1Ni@!S#Wlm|7j*Hj)%>qe0Mllyh8?LRU9B+Ab?%H$ye0&x2EVW9sFik9;m)YRF*@lTG{>Ig0Lzuq5) z1pKzp=eE)R0rw|8KFHhqhZYdPb0NfUb(Glsjb~=(@T-+M*#EJPH(NVM3BMwue_NMP zX_)_s`6p4|CJKCmAHSNA2*Pi5G)w;tYHnq3`X|RNgvCYmUr{#T_d3EQVEqH`PkQ^b zilQ?P000y@*l)bb-+2~BwhnH8^5c +#include +#include +#include +#include +#include +#include +#include + +#define forn(i, n) for (int i = 0; i < (n); i++) +#define EPS 1e-8 + +using namespace std; + +struct Vector { + long double x; + long double y; + + Vector(long double xi, long double yi): x(xi), y(yi) {}; + + long double length() { + return hypot(x, y); + } + + long double angle() { + return atan2(y, x); + } + +}; + +struct Column { + Vector position; + long double radius; + + Column(long double x, long double y, long double r) : position(x,y), radius(r) {}; +}; + +typedef Vector Lamp; +typedef pair Interval; +typedef pair Segment; + + +inline long double length(const Segment& s) { + return Vector(s.second.x - s.first.x, s.second.y - s.first.y).length(); +} + +inline long double length(const Interval& i) { + assert(i.first <= i.second); + return i.second - i.first; +} + + +pair< long double, bool > intersect_segments(const Segment& s1, const Segment& s2) { + Vector p1 = s1.first; + Vector p2 = s1.second; + Vector p3 = s2.first; + Vector p4 = s2.second; + + long double den = (p4.y-p3.y)*(p2.x-p1.x) - (p4.x-p3.x)*(p2.y-p1.y); + + long double ua_num = (p4.x-p3.x)*(p1.y-p3.y) - (p4.y-p3.y)*(p1.x-p3.x); + long double ub_num = (p2.x-p1.x)*(p1.y-p3.y) - (p2.y-p1.y)*(p1.x-p3.x); + + if (fabs(den) < EPS) { + // Caso en que los Segments son paralelos + if (fabs(ua_num - ub_num) < EPS && fabs(ub_num) < EPS) { + // Las rectas son coincidentes, esto no deberia ocurrir + assert(false); + } + return make_pair(0, false); + } + + if (ub_num/den >= 0) { + return make_pair(ua_num/den, true); + } + return make_pair(0, false); +} + + +Interval intersect_intervals(const Interval& i1, const Interval& i2) { + + long double d0 = max(i1.first, i2.first); + long double d1 = min(i1.second, i2.second); + + if (d1 < d0) { + return Interval(0, 0); + } else { + return Interval(d0, d1); + } +} + + +Interval dark_range(const Segment& wall, const Lamp& lamp, const Column& column) { + Vector bisectriz(column.position.x - lamp.x, column.position.y - lamp.y); + long double p = asin(column.radius/bisectriz.length()); + long double alpha = bisectriz.angle(); + + Vector d1(cos(alpha + p), sin(alpha + p)); + Vector d2(cos(alpha - p), sin(alpha - p)); + + pair< long double, bool > p1 = intersect_segments(wall, Segment(lamp, Vector(lamp.x + d1.x, lamp.y + d1.y))); + pair< long double, bool > p2 = intersect_segments(wall, Segment(lamp, Vector(lamp.x + d2.x, lamp.y + d2.y))); + + long double wall_length = length(wall); + + // Se sabe que los puntos de interseccion estan ordenados correctamente + // porque el angulo de diferencia entre las semirectas es menor a 180, + // entonces no es necesario chequearlo. + Interval res; + + if (!p1.second) { + if (!p2.second) { + return Interval(0, 0); + } else { + res = Interval(0, p2.first); + } + } else { + if (!p2.second) { + res = Interval(p1.first, 1); + } else { + res = Interval(p1.first, p2.first); + } + } + + res = intersect_intervals(res, Interval(0,1)); + return Interval(res.first * wall_length, res.second * wall_length); +} + +void invert_range(const list& ints, long double fin, list& out) { + + if (!ints.size()) { + out.push_back(Interval(0,fin)); + return; + } + + + list::const_iterator it = ints.begin(); + if (it->first > 0) { + out.push_back(Interval(0, it->first)); + } + + it++; + + list::const_iterator itprev = ints.begin(); + while (it != ints.end()) { + out.push_back(Interval(itprev->second, it->first)); + it++; + itprev++; + } + + if (itprev->second < fin) { + out.push_back(Interval(itprev->second, fin)); + } +} + + +void reduce_union(list& l_o, list& out) { + // elimino repetidos para acelerar el sort + list l; + + for (list::const_iterator it = l_o.begin(); it != l_o.end(); it++) { + if (it->first < it->second) { + l.push_back(Interval(it->first, it->second)); + } else if (it->first > it->second) { + assert(false); + } + } + + + if (!l.size()) return; + + l.sort(); + + list::const_iterator it = l.begin(); + Interval cand = *it; + Interval other; + + it++; + while (it != l.end()) { + other = *it; + if (other.first < other.second) { + if (other.first > cand.second) { + out.push_back(cand); + cand = other; + } else { + if (other.second > cand.second) { + cand = Interval(cand.first, other.second); + } + } + } + it++; + } + + out.push_back(cand); +} + + +long double solve(const list& lamps, const list& columns, int max_x, int max_y) { + list walls; + walls.push_back(Segment(Vector(max_x,0), Vector(0, 0))); + + long double total = 0; + + for (list::iterator p = walls.begin(); p != walls.end(); p++) { + list lit_on_this_wall; + for (list::const_iterator l = lamps.begin(); l != lamps.end(); l++) { + list dark_zones; + for (list::const_iterator c = columns.begin(); c != columns.end(); c++) { + dark_zones.push_back(dark_range(*p, *l, *c)); + } + + list merged_dark_zones; + list lit_zone; + + reduce_union(dark_zones, merged_dark_zones); + invert_range(merged_dark_zones, length(*p), lit_zone); + + lit_on_this_wall.splice(lit_on_this_wall.end(), lit_zone); + } + + list merged_lit_on_this_wall; + reduce_union(lit_on_this_wall, merged_lit_on_this_wall); + + for (list::iterator it = merged_lit_on_this_wall.begin(); it != merged_lit_on_this_wall.end(); it++) { + total += length(*it); + } + } + + return total; +} + + +int main() { + + int nl, nc, max_x, max_y; + + for (;;) { + scanf("%d %d %d %d", &nl, &nc, &max_x, &max_y); + + if (!(nl || nc || max_x || max_y)) { + break; + } + + list lamps; + list columns; + + int x, y, r; + + forn(i, nl) { + scanf("%d %d", &x, &y); + lamps.push_back(Lamp(x,y)); + } + + forn(i, nc) { + scanf("%d %d %d", &x, &y, &r); + columns.push_back(Column(x, y, r)); + } + + printf("%.4Lf\n", solve(lamps, columns, max_x, max_y)); + } +} diff --git a/ICPC Live Archive/3928 - Ballroom lights/3928.cpp b/ICPC Live Archive/3928 - Ballroom lights/3928.cpp new file mode 100644 index 0000000..418e597 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/3928.cpp @@ -0,0 +1,235 @@ +// Andrés Mejía +using namespace std; +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#define foreach(x, v) for (typeof (v).begin() x=(v).begin(); x !=(v).end(); ++x) +#define For(i, a, b) for (int i=(a); i<(b); ++i) +#define D(x) cout << #x " is " << x << endl + +const double EPS = 1e-9; +int cmp(double x, double y = 0, double tol = EPS) { + return (x <= y + tol) ? (x + tol < y) ? -1 : 0 : 1; +} + +struct point { + long double x, y; + point(){} + point(long double x, long double y) : x(x), y(y) {} +}; + +typedef pair segment; +typedef pair interval; + +struct circle { + point center; + int radius; +}; + +const int MAXB = 1005; +circle columns[MAXB]; +point bulbs[MAXB]; + +inline long double length(const segment &s) { + long double dx = s.first.x - s.second.x; + long double dy = s.first.y - s.second.y; + return hypotl(dx, dy); +} + +pair< bool, long double > segmentIntersection(const segment& s1, const segment& s2) { + point p1 = s1.first; + point p2 = s1.second; + point p3 = s2.first; + point p4 = s2.second; + + long double den = (p4.y-p3.y)*(p2.x-p1.x) - (p4.x-p3.x)*(p2.y-p1.y); + long double ua_num = (p4.x-p3.x)*(p1.y-p3.y) - (p4.y-p3.y)*(p1.x-p3.x); + long double ub_num = (p2.x-p1.x)*(p1.y-p3.y) - (p2.y-p1.y)*(p1.x-p3.x); + + if (cmp(den, 0) == 0) { + // Caso en que los segmentos son paralelos + if (cmp(ua_num - ub_num, 0) == 0 && cmp(ub_num, 0) == 0) { + // Las rectas son coincidentes, esto no deberia ocurrir + assert(false); + } + return make_pair(false, 0); + } + + if (cmp(ub_num/den, 0) >= 0) { + return make_pair(true, ua_num/den); + } + return make_pair(false, 0); +} + + +interval findShadow(const segment &wall, const point &light, const circle &column) { + long double dx = 1.0L * column.center.x - light.x; + long double dy = 1.0L * column.center.y - light.y; + long double h = sqrt(dx * dx + dy * dy); + long double beta = atan2(dy, dx); + long double alpha = asin(column.radius / h); + + //printf("Radius = %d, h = %Lf, r / h = %Lf\n", column.radius, h, column.radius / h); + //printf("beta = %Lf\n", beta); + //printf("alpha = %Lf\n", alpha); + + long double d = sqrt(h * h - column.radius * column.radius); + point a(light.x + d * cos(beta + alpha), light.y + d * sin(beta + alpha)); + point b(light.x + d * cos(beta - alpha), light.y + d * sin(beta - alpha)); + + // printf("Must intersect segment that starts at (%Lf, %Lf) and advances up to (%Lf, %Lf)\n", light.x, light.y, light.x + d * cos(beta + alpha), light.y + d * sin(beta + alpha)); + // printf("Must intersect segment that starts at (%Lf, %Lf) and advances up to (%Lf, %Lf)\n", light.x, light.y, light.x + d * cos(beta - alpha), light.y + d * sin(beta - alpha)); + + pair p1 = segmentIntersection(wall, segment(light, a) ); + pair p2 = segmentIntersection(wall, segment(light, b) ); + + interval shadow; + long double length = hypotl(wall.first.x - wall.second.x, wall.first.y - wall.second.y); + + if (!p1.first) { + if (!p2.first) { + // Everything's lit, no shadow. + return interval(0, 0); + } else { + shadow = interval(0, p2.second); + } + } else { + if (!p2.first) { + shadow = interval(p1.second, 1); + } else { + shadow = interval(p1.second, p2.second); + } + } + shadow.first = max(0.0L, min(1.0L, shadow.first) ); + shadow.second = max(0.0L, min(1.0L, shadow.second) ); + + shadow.first *= length; + shadow.second *= length; + //printf("Shadow: [%Lf, %Lf]\n", shadow.first, shadow.second); + return shadow; +} + +vector< interval > merge(vector &v) { + sort(v.begin(), v.end()); + vector< interval > ans; + if (v.size() <= 1) return v; + long double left = v[0].first, right = v[0].second; + for (int i = 0; i < v.size(); ++i) { + if (i + 1 < v.size() and cmp(left, v[i+1].first) <= 0 and cmp(v[i+1].first, right) <= 0 ) { + right = max(right, v[i+1].second); + } else { + if (cmp(right - left, 0) > 0) { + ans.push_back( interval(left, right) ); + } + if (i + 1 < v.size()) { + left = v[i + 1].first; + right = v[i + 1].second; + } + } + } + return ans; +} + +vector< interval > invert(const vector v, long double length) { + if (v.size() == 0) { + return vector(1, interval(0, length) ); // Everything + } + + vector< interval > ans; + // Before the beginning + if (cmp(0, v[0].first) < 0) { + ans.push_back(interval(0, v[0].first)); + } + + // between + for (int i = 0; i < v.size() - 1; ++i) { + ans.push_back(interval(v[i].second, v[i + 1].first) ); + } + + // After the end + if (cmp(v.back().second, length) < 0) { + ans.push_back(interval(v.back().second, length)); + } + return ans; +} + +int main(){ + int L, C, X, Y; + while (scanf("%d %d %d %d", &L, &C, &X, &Y) == 4) { + if (L == 0 and C == 0 and X == 0 and Y == 0) break; + for (int i = 0; i < L; ++i) { + int x, y; + scanf("%d %d", &x, &y); + bulbs[i].x = x; + bulbs[i].y = y; + } + for (int i = 0; i < C; ++i){ + int x, y, r; + scanf("%d %d %d", &x, &y, &r); + columns[i].center.x = x; + columns[i].center.y = y; + columns[i].radius = r; + } + + vector< segment > walls; + walls.push_back( segment(point(0, 0), point(0, Y)) ); + walls.push_back( segment(point(0, Y), point(X, Y)) ); + walls.push_back( segment(point(X, Y), point(X, 0)) ); + walls.push_back( segment(point(X, 0), point(0, 0)) ); + + long double ans = 0; + for (int i = 0; i < walls.size(); ++i) { + vector< interval > allLights; // lights on this wall caused by all different lightbulbs + for (int j = 0; j < L; ++j) { + vector< interval > shadows; // shadows on this wall caused only by this light + for (int k = 0; k < C; ++k) { + shadows.push_back( findShadow(walls[i], bulbs[j], columns[k]) ); + } + + // printf("Shadows on wall (%.0Lf, %.0Lf) to (%.0Lf, %.0Lf) caused by light at (%.0Lf, %.0Lf):\n", + // walls[i].first.x, walls[i].first.y, walls[i].second.x, walls[i].second.y, bulbs[j].x, bulbs[j].y); + // printf("Before merging:\n"); + // for (int k = 0; k < shadows.size(); ++k) { printf("[%Lf, %Lf] ", shadows[k].first, shadows[k].second); } puts(""); + + shadows = merge(shadows); // Merge overlapping shadows + + // printf("After merging:\n"); + // for (int k = 0; k < shadows.size(); ++k) { printf("[%Lf, %Lf] ", shadows[k].first, shadows[k].second); } puts(""); + + // Everything that's not a shadow caused by this light, is certainly lit. + vector lights = invert(shadows, length(walls[i]) ); + + // printf("Sections I know to be lit on wall (%.0Lf, %.0Lf) to (%.0Lf, %.0Lf) caused by light at (%.0Lf, %.0Lf):\n", + // walls[i].first.x, walls[i].first.y, walls[i].second.x, walls[i].second.y, bulbs[j].x, bulbs[j].y); + // for (int k = 0; k < lights.size(); ++k) { printf("[%Lf, %Lf] ", lights[k].first, lights[k].second); } puts(""); + allLights.insert(allLights.end(), lights.begin(), lights.end()); + } + allLights = merge(allLights); // Merge overlapping lit zones + for (int i = 0; i < allLights.size(); ++i) { + //printf("Lit: [%Lf, %Lf]\n", allLights[i].first, allLights[i].second); + ans += allLights[i].second - allLights[i].first; + } + } + printf("%.4Lf\n", ans); + + } + return 0; +} \ No newline at end of file diff --git a/ICPC Live Archive/3928 - Ballroom lights/a.out b/ICPC Live Archive/3928 - Ballroom lights/a.out new file mode 100755 index 0000000000000000000000000000000000000000..c35c15a3ad60b6be294b2393ba0ca836ec4ec615 GIT binary patch literal 86956 zcwX&&3tUxI7Wd|%Vw#Yt;j2)wC`|!Tu`Ka%^E#rDXw&mRE8baNYZ2>r zxr6tmpJN7IoGJr1^pT&y)>C-@i|ZXCUiDDvZbJ4I&S%3*ii?Kl z=FAzMbysc{pYJQA9{awz>i5rV9rKUX@13~&t3UnWO6-GLfo@oc%iP8O?0;%L^Y@4K zOct_Ek?WjutXy+{jOqrcHXcFM%>xIvwvs* z&i`9QU*zB88~fq5X8d5Z})N=(myQSz3WiYXLG#`!+Jl z0(&=Dw7HSPEUm?%%_Hzo>)gn=op5-X%mC-ME(~q%yu)&^4gQ)t!44`@X*pP7X+pLs zgxIF{-o--FtxJyFV67;vwN{j@vsTPn1In(^9+@G8wQZ*rAl6FDI=R~bb%3q3Nn0=r zPFF(pERArw3DTY0EyqHvJ1lirR`U>RWywwwlnR0(H%39OI%}AvHgcm#-WIu{Zkgqn zwQbr?Ya1NKQ&(CVi-(t$9up;hZN5YYN9y24Pv9k`JB7U?p>`Sal-J#x7`gG*V<_Tn zR7cx!od-G3)kSWs8_>A4E^;MGjNAxPm(<^IvuqY*V&`tFqKqEC24;F$l;qq_3W~aTi|GAT7>MChKgB@PG^5d zXF*a5)XGvB`zi-u)cAkQl{voJnLM_Qm0a0J4vN<-oCT|*pTK zlr|4*Q8f*0V^-PQA(ZKJt>Id>k%fRid>M}XilstUL@3!ePp68=!&@-XK1wCrQEkL@ z>Yk%is|DBc(MzY338Bu?NDfSsV=PLJu_zv6U#9CLx%HGBW0=m3{B@l+>qJ}IR_!9F zsMSf-lh}q8Tb(M4-3D5~sA0$PH*FCqwqdsFjgNq5!)(6RFbJq!Cz8x}soV8~!=|ZW zx+R5#?$HKGp(#q}eZU)s3*q)-+kjW+5mWNm-n=MPb53N&*CFHH`B84I^3NH%}e#3-HrK8^ZDjvN@jJJgu`+cX}?&i!Aby)n(b z|9?f}mxSD3j{{aY_xq2;I1S%8N>)423SMwpLDvfOHk4Xn8e|Mnk$r&ovrZA>2vR0jYKlqbPlhMShM&3id<*MI7 zqD8}iBxmprd4w-h$qBT;aBks|t>wW0J-mdfg-x^ne{SmKT%2vn1D^p@1W7%HZxX#+~UttbxMLhJL%9$49z(l^jO~F7T zz%&u2#-ZrmEm625#~A7NIA(bjj{?6XM%G(ackh;Xm&{hm98a0SxwV`^<3Y^c#j#PC z;o57co%PaE90Ew8!6YDsOG|SuZMIA1JyS6AY*ktVm6m2G?F$PI#+5C!6xcvr2iYLe z{yiDbY*~kAs#Z2oIn>44{uA<$6Q&x^ye=`-5>su!yiAxag*YZ(olG@crVjzR7r+0o z+K3d4qZqygmU|Oivl9mv(_z;NF>4v9 zNKP5oWR*0CwXUGr;mT0w6$m-rik0MZtCq^jrA6se@|HBL)Na{rX>xiiq_$algX9)T zZnosgBsX7j%OE+t&$SMAD=7efWt-Z@krHX7gj|!YOq06E&Y@W{9+j9Tm56szBH2la z6elID4kemza;ltBb`;9~kA-AMImwQ8k{#nDJI*27y*4RS8(M}}Z6INCZK7R)gQH@* zQ~SqL=49F0$Y>Fh9gAVo1-jT{IWYu{lg(A=s1hF6-oM7ZtSACR%d(Ksp1H{Q;*nz_wdvCX>mKnH78hp(;(0lN+l-J49Ac6rRSThG*HflS&M z%SVeJ+hL&x?+!nYty?v%9!kgcEogAn1A6HbsPqOW!Mm*$4c3r4Ye<7EAsk9*DiyjK z4Nkgx%Dv5z+tN@8MQ1j6$hDSpRYbHwF3Z6&mWIgXGpPIFfN31cyJ(`2ml(&# zm>(1mMhq|JueB0ebR-R$3}S`n zdZG>`<9w;pJ!3DaODmB1;(x9C9Ep)T5qyX+w?D<7A4+sYt8aYR`_o-fZkx7?#TDS3hV(U0G z(an^5KqwvjMyrvzzfr!iDTPlwPPwVL=AueVt>>Zr#@#}sR>g)^S~go(IqbC0XtdLQ zp?FITt`SlB>rimTcB~szF}30gyhMyXE(hRG4(EJh3i_H_GLzcH59$|ZbRDUMeIt9T z%>lTEG?v~rDFqu|FY_~U&^xpnuYyT^OBu9d^TjxoV1rgZO9=yiq?~l<@F79Xo+8U= zf`OqmP%CYb7kL|+q$h^F*nh>x9QoEe@@evM$>Xr$HaAak!&BDY27D*CEF|Ih)s9AJ5_I!ujAe7=@(*SA z)UmB%)_a<1zm7cz9(wy~X(g!a+N*K!tf#?~?N%6Nsc;n5yr9yup88Bmy8CLn)Ze?M z`Xt_fGoG^Hskptb;+g$l;MLt$SUI;@)>F1dm2KHrq2Gimd0rjubv3q7ore~t(?4A0 z(CAtkMU6Cy1{s7!E?q@HOHJjhHOk&$q8T_rO*9`;mjLXhtN0FqQ&DhYyrUdg6Jnyh zc?E(j`(XNNg6ZoZSfn~38aMHf~n;krkJgL@Z6xoTVims+IEtQNXS5h8C; 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+ +struct Vector { + long double x; + long double y; + + Vector(long double xi, long double yi): x(xi), y(yi) {}; + + long double norma() { + return hypot(x, y); + } + + long double angulo() { + return atan2(y, x); + } + +}; + +struct Columna { + Vector posicion; + long double radio; + + Columna(long double x, long double y, long double r) : posicion(x,y), radio(r) {}; +}; + +typedef Vector Lampara; +typedef pair Intervalo; +typedef pair Segmento; + + +inline long double largo(const Segmento& s) { + return Vector(s.second.x - s.first.x, s.second.y - s.first.y).norma(); +} + +inline long double largo(const Intervalo& i) { + assert(i.first <= i.second); + return i.second - i.first; +} + + +MaybeDouble intersect_segments(const Segmento& s1, const Segmento& s2) { + Vector p1 = s1.first; + Vector p2 = s1.second; + Vector p3 = s2.first; + Vector p4 = s2.second; + + long double den = (p4.y-p3.y)*(p2.x-p1.x) - (p4.x-p3.x)*(p2.y-p1.y); + + long double ua_num = (p4.x-p3.x)*(p1.y-p3.y) - (p4.y-p3.y)*(p1.x-p3.x); + long double ub_num = (p2.x-p1.x)*(p1.y-p3.y) - (p2.y-p1.y)*(p1.x-p3.x); + + if (fabs(den) < TOLERANCIA) { + // Caso en que los segmentos son paralelos + if (fabs(ua_num - ub_num) < TOLERANCIA && fabs(ub_num) < TOLERANCIA) { + // Las rectas son coincidentes, esto no deberia ocurrir + assert(false); + return MaybeDouble((p1.norma() > p2.norma()? 0 : 1), true); + } + return MaybeDouble(0, false); + } + + if (ub_num/den >= 0) { + return MaybeDouble(ua_num/den, true); + } + return MaybeDouble(0, false); +} + + +Intervalo interseccion_intervalos(const Intervalo& i1, const Intervalo& i2) { + + long double d0 = max(i1.first, i2.first); + long double d1 = min(i1.second, i2.second); + + if (d1 < d0) { + return Intervalo(0, 0); + } else { + return Intervalo(d0, d1); + } +} + + +Intervalo rango_oscurecido(const Segmento& pared, const Lampara& lampara, const Columna& columna) { + Vector bisectriz(columna.posicion.x - lampara.x, columna.posicion.y - lampara.y); + long double p = asin(columna.radio/bisectriz.norma()); + long double alpha = bisectriz.angulo(); + + Vector d1(cos(alpha + p), sin(alpha + p)); + Vector d2(cos(alpha - p), sin(alpha - p)); + + MaybeDouble p1 = intersect_segments(pared, Segmento(lampara, Vector(lampara.x + d1.x, lampara.y + d1.y))); + MaybeDouble p2 = intersect_segments(pared, Segmento(lampara, Vector(lampara.x + d2.x, lampara.y + d2.y))); + printf("p1 = [%d, %Lf]\n", p1.valido, p1.valor); + printf("p2 = [%d, %Lf]\n", p2.valido, p2.valor); + + + long double unidad = largo(pared); + + // Se sabe que los puntos de interseccion estan ordenados correctamente + // porque el angulo de diferencia entre las semirectas es menor a 180, + // entonces no es necesario chequearlo. + Intervalo res; + + if (!p1.valido) { + if (!p2.valido) { + return Intervalo(0, 0); + } else { + res = Intervalo(0, p2.valor); + } + } else { + if (!p2.valido) { + res = Intervalo(p1.valor, 1); + } else { + res = Intervalo(p1.valor, p2.valor); + } + } + + res = interseccion_intervalos(res, Intervalo(0,1)); + printf("Shadow: [%Lf, %Lf]\n",res.first * unidad, res.second * unidad); + return Intervalo(res.first * unidad, res.second * unidad); +} + +void invertir_rango(const list& ints, long double fin, list& out) { + + if (!ints.size()) { + out.push_back(Intervalo(0,fin)); + return; + } + + + list::const_iterator it = ints.begin(); + if (it->first > 0) { + out.push_back(Intervalo(0, it->first)); + } + + it++; + + list::const_iterator itprev = ints.begin(); + while (it != ints.end()) { + out.push_back(Intervalo(itprev->second, it->first)); + it++; + itprev++; + } + + if (itprev->second < fin) { + out.push_back(Intervalo(itprev->second, fin)); + } +} + + +void reduce_union(list& l_o, list& out) { + // elimino repetidos para acelerar el sort + list l; + + for (list::const_iterator itcito = l_o.begin(); itcito != l_o.end(); itcito++) { + if (itcito->first < itcito->second) { + l.push_back(Intervalo(itcito->first, itcito->second)); + } else if (itcito->first > itcito->second) { + assert(false); + } + } + + + if (!l.size()) return; + + l.sort(); + + list::const_iterator it = l.begin(); + Intervalo cand = *it; + Intervalo otro; + + it++; + while (it != l.end()) { + otro = *it; + if (otro.first < otro.second) { + if (otro.first > cand.second) { + out.push_back(cand); + cand = otro; + } else { + if (otro.second > cand.second) { + cand = Intervalo(cand.first, otro.second); + } + } + } + it++; + } + + out.push_back(cand); +} + + +long double resolver(const list& lamparas, const list& columnas, int max_x, int max_y) { + list paredes; + paredes.push_back(Segmento(Vector(0,0), Vector(0, max_y))); + paredes.push_back(Segmento(Vector(0,max_y), Vector(max_x, max_y))); + paredes.push_back(Segmento(Vector(max_x,max_y), Vector(max_x, 0))); + paredes.push_back(Segmento(Vector(max_x,0), Vector(0, 0))); + + long double total = 0; + + for (list::iterator p = paredes.begin(); p != paredes.end(); p++) { + list luces_pared; + for (list::const_iterator l = lamparas.begin(); l != lamparas.end(); l++) { + list zonas_tapadas; + for (list::const_iterator c = columnas.begin(); c != columnas.end(); c++) { + zonas_tapadas.push_back(rango_oscurecido(*p, *l, *c)); + } + + list tapadas_unidas; + list zona_iluminada; + + reduce_union(zonas_tapadas, tapadas_unidas); + invertir_rango(tapadas_unidas, largo(*p), zona_iluminada); + + luces_pared.splice(luces_pared.end(), zona_iluminada); + } + + list luces_pared_unidas; + reduce_union(luces_pared, luces_pared_unidas); + + for (list::iterator it = luces_pared_unidas.begin(); it != luces_pared_unidas.end(); it++) { + printf("Lit: [%Lf, %Lf]\n", it->first, it->second); + total += largo(*it); + } + } + + return total; +} + + +int main() { + + int nl, nc, max_x, max_y; + + for (;;) { + scanf("%d %d %d %d", &nl, &nc, &max_x, &max_y); + + if (!(nl || nc || max_x || max_y)) { + break; + } + + list lamparas; + list columnas; + + int x, y, r; + + forn(i, nl) { + scanf("%d %d", &x, &y); + 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b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/.hg_archival.txt new file mode 100644 index 0000000..d93a5e8 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/.hg_archival.txt @@ -0,0 +1,5 @@ +repo: 02c0d172e96fdb16a2f67e65fadeebceb1ea4cae +node: d9b17e5cb11016f4963f3fd7015b964769e655c6 +branch: default +latesttag: null +latesttagdistance: 127 diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/3nmas1/main.cpp b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/3nmas1/main.cpp new file mode 100644 index 0000000..3b3deba --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/3nmas1/main.cpp @@ -0,0 +1,53 @@ +#include +#include +#include +using namespace std; + +typedef unsigned int uint; +typedef unsigned short ushort; + +#define Max_memo 1000001 +vector d(Max_memo, 0); + +#define memorizado(x) ((x) < Max_memo && d[(x)] != 0) +#define next(n) ((n) % 2 == 0 ? (n) / 2 : 3 * (n) + 1) + +ushort periodo(uint n) { + if (memorizado(n)) { + return d[n]; + } else { + ushort p = periodo(next(n)) + 1; + if (n < Max_memo) { + d[n] = p; + } + return p; + } +} + +ushort resolver(uint x, uint y){ + ushort res = 0; + uint i = min(x,y); + uint sup = max(x,y); + ushort aux; + i = max(sup/2,i); + + while(i <= sup){ + aux = periodo(i); + if (aux > res){ + res = aux; + } + i++; + } + return res; +} + +int main(int argc, char **argv) +{ + uint x, y; + d[1] = 1; + while (scanf("%u %u",&x,&y)==2) { + cout << x <<" "<< y <<" " << resolver(x, y) << endl; + } + return 0; +} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/bishops/bishops_con_tabla.py b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/bishops/bishops_con_tabla.py new file mode 100644 index 0000000..b6f8c92 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/bishops/bishops_con_tabla.py @@ -0,0 +1,51 @@ +casillas_por_diag_por_m = lambda m:\ + (lambda k:k+1 if k < m else 2*m-k-1) + +def alfiles(n,k): + filas_negras = range(0,2*n-1,2) #son filas si giramos el tablero 45 grados + filas_blancas = range(1,2*n-1,2) + casillas_por_diag = casillas_por_diag_por_m(n) + filas_negras.sort(cmp=lambda x,y: -1 if casillas_por_diag(x) < casillas_por_diag(y) else \ + 1 if casillas_por_diag(x) > casillas_por_diag(y) else 0) + filas_blancas.sort(cmp=lambda x,y: -1 if casillas_por_diag(x) < casillas_por_diag(y) else \ + 1 if casillas_por_diag(x) > casillas_por_diag(y) else 0) + # Memorizacion de resultados + mem_negras=[[None for t in xrange(k+1)] for y in xrange(n+1)] + mem_blancas=[[None for t in xrange(k+1)] for y in xrange(n+1)] + + #inicializamos las tables + for i in xrange(n+1): + mem_blancas[i][0]=1 + mem_negras[i][0]=1 + + for j in xrange(1,k+1): + mem_blancas[0][j]=0 + mem_negras[0][j]=0 + + acum = 0 + + if n%2==1: + for t in xrange(k+1): + acum += contar(n,t,filas_negras,mem_negras,casillas_por_diag)*contar(n-1,k-t,filas_blancas,mem_blancas,casillas_por_diag) + else: + for t in xrange(k+1): + acum += contar(n,t,filas_negras,mem_negras,casillas_por_diag)*contar(n,k-t,filas_negras,mem_negras,casillas_por_diag) + print acum + +def contar(i,j,fs,mem,map): + if mem[i][j] == None: + aux = contar(i-1,j-1,fs,mem,map) + aux2 =map(fs[i-1])-(j-1) + mem[i][j] = aux*aux2 + mem[i][j] += contar(i-1,j,fs,mem,map) + return mem[i][j] + + +alfiles(8,7) +alfiles(4,6) +alfiles(6,7) +alfiles(5,10) +alfiles(5,8) +alfiles(5,2) +alfiles(500,300) + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/bishops/main.cpp b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/bishops/main.cpp new file mode 100644 index 0000000..62d6e5c --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/bishops/main.cpp @@ -0,0 +1,66 @@ +#include +#include + +using namespace std; + +typedef unsigned int uint; +typedef unsigned long long int uint64; + +#define forsn(i, s, n) for (uint i = (s); i < (n); i++) +#define forn(i, n) forsn (i, 0, n) + +#define num_diagonals(n) (2 * (n) - 1) + +typedef vector vuint64; +typedef vector vvuint64; + +#define BLACK 0 +#define WHITE 1 +// m: output matrix, should have 2 rows and k + 1 columns +// black_white == 1 iff we are dealing with the white cells and an odd value of n +vuint64 *put_bishops_monochrome(uint n, uint k, bool black_white, vvuint64& m) { + bool row = 0; + + m[0][0] = 1; // we can always put 0 bishops + m[1][0] = 1; + + forn (i, n - black_white) { + uint num_cells = 2 * (i / 2) + 1 + black_white; + forsn (j, 1, k + 1) { + m[row][j] = m[!row][j] + m[!row][j - 1] * (num_cells - (j - 1)); + } + row = !row; + } + return &m[!row]; +} + +uint64 put_bishops(uint n, uint k) { + if (k == 0) return 1; + if (k == 1 && n == 1) return 1; + if (k > num_diagonals(n) - 1) return 0; + + vvuint64 matrix_black(2, vuint64(k + 1, 0)); + vvuint64 matrix_white(2, vuint64(k + 1, 0)); + + vuint64& black(*put_bishops_monochrome(n, k, BLACK, matrix_black)); + vuint64& white(n % 2 == 0 ? black : *put_bishops_monochrome(n, k, WHITE, matrix_white)); + + uint64 ways = 0; + uint lower = k > (n - 1) ? k - (n - 1) : 0; + uint upper = min(k, n - 1) + 1; + forsn (a, lower, upper) { + ways += black[a] * white[k - a]; + } + return ways; +} + +int main() { + uint n, k; + while (true) { + scanf("%u %u", &n, &k); + if (n == 0 && k == 0) break; + cout << put_bishops(n, k) << endl; + } + return 0; +} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/3nmas1.tex b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/3nmas1.tex new file mode 100644 index 0000000..7319ddb --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/3nmas1.tex @@ -0,0 +1,157 @@ +\section{100 - The $3n + 1$ problem} + +\textbf{Problema:} dados $i$ y $j$, encontrar la longitud m\'axima del ciclo, seg\'un la sucesi\'on de Collatz, para todos los +n\'umeros entre $i$ y $j$, donde $i, j$ est\'an en el rango $[1,1\,000\,000)$. + +\begin{figure}[H] +\centering +\includegraphics[scale=0.70]{./figuras/collatz_conjecture.png} +\end{figure} + +\subsection{Resoluci\'on} +Para resolver este ejercicio se calculan los per\'iodos de todos los n\'umeros entre $i$ y $j$, +memorizando en un arreglo los per\'iodos ya calculados, para de esta manera no repetir c\'alculos. + +Como estructura para memorizar, se utiliza un arreglo de un mill\'on de posiciones. +En general, para calcular el per\'iodo de los n\'umeros en $[1,n]$, +{\em podr\'ia} ser necesario calcular valores fuera de ese rango. La decisi\'on que tomamos fue no +memorizar el per\'iodo de los n\'umeros mayores que $999\,999$. +Ensayamos otras implementaciones que usaban un \texttt{map} para +memorizar los per\'iodos de todos los valores, pero en la pr\'actica +(adem\'as de cambiar la complejidad por usar un diccionario sobre \'arbol binario) +esto introduc\'ia un factor constante que lo hac\'ia bastante m\'as lento. + +Si hubiera muchas b\'usquedas en intervalos grandes, se podr\'ia pensar en usar alguna +estructura de datos auxiliar que permitiera determinar r\'apidamente el +m\'aximo de un intervalo de un arreglo (como rmq). A modo de prueba, implementamos +una versi\'on simple de rmq (en la que una consulta cuesta $O(\sqrt{n})$), pero +el algorimo que usaba esa estructura tambi\'en resultaba comparativamente +costoso en la pr\'actica. + +%, porque usando un arreglo esto podr\'ia eventualmente necesitar una gran cantidad de memoria. +%%Es por esta razón que podría ocurrir que se repitan calculos, sin embargo creemos que el impacto que tienen esas repeticiones es despreciable. +%A la hora de realizar varias b\'usquedas, cada una se beneficia de los c\'a de periodos hechos en las anteriores. No obstante ello, si hay muchas busquedas grandes, todas recorren el rango entero. Esto podría hacerse de modo mas eficiente a fin de reducir el tiempo de las busquedas, sin embargo consideramos que eso escapa al problema. + +Como observaci\'on adicional, se puede ver que, si $i \leq \lfloor j / 2 \rfloor$, no es +necesario buscar el m\'aximo en todo el intervalo $[i,j]$, +porque todos los valores menores que $j / 2$ tienen a su doble +dentro del intervalo. Por lo cual, dado que $periodo(2x) = periodo(x) + 1$, +el valor m\'aximo no se alcanza antes de $\lceil j / 2 \rceil$. + +\begin{algorithm}[H] +\begin{algorithmic} +\caption{M\'aximo per\'iodo en un intervalo} +\PARAMS{$i,j$: bordes del intervalo donde buscar (se asume $i \leq j$)} +\ENSURE{ $maximo$: largo del per\'iodo máximo} +\STATE $periodo_1 := 1$ +\STATE $desde := max(i,\lceil j/2 \rceil)$ +\STATE $maximo := 0$ +\FOR{cada $n$ entre $desde$ y $j$} + \STATE $maximo := max(maximo, periodo_n)$ +\ENDFOR +%\RETURN $maximo$ +\end{algorithmic} +\end{algorithm} + +\begin{algorithm}[H] +\begin{algorithmic} +\caption{Per\'iodo de un n\'umero de acuerdo con la relaci\'on de Collatz} +\PARAMS{$i$: n\'umero cuyo per\'iodo interesa conocer} +\IF{$periodo_i$ est\'a memorizado} + \RETURN valor memorizado +\ELSE + \STATE $p := periodo_{i'} + 1$ donde $i'$ es el siguiente de $i$ seg\'un la relaci\'on de Collatz + \STATE memorizar $periodo_i = p$ si corresponde + \RETURN $p$ +\ENDIF +\end{algorithmic} +\end{algorithm} + +Con respecto a la complejidad, si se tiene como entrada el intervalo $[i,j]$ (asumiendo +$i \leq j$), se calcula el per\'iodo de a lo sumo $j - i + 1$ números. Ahora bien, $O(j-i) \subseteq O(j)$. +En muchos casos, calcular el per\'iodo requiere pocos pasos, porque alcanza con +buscar en el arreglo un per\'iodo ya calculado en otro paso; pero esto no ocurre siempre. +Sea $P$ el per\'iodo máximo en el intervalo sobre el que se realiza la consulta. Como cota superior +para el peor caso, calcular cada per\'iodo requiere $P$ pasos. Por esta raz\'on, la complejidad +del algoritmo es $O(P \cdot j)$. +Esta cota es bastante pesimista, ya que muy pocas veces se hacen +$P$ c\'alculos por número. + +%En particular, una vez que ya se calcularon todos +%los per\'iodos, las posteriores b\'usquedas requieren $O(max(i,j))$, ya que +%s\'olo se debe buscar el m\'aximo entre los valores de un arreglo. +En particular, si se realizan $n$ consultas, la complejidad, calculada +de la manera anterior, ser\'ia $O(P \cdot \sum_{k=1}^{n}{j_k})$, +donde $[i_k,j_k]$ es el intervalo de la $k$-\'esima consulta. +Pero, dado que acceder a un elemento ya memorizado es $O(1)$, el costo +del algoritmo es a lo sumo el de inicializar todo el arreglo una vez +m\'as el de buscar el m\'aximo para responder cada consulta, es +decir $O(P \cdot j_{\max} + \sum_{k=1}^{n}{j_k})$, donde $j_{\max} = \max_k{j_k}$. + +En el intervalo $[1,999\,999]$ el valor de $P$ es $525$. Sin embargo, en +general, $P$ no es f\'acil de acotar. De hecho, si se pudiera acotar siempre, +se habr\'ia resuelto la conjetura de Collatz. + +\subsection{Implementación} + +\noindent +\ttfamily +\shorthandoff{"}\\ +\hlstd{}\hlline{\ 1\ }\hldir{\#include\ $<$stdio.h$>$}\\ +\hlline{\ 2\ }\hlstd{}\hldir{\#include\ $<$iostream$>$}\\ +\hlline{\ 3\ }\hlstd{}\hldir{\#include\ $<$vector$>$}\\ +\hlline{\ 4\ }\hlstd{}\hlkwa{using\ namespace\ }\hlstd{std}\hlsym{;}\\ +\hlline{\ 5\ }\hlstd{}\\ +\hlline{\ 6\ }\hlkwc{typedef\ }\hlstd{}\hlkwb{unsigned\ int\ }\hlstd{uint}\hlsym{;}\\ +\hlline{\ 7\ }\hlstd{}\hlkwc{typedef\ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{ushort}\hlsym{;}\\ +\hlline{\ 8\ }\hlstd{}\\ +\hlline{\ 9\ }\hldir{\#define\ Max\textunderscore memo\ 1000001}\\ +\hlline{10\ }\hlstd{vector}\hlsym{$<$}\hlstd{ushort}\hlsym{$>$\ }\hlstd{}\hlkwd{d}\hlstd{}\hlsym{(}\hlstd{Max\textunderscore memo}\hlsym{,\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{);}\\ +\hlline{11\ }\hlstd{}\\ +\hlline{12\ }\hldir{\#define\ memorizado(x)\ ((x)\ $<$\ Max\textunderscore memo\ \&\&\ d{[}(x){]}\ !=\ 0)}\\ +\hlline{13\ }\hlstd{}\hldir{\#define\ next(n)\ ((n)\ \%\ 2\ ==\ 0\ ?\ (n)\ /\ 2\ :\ 3\ {*}\ (n)\ +\ 1)}\\ +\hlline{14\ }\hlstd{\\ +\hlline{15\ }ushort\ }\hlkwd{periodo}\hlstd{}\hlsym{(}\hlstd{uint\ n}\hlsym{)\ \{}\\ +\hlline{16\ }\hlstd{\ }\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwd{memorizado}\hlstd{}\hlsym{(}\hlstd{n}\hlsym{))\ \{}\\ +\hlline{17\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{return\ }\hlstd{d}\hlsym{{[}}\hlstd{n}\hlsym{{]};}\\ +\hlline{18\ }\hlstd{\ }\hlsym{\}\ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{19\ }\hlstd{}\hlstd{\ \ }\hlstd{ushort\ p\ }\hlsym{=\ }\hlstd{}\hlkwd{periodo}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{next}\hlstd{}\hlsym{(}\hlstd{n}\hlsym{))\ +\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{20\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{n\ }\hlsym{$<$\ }\hlstd{Max\textunderscore memo}\hlsym{)\ \{}\\ +\hlline{21\ }\hlstd{}\hlstd{\ \ \ }\hlstd{d}\hlsym{{[}}\hlstd{n}\hlsym{{]}\ =\ }\hlstd{p}\hlsym{;}\\ +\hlline{22\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{23\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{return\ }\hlstd{p}\hlsym{;}\\ +\hlline{24\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{25\ }\hlstd{}\hlsym{\}}\\ +\hlline{26\ }\hlstd{\\ +\hlline{27\ }ushort\ }\hlkwd{resolver}\hlstd{}\hlsym{(}\hlstd{uint\ x}\hlsym{,\ }\hlstd{uint\ y}\hlsym{)\{}\\ +\hlline{28\ }\hlstd{\ ushort\ res\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{29\ }\hlstd{\ uint\ i\ }\hlsym{=\ }\hlstd{}\hlkwd{min}\hlstd{}\hlsym{(}\hlstd{x}\hlsym{,}\hlstd{y}\hlsym{);}\\ +\hlline{30\ }\hlstd{\ uint\ sup\ }\hlsym{=\ }\hlstd{}\hlkwd{max}\hlstd{}\hlsym{(}\hlstd{x}\hlsym{,}\hlstd{y}\hlsym{);}\\ +\hlline{31\ }\hlstd{\ ushort\ aux}\hlsym{;}\\ +\hlline{32\ }\hlstd{\ i\ }\hlsym{=\ }\hlstd{}\hlkwd{max}\hlstd{}\hlsym{(}\hlstd{sup}\hlsym{/}\hlstd{}\hlnum{2}\hlstd{}\hlsym{,}\hlstd{i}\hlsym{);}\\ +\hlline{33\ }\hlstd{\\ +\hlline{34\ }\ }\hlkwa{while}\hlstd{}\hlsym{(}\hlstd{i\ }\hlsym{$<$=\ }\hlstd{sup}\hlsym{)\{}\\ +\hlline{35\ }\hlstd{}\hlstd{\ \ }\hlstd{aux\ }\hlsym{=\ }\hlstd{}\hlkwd{periodo}\hlstd{}\hlsym{(}\hlstd{i}\hlsym{);}\\ +\hlline{36\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{aux\ }\hlsym{$>$\ }\hlstd{res}\hlsym{)\{}\\ +\hlline{37\ }\hlstd{}\hlstd{\ \ \ }\hlstd{res\ }\hlsym{=\ }\hlstd{aux}\hlsym{;}\\ +\hlline{38\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{39\ }\hlstd{}\hlstd{\ \ }\hlstd{i}\hlsym{++;}\\ +\hlline{40\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{41\ }\hlstd{\ }\hlkwa{return\ }\hlstd{res}\hlsym{;}\\ +\hlline{42\ }\hlstd{}\hlsym{\}}\\ +\hlline{43\ }\hlstd{}\\ +\hlline{44\ }\hlkwb{int\ }\hlstd{}\hlkwd{main}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{int\ }\hlstd{argc}\hlsym{,\ }\hlstd{}\hlkwb{char\ }\hlstd{}\hlsym{{*}{*}}\hlstd{argv}\hlsym{)}\\ +\hlline{45\ }\hlstd{}\hlsym{\{}\\ +\hlline{46\ }\hlstd{\ uint\ x}\hlsym{,\ }\hlstd{y}\hlsym{;}\\ +\hlline{47\ }\hlstd{\ d}\hlsym{{[}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]}\ =\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{48\ }\hlstd{\ }\hlkwa{while\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwd{scanf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%u\ \%u"}\hlstd{}\hlsym{,\&}\hlstd{x}\hlsym{,\&}\hlstd{y}\hlsym{)==}\hlstd{}\hlnum{2}\hlstd{}\hlsym{)\ \{}\\ +\hlline{49\ }\hlstd{}\hlstd{\ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{x\ }\hlsym{$<$$<$}\hlstd{}\hlstr{"\ "}\hlstd{}\hlsym{$<$$<$\ }\hlstd{y\ }\hlsym{$<$$<$}\hlstd{}\hlstr{"\ "}\hlstd{\ }\hlsym{$<$$<$\ }\hlstd{}\hlkwd{resolver}\hlstd{}\hlsym{(}\hlstd{x}\hlsym{,\ }\hlstd{y}\hlsym{)\ $<$$<$\ }\hlstd{endl}\hlsym{;}\\ +\hlline{50\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{51\ }\hlstd{\ }\hlkwa{return\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{52\ }\hlstd{}\hlsym{\}}\\ +\hlline{53\ }\hlstd{}\\ +\mbox{} +\normalfont +\shorthandon{"} + + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/algorithm.sty b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/algorithm.sty new file mode 100644 index 0000000..34e1f1f --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/algorithm.sty @@ -0,0 +1,96 @@ +% ALGORITHM STYLE -- Released 8 April 1996 +% for LaTeX-2e +% Copyright -- 1994 Peter Williams +% +% E-mail pwil3058@bigpond.net.au +% +% This style file is free software; you can redistribute it and/or +% modify it under the terms of the GNU Lesser General Public +% License as published by the Free Software Foundation; either +% version 2 of the License, or (at your option) any later version. +% +% This style file is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +% Lesser General Public License for more details. +% +% You should have received a copy of the GNU Lesser General Public +% License along with this style file; if not, write to the +% Free Software Foundation, Inc., 59 Temple Place - Suite 330, +% Boston, MA 02111-1307, USA. +% +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{algorithm} +\typeout{Document Style `algorithm' - floating environment} + +\RequirePackage{float} +\RequirePackage{ifthen} +\newcommand{\ALG@within}{nothing} +\newboolean{ALG@within} +\setboolean{ALG@within}{false} +\newcommand{\ALG@floatstyle}{ruled} +\newcommand{\ALG@name}{Algorithm} +\newcommand{\listalgorithmname}{List of \ALG@name s} + +% Declare Options +% first appearance +\DeclareOption{plain}{ + \renewcommand{\ALG@floatstyle}{plain} +} +\DeclareOption{ruled}{ + \renewcommand{\ALG@floatstyle}{ruled} +} +\DeclareOption{boxed}{ + \renewcommand{\ALG@floatstyle}{boxed} +} +% then numbering convention +\DeclareOption{part}{ + \renewcommand{\ALG@within}{part} + \setboolean{ALG@within}{true} +} +\DeclareOption{chapter}{ + \renewcommand{\ALG@within}{chapter} + \setboolean{ALG@within}{true} +} +\DeclareOption{section}{ + \renewcommand{\ALG@within}{section} + \setboolean{ALG@within}{true} +} +\DeclareOption{subsection}{ + \renewcommand{\ALG@within}{subsection} + \setboolean{ALG@within}{true} +} +\DeclareOption{subsubsection}{ + \renewcommand{\ALG@within}{subsubsection} + \setboolean{ALG@within}{true} +} +\DeclareOption{nothing}{ + \renewcommand{\ALG@within}{nothing} + \setboolean{ALG@within}{true} +} +\DeclareOption*{\edef\ALG@name{\CurrentOption}} + +% ALGORITHM +% +\ProcessOptions +\floatstyle{\ALG@floatstyle} +\ifthenelse{\boolean{ALG@within}}{ + \ifthenelse{\equal{\ALG@within}{part}} + {\newfloat{algorithm}{htbp}{loa}[part]}{} + \ifthenelse{\equal{\ALG@within}{chapter}} + {\newfloat{algorithm}{htbp}{loa}[chapter]}{} + \ifthenelse{\equal{\ALG@within}{section}} + {\newfloat{algorithm}{htbp}{loa}[section]}{} + \ifthenelse{\equal{\ALG@within}{subsection}} + {\newfloat{algorithm}{htbp}{loa}[subsection]}{} + \ifthenelse{\equal{\ALG@within}{subsubsection}} + {\newfloat{algorithm}{htbp}{loa}[subsubsection]}{} + \ifthenelse{\equal{\ALG@within}{nothing}} + {\newfloat{algorithm}{htbp}{loa}}{} +}{ + \newfloat{algorithm}{htbp}{loa} +} +\floatname{algorithm}{\ALG@name} + +\newcommand{\listofalgorithms}{\listof{algorithm}{\listalgorithmname}} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/algorithmic.sty b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/algorithmic.sty new file mode 100644 index 0000000..4dcaa7c --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/algorithmic.sty @@ -0,0 +1,194 @@ +% ALGORITHMIC STYLE for LaTeX version 2e +% +% This style file is free software; you can redistribute it and/or +% modify it under the terms of the GNU Lesser General Public +% License as published by the Free Software Foundation; either +% version 2 of the License, or (at your option) any later version. +% +% This style file is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +% Lesser General Public License for more details. +% +% You should have received a copy of the GNU Lesser General Public +% License along with this style file; if not, write to the +% Free Software Foundation, Inc., 59 Temple Place - Suite 330, +% Boston, MA 02111-1307, USA. +% +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{algorithmic}[2006/06/02] +\typeout{Document Style `algorithmic' - environment} +% +\RequirePackage{ifthen} +\RequirePackage{calc} +\RequirePackage{keyval} +\newboolean{ALC@noend} +\setboolean{ALC@noend}{false} +\newcounter{ALC@line} +\newcounter{ALC@rem} +\newcounter{ALC@depth} +\newlength{\ALC@tlm} +% +\DeclareOption{noend}{\setboolean{ALC@noend}{true}} +% +\ProcessOptions +% +% For keyval-style options +\def\algsetup{\setkeys{ALG}} +% +% For indentation of algorithms +\newlength{\algorithmicindent} +\setlength{\algorithmicindent}{0pt} +\define@key{ALG}{indent}{\setlength{\algorithmicindent}{#1}} +\ifthenelse{\lengthtest{\algorithmicindent=0pt}}% + {\setlength{\algorithmicindent}{1em}}{} +% +% For line numbers' delimiters +\newcommand{\ALC@linenodelimiter}{:} +\define@key{ALG}{linenodelimiter}{\renewcommand{\ALC@linenodelimiter}{#1}} + +% +% For line numbers' size +\newcommand{\ALC@linenosize}{\footnotesize} +\define@key{ALG}{linenosize}{\renewcommand{\ALC@linenosize}{#1}} + +% +% ALGORITHMIC +\newcommand{\algorithmicrequire}{\textbf{Require:}} +\newcommand{\algorithmicensure}{\textbf{Ensure:}} +\newcommand{\algorithmicparams}[1]{\textcolor{RawSienna}{\textbf{Entrada:}} #1} +\newcommand{\algorithmiccomment}[1]{\textcolor{Purple}{\{#1\}}} +\newcommand{\algorithmicend}{\textbf{end}} +\newcommand{\algorithmicif}{\textbf{if}} +\newcommand{\algorithmicthen}{\textbf{then}} +\newcommand{\algorithmicelse}{\textbf{else}} +\newcommand{\algorithmicelsif}{\algorithmicelse\ \algorithmicif} +\newcommand{\algorithmicendif}{\algorithmicend\ \algorithmicif} +\newcommand{\algorithmicfor}{\textbf{for}} +\newcommand{\algorithmicforall}{\textbf{for all}} +\newcommand{\algorithmicdo}{\textbf{do}} +\newcommand{\algorithmicendfor}{\algorithmicend\ \algorithmicfor} +\newcommand{\algorithmicwhile}{\textbf{while}} +\newcommand{\algorithmicendwhile}{\algorithmicend\ \algorithmicwhile} +\newcommand{\algorithmicloop}{\textbf{loop}} +\newcommand{\algorithmicendloop}{\algorithmicend\ \algorithmicloop} +\newcommand{\algorithmicrepeat}{\textbf{repeat}} +\newcommand{\algorithmicuntil}{\textbf{until}} +\newcommand{\algorithmicprint}{\textbf{print}} +\newcommand{\algorithmicreturn}{\textbf{return}} +\newcommand{\algorithmictrue}{\textbf{true}} +\newcommand{\algorithmicfalse}{\textbf{false}} +\def\ALC@setref{% + \def\@currentlabel{\theALC@line}% +} +\def\ALC@item[#1]{% +\if@noparitem \@donoparitem + \else \if@inlabel \indent \par \fi + \ifhmode \unskip\unskip \par \fi + \if@newlist \if@nobreak \@nbitem \else + \addpenalty\@beginparpenalty + \addvspace\@topsep \addvspace{-\parskip}\fi + \else \addpenalty\@itempenalty \addvspace\itemsep + \fi + \global\@inlabeltrue +\fi +\everypar{\global\@minipagefalse\global\@newlistfalse + \if@inlabel\global\@inlabelfalse \hskip -\parindent \box\@labels + \penalty\z@ \fi + \everypar{}}\global\@nobreakfalse +\if@noitemarg \@noitemargfalse \if@nmbrlist \refstepcounter{\@listctr}\fi \fi +\sbox\@tempboxa{\makelabel{#1}}% +\global\setbox\@labels + \hbox{\unhbox\@labels \hskip \itemindent + \hskip -\labelwidth \hskip -\ALC@tlm + \ifdim \wd\@tempboxa >\labelwidth + \box\@tempboxa + \else \hbox to\labelwidth {\unhbox\@tempboxa}\fi + \hskip \ALC@tlm}\ignorespaces} +% +\newenvironment{algorithmic}[1][0]{ +\setcounter{ALC@depth}{\@listdepth}% +\let\@listdepth\c@ALC@depth% +\let\@item\ALC@item% + \newcommand{\ALC@lno}{% +\ifthenelse{\equal{\arabic{ALC@rem}}{0}} +{{\ALC@linenosize \arabic{ALC@line}\ALC@linenodelimiter}}{}% +} +\let\@listii\@listi +\let\@listiii\@listi +\let\@listiv\@listi +\let\@listv\@listi +\let\@listvi\@listi +\let\@listvii\@listi + \newenvironment{ALC@g}{ + \begin{list}{\ALC@lno}{ \itemsep\z@ \itemindent\z@ + \listparindent\z@ \rightmargin\z@ + \topsep\z@ \partopsep\z@ \parskip\z@\parsep\z@ + \leftmargin \algorithmicindent%1em + \addtolength{\ALC@tlm}{\leftmargin} + } + } + {\end{list}} + \newcommand{\ALC@it}{\refstepcounter{ALC@rem}\refstepcounter{ALC@line}\ifthenelse{\equal{\arabic{ALC@rem}}{#1}}{\setcounter{ALC@rem}{0}}{}\item\ALC@setref} + \newcommand{\ALC@com}[1]{\ifthenelse{\equal{##1}{default}}% +{}{\ \algorithmiccomment{##1}}} + \newcommand{\REQUIRE}{\item[\algorithmicrequire]} + \newcommand{\ENSURE}{\item[\algorithmicensure]} + \newcommand{\PRINT}{\ALC@it\algorithmicprint{}\ \ } + \newcommand{\RETURN}{\ALC@it\algorithmicreturn{}\ \ } + \newcommand{\TRUE}{\algorithmictrue{}} + \newcommand{\FALSE}{\algorithmicfalse{}} + \newcommand{\STATE}{\ALC@it} + \newcommand{\STMT}{\ALC@it} + \newcommand{\PARAMS}[1]{\item[\algorithmicparams{##1}]} + \newcommand{\COMMENT}[1]{\algorithmiccomment{##1}} + \newenvironment{ALC@if}{\begin{ALC@g}}{\end{ALC@g}} + \newenvironment{ALC@for}{\begin{ALC@g}}{\end{ALC@g}} + \newenvironment{ALC@whl}{\begin{ALC@g}}{\end{ALC@g}} + \newenvironment{ALC@loop}{\begin{ALC@g}}{\end{ALC@g}} + \newenvironment{ALC@rpt}{\begin{ALC@g}}{\end{ALC@g}} + \renewcommand{\\}{\@centercr} + \newcommand{\IF}[2][default]{\ALC@it\algorithmicif\ ##2\ \algorithmicthen% +\ALC@com{##1}\begin{ALC@if}} + \newcommand{\ELSE}[1][default]{\end{ALC@if}\ALC@it\algorithmicelse% +\ALC@com{##1}\begin{ALC@if}} + \newcommand{\ELSIF}[2][default]% +{\end{ALC@if}\ALC@it\algorithmicelsif\ ##2\ \algorithmicthen% +\ALC@com{##1}\begin{ALC@if}} + \newcommand{\FOR}[2][default]{\ALC@it\algorithmicfor\ ##2\ \algorithmicdo% +\ALC@com{##1}\begin{ALC@for}} + \newcommand{\FORALL}[2][default]{\ALC@it\algorithmicforall\ ##2\ % +\algorithmicdo% +\ALC@com{##1}\begin{ALC@for}} + \newcommand{\WHILE}[2][default]{\ALC@it\algorithmicwhile\ ##2\ % +\algorithmicdo% +\ALC@com{##1}\begin{ALC@whl}} + \newcommand{\LOOP}[1][default]{\ALC@it\algorithmicloop% +\ALC@com{##1}\begin{ALC@loop}} + \newcommand{\REPEAT}[1][default]{\ALC@it\algorithmicrepeat% +\ALC@com{##1}\begin{ALC@rpt}} + \newcommand{\UNTIL}[1]{\end{ALC@rpt}\ALC@it\algorithmicuntil\ ##1} + \ifthenelse{\boolean{ALC@noend}}{ + \newcommand{\ENDIF}{\end{ALC@if}} + \newcommand{\ENDFOR}{\end{ALC@for}} + \newcommand{\ENDWHILE}{\end{ALC@whl}} + \newcommand{\ENDLOOP}{\end{ALC@loop}} + }{ + \newcommand{\ENDIF}{\end{ALC@if}\ALC@it\algorithmicendif} + \newcommand{\ENDFOR}{\end{ALC@for}\ALC@it\algorithmicendfor} + \newcommand{\ENDWHILE}{\end{ALC@whl}\ALC@it\algorithmicendwhile} + \newcommand{\ENDLOOP}{\end{ALC@loop}\ALC@it\algorithmicendloop} + } + \renewcommand{\@toodeep}{} + \begin{list}{\ALC@lno}{\setcounter{ALC@rem}{0}\setcounter{ALC@line}{0}% + \itemsep\z@ \itemindent\z@ \listparindent\z@% + \partopsep\z@ \parskip\z@ \parsep\z@% + \labelsep 0.5em \topsep 0.2em% +\ifthenelse{\equal{#1}{0}} + {\labelwidth 0.5em } + {\labelwidth 1.2em } +\leftmargin\labelwidth \addtolength{\leftmargin}{\labelsep} + \ALC@tlm\labelsep + } +} +{\end{list}} diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/bishops.tex b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/bishops.tex new file mode 100644 index 0000000..416ec3d --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/bishops.tex @@ -0,0 +1,222 @@ +\section{861 - Little bishops} + +\textbf{Problema:} dados dos enteros $n$ y $k$, devolver la cantidad +de formas de ubicar $k$ alfiles en un tablero de $n \times n$, de manera tal +que ninguno de ellos sea atacado por otro. + +\subsection{Resoluci\'on} +Para resolverlo, primero notamos que las casillas negras y las blancas +son independientes, en el sentido de que un alfil en una casilla de un color +nunca puede atacar a un alfil en una casilla del color opuesto. +Por esta raz\'on, la cantidad de formas de ubicar $k$ alfiles +en un tablero de $n \times n$ se puede calcular de la siguiente manera: + +Sea $a_k$ la cantidad de formas de ubicar $k$ alfiles sin que se ataquen +en un tablero de $n \times n$. Si $a_k^B$ es la cantidad de formas de ubicar +$k$ alfiles sin que se ataquen en las casillas blancas y +$a_k^N$ es la cantidad de formas de hacerlo en las negras, entonces vale que: + +$$a_k = \sum_{i=0}^k{a_i^N \cdot a_{k-i}^B}$$ + +Por otro lado, mirando s\'olo las casillas negras +(es an\'alogo para las blancas) y rotando el tablero $45º$, +el problema de ubicar alfiles se puede interpretar como un +problema de ubicar torres. + +\begin{figure}[H] +\centering +\includegraphics[scale=0.30]{./figuras/tablero1.png} +\caption{Interpretaci\'on del problema de los alfiles como uno de torres} +\end{figure} + +Consideramos ahora el problema de ubicar torres, sin que se ataquen, +en un tablero de varias filas, cada una de las cuales puede tener un +n\'umero diferente de columnas. +Es f\'acil ver que a lo sumo puede haber una torre por fila, y que +permutar filas no modifica la cantidad de torres que se pueden ubicar. +Sea $columnas(i)$ la cantidad de columnas de la fila $i$. +Si se ordenan las filas crecientemente por su cantidad de columnas, +vale que las columnas de cada fila +están incluidas en las de las filas que están abajo. Esto quiere +decir que, al ubicar una torre, la columna en la que fue ubicada queda +inutilizable para las filas siguientes. + +A partir de esto podemos definir la siguiente recurrencia: + +Sea $cantidad(i,j)=$ cantidad de formas de poner $j$ torres usando las +primeras $i$ filas (ordenadas crecientemente por cantidad de columnas). Vale entonces +que: + +$cantidad(i,0) = 1 $, porque hay solo una forma de no poner ninguna torre. + +$cantidad(0,j) = 0 \ si \ j > 0$, porque no hay forma de poner alguna torre si no quedan casillas. + +$cantidad(i,j) = cantidad(i-1,j) + cantidad(i-1,j-1) \cdot (columnas(i)-(j-1))\ si \ i > 0$, +porque o bien se ponen las $j$ torres en la filas anteriores, o bien se pone una en +la fila actual y el resto en las anteriores. Al hacer eso, se est\'an ocupando $j-1$ +columnas; las restantes quedan libres, por lo cual para cada posible forma de ubicar +las torres en las anteriores filas hay $columnas(i) - (j-1)$ columnas libres que +pueden usarse. + +Aplicamos la resoluci\'on del problema de ubicar torres sobre las diagonales +negras y las diagonales blancas, para as\'i calcular $a^N_k$ y $a^B_k$. +Pueden hacerse las siguientes optimizaciones: +\begin{itemize} +\item No es necesario ``ordenar'' las diagonales, basta con notar que para las +casillas negras las longitudes de las diagonales son 1, 1, 3, 3, ..., etc. (para +las casillas blancas es similar pero empezando desde 2). + +\item Si $n$ es par, las casillas blancas y las negras son sim\'etricas, +por lo cual la cantidad de formas de ubicar las piezas es la misma para +unas y otras (es decir, $a^B_k = a^N_k$). En ese caso, basta con resolver +el problema para las casillas de uno de los colores. + +\item Si $n > 1$, la cantidad m\'axima de alfiles que se pueden poner en un tablero de $n \times n$ es $2n - 2$. +Esto es porque hay $2n - 1$ diagonales pero adem\'as no pueden ubicarse dos alfiles en esquinas opuestas\footnote{ +Adem\'as est\'a demostrado: + +Dudeney, H. E. ``Bishops--Unguarded'' and ``Bishops--Guarded.'' \S 297 and 298 in Amusements in Mathematics. New York: Dover, pp. 88-89 and 96, 1970. + +Madachy, J. Madachy's Mathematical Recreations. New York: Dover, pp. 36-46, 1979. } +con lo cual si el $k$ ingresado es mayor, se puede devolver 0 sin procesar nada. + +\item En todas las diagonales de un color, se pueden poner a lo sumo $n - 1$ alfiles, esto es fácil de ver, si consideramos un tablero ubicado como el de la figura, las casillas negras tienen $n$ diagonales ascendentes, pero dos son de una sola casilla y están en la misma diagonal descendente. Si $n$ es par las casillas blancas son simétricas a las negras, por lo que la cantidad de alfiles que se pueden ubicar es la misma. Si en cambio $n$ es impar, hay $n-1$ diagonales blancas ascendentes, que a lo sumo pueden tener un alfil cada una. +Es por esta razón que no hace falta hacer la sumatoria desde $0$ hasta $k$, sino que se puede hacer +desde $max(0, k - (n - 1))$ hasta $min(k, n - 1)$. Esto s\'olo vale si $n > 1$, ya que con $n = 1$ +no hay casillas blancas. +\end{itemize} + +En base a la recurrencia planteada, se ve que basta con llenar una matriz $M$ de $(n + 1) \times (k + 1)$ +para las negras y otra para las blancas, de modo que $M[i][j]=cantidad(i,j)$. El siguiente es el +algoritmo de llenado de la tabla para las casillas negras. Si el tablero es impar, el algoritmo +para las casillas blancas es similar. Dado que en cada paso s\'olo se necesita la fila anterior, +en la implementaci\'on la matriz se representa guardando s\'olo las \'ultimas dos filas, +cada una de $k + 1$ elementos. + +\begin{algorithm}[H] +\begin{algorithmic} +\caption{\texttt{ubicar\_en\_negras}: maneras de ubicar $\leq k$ alfiles en las casillas negras de un tablero de $n \times n$} +\PARAMS{$n$: alto del tablero, $k$: m\'axima cantidad de alfiles que se quieren poner} +\STATE $M$ := matriz de $(n + 1)$ filas y $(k+1)$ columnas %%tal que $M_{ij}=0$ +%\STATE\COMMENT{$M_{i,j}$ = cantidad de maneras de poner $j$ alfiles en las diagonales negras $[0,i)$} +\STATE $M_{i,0} := 1$ para todo $i$ +\STATE $M_{0,j} := 0$ para todo $j > 0$ +\FOR{cada $i$ en $[1,n]$} + \STATE $casillas$ := n\'umero de casillas de la $(i - 1)$-\'esima diagonal negra + \FOR{cada $j$ en $[1,k]$} + \STATE $M_{i,j} := M_{i-1,j} + M_{i-1,j-1}*(casillas - (j-1))$ + \ENDFOR +\ENDFOR +\STATE $resultado := M[n]$ \COMMENT{\'ultima fila de la matriz} +\RETURN $resultado$ \COMMENT{$resultado[j] = $ cantidad de maneras de poner $j$ alfiles en las casillas negras del tablero} +\end{algorithmic} +\end{algorithm} + +\begin{algorithm}[H] +\begin{algorithmic} +\caption{Maneras de ubicar $k$ alfiles en un tablero de $n \times n$} +\PARAMS{$n$: alto del tablero, $k$: cantidad de alfiles que se quieren poner} +\STATE Si $k=0$ devolver 1. +\STATE Si el tablero es s\'olo una casilla y $k=1$, devolver 1. +\STATE Si $k >$ m\'aximo numero de alfiles en un tablero de $n \times n$ devolver 0. +\STATE $negras :=$ \texttt{ubicar\_en\_negras($n$, $k$)} +\STATE $blancas :=$ si $n$ es par, es igual a $negras$; si no, \texttt{ubicar\_en\_blancas($n$, $k$)} +\STATE $maneras := 0$ +\STATE $inf := max(k - (n - 1), 0)$ +\STATE $sup := min(k, n - 1) + 1$ +\FOR{cada $a$ en [$inf$, $sup$]} + \STATE $maneras := maneras + negras_a * blancas_{k - a}$ +\ENDFOR +\RETURN $maneras$ +\end{algorithmic} +\end{algorithm} + +Con respecto a la complejidad, vimos que si $k > 2n-2$ no es necesario calcular +la matriz. Esto se puede ver en $O(1)$. %Si $k <= 2n-2$ entonces tenemos que contar. +Por lo tanto, para calcular la complejidad del resto del algoritmo, se +puede asumir que $k \in O(n)$. + +Computar cada matriz toma $O(n \cdot k)$, que es $O(n^2)$. A lo sumo se computan +dos matrices. El costo de recorrer las \'ultimas filas y hacer el producto es +$O(k)$, que nuevamente es $O(n)$. Por lo tanto, la complejidad temporal en peor caso +es $O(n^2)$. + +En cuanto a la memoria, alcanza con guardar las \'ultimas dos filas de la matriz +en cada paso, por lo cual es la complejidad es $O(k)$ que es $O(n)$. + +\subsection{Implementación} + +\noindent +\ttfamily +\shorthandoff{"}\\ +\hlstd{}\hlline{\ 1\ }\hldir{\#include\ $<$iostream$>$}\\ +\hlline{\ 2\ }\hlstd{}\hldir{\#include\ $<$vector$>$}\\ +\hlline{\ 3\ }\hlstd{}\\ +\hlline{\ 4\ }\hlkwa{using\ namespace\ }\hlstd{std}\hlsym{;}\\ +\hlline{\ 5\ }\hlstd{}\\ +\hlline{\ 6\ }\hlkwc{typedef\ }\hlstd{}\hlkwb{unsigned\ int\ }\hlstd{uint}\hlsym{;}\\ +\hlline{\ 7\ }\hlstd{}\hlkwc{typedef\ }\hlstd{}\hlkwb{unsigned\ long\ long\ int\ }\hlstd{uint64}\hlsym{;}\\ +\hlline{\ 8\ }\hlstd{}\\ +\hlline{\ 9\ }\hldir{\#define\ forsn(i,\ s,\ n)}\hlstd{\ \ }\hldir{for\ (uint\ i\ =\ (s);\ i\ $<$\ (n);\ i++)}\\ +\hlline{10\ }\hlstd{}\hldir{\#define\ forn(i,\ n)}\hlstd{\ \ }\hldir{forsn\ (i,\ 0,\ n)}\\ +\hlline{11\ }\hlstd{}\\ +\hlline{12\ }\hldir{\#define\ num\textunderscore diagonals(n)\ (2\ {*}\ (n)\ {-}\ 1)}\\ +\hlline{13\ }\hlstd{}\\ +\hlline{14\ }\hlkwc{typedef\ }\hlstd{vector}\hlsym{$<$}\hlstd{uint64}\hlsym{$>$\ }\hlstd{vuint64}\hlsym{;}\\ +\hlline{15\ }\hlstd{}\hlkwc{typedef\ }\hlstd{vector}\hlsym{$<$}\hlstd{vuint64}\hlsym{$>$\ }\hlstd{vvuint64}\hlsym{;}\\ +\hlline{16\ }\hlstd{}\\ +\hlline{17\ }\hldir{\#define\ BLACK\ 0}\\ +\hlline{18\ }\hlstd{}\hldir{\#define\ WHITE\ 1}\\ +\hlline{19\ }\hlstd{}\hlslc{//\ m:\ output\ matrix,\ should\ have\ 2\ rows\ and\ k\ +\ 1\ columns}\\ +\hlline{20\ }\hlstd{}\hlslc{//\ black\textunderscore white\ ==\ 1\ iff\ we\ are\ dealing\ with\ the\ white\ cells\ and\ an\ odd\ value\ of\ n\ }\\ +\hlline{21\ }\hlstd{vuint64\ }\hlsym{{*}}\hlstd{}\hlkwd{put\textunderscore bishops\textunderscore monochrome}\hlstd{}\hlsym{(}\hlstd{uint\ n}\hlsym{,\ }\hlstd{uint\ k}\hlsym{,\ }\hlstd{}\hlkwb{bool\ }\hlstd{black\textunderscore white}\hlsym{,\ }\hlstd{vvuint64}\hlsym{\&\ }\hlstd{m}\hlsym{)\ \{}\\ +\hlline{22\ }\hlstd{\ }\hlkwb{bool\ }\hlstd{row\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{23\ }\hlstd{\\ +\hlline{24\ }\ m}\hlsym{{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}\ =\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;\ }\hlstd{}\hlslc{//\ we\ can\ always\ put\ 0\ bishops}\\ +\hlline{25\ }\hlstd{\ m}\hlsym{{[}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]}{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}\ =\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{26\ }\hlstd{\ \\ +\hlline{27\ }\ }\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{n\ }\hlsym{{-}\ }\hlstd{black\textunderscore white}\hlsym{)\ \{}\\ +\hlline{28\ }\hlstd{}\hlstd{\ \ }\hlstd{uint\ num\textunderscore cells\ }\hlsym{=\ }\hlstd{}\hlnum{2\ }\hlstd{}\hlsym{{*}\ (}\hlstd{i\ }\hlsym{/\ }\hlstd{}\hlnum{2}\hlstd{}\hlsym{)\ +\ }\hlstd{}\hlnum{1\ }\hlstd{}\hlsym{+\ }\hlstd{black\textunderscore white}\hlsym{;}\\ +\hlline{29\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{forsn\ }\hlstd{}\hlsym{(}\hlstd{j}\hlsym{,\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{,\ }\hlstd{k\ }\hlsym{+\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ \{}\\ +\hlline{30\ }\hlstd{}\hlstd{\ \ \ }\hlstd{m}\hlsym{{[}}\hlstd{row}\hlsym{{]}{[}}\hlstd{j}\hlsym{{]}\ =\ }\hlstd{m}\hlsym{{[}!}\hlstd{row}\hlsym{{]}{[}}\hlstd{j}\hlsym{{]}\ +\ }\hlstd{m}\hlsym{{[}!}\hlstd{row}\hlsym{{]}{[}}\hlstd{j\ }\hlsym{{-}\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]}\ {*}\ (}\hlstd{num\textunderscore cells\ }\hlsym{{-}\ (}\hlstd{j\ }\hlsym{{-}\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{));}\\ +\hlline{31\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{32\ }\hlstd{}\hlstd{\ \ }\hlstd{row\ }\hlsym{=\ !}\hlstd{row}\hlsym{;}\\ +\hlline{33\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{34\ }\hlstd{\ }\hlkwa{return\ }\hlstd{}\hlsym{\&}\hlstd{m}\hlsym{{[}!}\hlstd{row}\hlsym{{]};}\\ +\hlline{35\ }\hlstd{}\hlsym{\}}\\ +\hlline{36\ }\hlstd{\\ +\hlline{37\ }uint64\ }\hlkwd{put\textunderscore bishops}\hlstd{}\hlsym{(}\hlstd{uint\ n}\hlsym{,\ }\hlstd{uint\ k}\hlsym{)\ \{}\\ +\hlline{38\ }\hlstd{\ }\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{k\ }\hlsym{==\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ }\hlstd{}\hlkwa{return\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{39\ }\hlstd{\ }\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{k\ }\hlsym{==\ }\hlstd{}\hlnum{1\ }\hlstd{}\hlsym{\&\&\ }\hlstd{n\ }\hlsym{==\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ }\hlstd{}\hlkwa{return\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{40\ }\hlstd{\ }\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{k\ }\hlsym{$>$\ }\hlstd{}\hlkwd{num\textunderscore diagonals}\hlstd{}\hlsym{(}\hlstd{n}\hlsym{)\ {-}\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ }\hlstd{}\hlkwa{return\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{41\ }\hlstd{\\ +\hlline{42\ }\ vvuint64\ }\hlkwd{matrix\textunderscore black}\hlstd{}\hlsym{(}\hlstd{}\hlnum{2}\hlstd{}\hlsym{,\ }\hlstd{}\hlkwd{vuint64}\hlstd{}\hlsym{(}\hlstd{k\ }\hlsym{+\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{,\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{));}\\ +\hlline{43\ }\hlstd{\ vvuint64\ }\hlkwd{matrix\textunderscore white}\hlstd{}\hlsym{(}\hlstd{}\hlnum{2}\hlstd{}\hlsym{,\ }\hlstd{}\hlkwd{vuint64}\hlstd{}\hlsym{(}\hlstd{k\ }\hlsym{+\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{,\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{));}\\ +\hlline{44\ }\hlstd{\\ +\hlline{45\ }\ vuint64}\hlsym{\&\ }\hlstd{}\hlkwd{black}\hlstd{}\hlsym{({*}}\hlstd{}\hlkwd{put\textunderscore bishops\textunderscore monochrome}\hlstd{}\hlsym{(}\hlstd{n}\hlsym{,\ }\hlstd{k}\hlsym{,\ }\hlstd{BLACK}\hlsym{,\ }\hlstd{matrix\textunderscore black}\hlsym{));}\\ +\hlline{46\ }\hlstd{\ vuint64}\hlsym{\&\ }\hlstd{}\hlkwd{white}\hlstd{}\hlsym{(}\hlstd{n\ }\hlsym{\%\ }\hlstd{}\hlnum{2\ }\hlstd{}\hlsym{==\ }\hlstd{}\hlnum{0\ }\hlstd{?\ black\ }\hlsym{:\ {*}}\hlstd{}\hlkwd{put\textunderscore bishops\textunderscore monochrome}\hlstd{}\hlsym{(}\hlstd{n}\hlsym{,\ }\hlstd{k}\hlsym{,\ }\hlstd{WHITE}\hlsym{,\ }\hlstd{matrix\textunderscore white}\hlsym{));}\\ +\hlline{47\ }\hlstd{\\ +\hlline{48\ }\ uint64\ ways\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{49\ }\hlstd{\ uint\ lower\ }\hlsym{=\ }\hlstd{k\ }\hlsym{$>$\ (}\hlstd{n\ }\hlsym{{-}\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ }\hlstd{?\ k\ }\hlsym{{-}\ (}\hlstd{n\ }\hlsym{{-}\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ :\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{50\ }\hlstd{\ uint\ upper\ }\hlsym{=\ }\hlstd{}\hlkwd{min}\hlstd{}\hlsym{(}\hlstd{k}\hlsym{,\ }\hlstd{n\ }\hlsym{{-}\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ +\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{51\ }\hlstd{\ }\hlkwd{forsn\ }\hlstd{}\hlsym{(}\hlstd{a}\hlsym{,\ }\hlstd{lower}\hlsym{,\ }\hlstd{upper}\hlsym{)\ \{}\\ +\hlline{52\ }\hlstd{}\hlstd{\ \ }\hlstd{ways\ }\hlsym{+=\ }\hlstd{black}\hlsym{{[}}\hlstd{a}\hlsym{{]}\ {*}\ }\hlstd{white}\hlsym{{[}}\hlstd{k\ }\hlsym{{-}\ }\hlstd{a}\hlsym{{]};}\\ +\hlline{53\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{54\ }\hlstd{\ }\hlkwa{return\ }\hlstd{ways}\hlsym{;}\\ +\hlline{55\ }\hlstd{}\hlsym{\}}\\ +\hlline{56\ }\hlstd{}\\ +\hlline{57\ }\hlkwb{int\ }\hlstd{}\hlkwd{main}\hlstd{}\hlsym{()\ \{}\\ +\hlline{58\ }\hlstd{\ uint\ n}\hlsym{,\ }\hlstd{k}\hlsym{;}\\ +\hlline{59\ }\hlstd{\ }\hlkwa{while\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwa{true}\hlstd{}\hlsym{)\ \{}\\ +\hlline{60\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{scanf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%u\ \%u"}\hlstd{}\hlsym{,\ \&}\hlstd{n}\hlsym{,\ \&}\hlstd{k}\hlsym{);}\\ +\hlline{61\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{n\ }\hlsym{==\ }\hlstd{}\hlnum{0\ }\hlstd{}\hlsym{\&\&\ }\hlstd{k\ }\hlsym{==\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ }\hlstd{}\hlkwa{break}\hlstd{}\hlsym{;}\\ +\hlline{62\ }\hlstd{}\hlstd{\ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{}\hlkwd{put\textunderscore bishops}\hlstd{}\hlsym{(}\hlstd{n}\hlsym{,\ }\hlstd{k}\hlsym{)\ $<$$<$\ }\hlstd{endl}\hlsym{;}\\ +\hlline{63\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{64\ }\hlstd{\ }\hlkwa{return\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{65\ }\hlstd{}\hlsym{\}}\\ +\hlline{66\ }\hlstd{}\\ +\mbox{} +\normalfont +\shorthandon{"} + + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/caratula.sty b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/caratula.sty new file mode 100644 index 0000000..7d4a979 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/caratula.sty @@ -0,0 +1,290 @@ +% ************************************************************************** +% +% Package 'caratula', version 0.3 (para componer caratulas de TPs del DC). +% +% En caso de dudas, problemas o sugerencias sobre este package escribir a +% Brian J. Cardiff (bcardif arroba gmail.com). +% Nico Rosner (nrosner arroba dc.uba.ar). +% +% ************************************************************************** + +% ----- Informacion sobre el package para el sistema ----------------------- + +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{caratula}[2005/08/09 v0.4 Para componer caratulas de TPs del DC] +\RequirePackage{ifthen} +\usepackage[pdftex]{graphicx} + +% ----- Imprimir un mensajito al procesar un .tex que use este package ----- + +\typeout{Cargando package 'caratula' v0.4 (2006/09/29)} + +% ----- Algunas variables -------------------------------------------------- + +\let\Materia\relax +\let\Submateria\relax +\let\Titulo\relax +\let\Subtitulo\relax +\let\Grupo\relax +\let\Fecha\relax +\let\Logoimagefile\relax +\let\Resumen\relax +\newcommand{\LabelIntegrantes}{} +\newboolean{showLU} +\newboolean{showDirectores} + +% ----- Comandos para que el usuario defina las variables ------------------ + +\def\materia#1{\def\Materia{#1}} +\def\submateria#1{\def\Submateria{#1}} +\def\titulo#1{\def\Titulo{#1}} +\def\subtitulo#1{\def\Subtitulo{#1}} +\def\grupo#1{\def\Grupo{#1}} +\def\fecha#1{\def\Fecha{#1}} +\def\logoimagefile#1{\def\Logoimagefile{#1}} +\def\resumen#1{\def\Resumen{#1}} + +% ----- Token list para los integrantes ------------------------------------ + +\newtoks\intlist\intlist={} + +\newtoks\intlistSinLU\intlistSinLU={} + +\newcounter{integrantesCount} +\setcounter{integrantesCount}{0} +\newtoks\intTabNombre\intTabNombre={} +\newtoks\intTabLU\intTabLU={} +\newtoks\intTabEmail\intTabEmail={} + +\newcounter{directoresCount} +\setcounter{directoresCount}{0} +\newtoks\direcTabNombre\direcTabNombre={} +\newtoks\direcTabEmail\direcTabEmail={} + +% ----- Comando para que el usuario agregue integrantes -------------------- + +\def\integrante#1#2#3{% + \intlist=\expandafter{\the\intlist\rule{0pt}{1.2em}#1&\tt #3\\[0.2em]}% + \intlistSinLU=\expandafter{\the\intlistSinLU\rule{0pt}{1.2em}#1 & \tt #3\\[0.2em]}% + % + \ifthenelse{\value{integrantesCount} > 0}{% + \intTabNombre=\expandafter{\the\intTabNombre & #1}% + \intTabLU=\expandafter{\the\intTabLU & #2}% + \intTabEmail=\expandafter{\the\intTabEmail & \tt #3}% + }{ + \intTabNombre=\expandafter{\the\intTabNombre #1}% + \intTabLU=\expandafter{\the\intTabLU #2}% + \intTabEmail=\expandafter{\the\intTabEmail \tt #3}% + }% + \addtocounter{integrantesCount}{1}% +} + +\def\director#1#2{% + \ifthenelse{\value{directoresCount} > 0}{% + \direcTabNombre=\expandafter{\the\direcTabNombre & #1}% + \direcTabEmail=\expandafter{\the\direcTabEmail & \tt #2}% + }{ + \direcTabNombre=\expandafter{\the\direcTabNombre #1}% + \direcTabEmail=\expandafter{\the\direcTabEmail \tt #2}% + }% + \addtocounter{directoresCount}{1}% +} + +% ----- Macro para generar la tabla de integrantes ------------------------- + +\newcommand{\tablaIntegrantes}{\ } + +\newcommand{\tablaIntegrantesVertical}{% +\ifthenelse{\boolean{showLU}}{% + \begin{tabular}[t]{| l @{\hspace{4ex}} c @{\hspace{4ex}} l|} + \hline + \multicolumn{1}{|c}{\rule{0pt}{1.2em} \LabelIntegrantes} & LU & \multicolumn{1}{c|}{Correo electr\'onico} \\[0.2em] + \hline \hline + \the\intlist + \hline + \end{tabular} +}{ + \begin{tabular}[t]{| l @{\hspace{4ex}} @{\hspace{4ex}} l|} + \hline + \multicolumn{1}{|c}{\rule{0pt}{1.2em} \LabelIntegrantes} & \multicolumn{1}{c|}{Correo electr\'onico} \\[0.2em] + \hline \hline + \the\intlistSinLU + \hline + \end{tabular} + }% +} + +\newcommand{\tablaIntegrantesHorizontal}{% + \begin{tabular}[t]{ *{\value{integrantesCount}}{c} } + \the\intTabNombre \\% +\ifthenelse{\boolean{showLU}}{ + \the\intTabLU \\% +}{} + \the\intTabEmail % + \end{tabular}% +} + +\newcommand{\tablaDirectores}{% +\ifthenelse{\boolean{showDirectores}}{% + \bigskip + Directores + + \smallskip + \begin{tabular}[t]{ *{\value{directoresCount}}{c} } + \the\direcTabNombre \\% + \the\direcTabEmail % + \end{tabular}% +}{}% +} + +% ----- Codigo para manejo de errores -------------------------------------- + +\def\se{\let\ifsetuperror\iftrue} +\def\ifsetuperror{% + \let\ifsetuperror\iffalse + \ifx\Materia\relax\se\errhelp={Te olvidaste de proveer una \materia{}.}\fi + \ifx\Titulo\relax\se\errhelp={Te olvidaste de proveer un \titulo{}.}\fi + \edef\mlist{\the\intlist}\ifx\mlist\empty\se% + \errhelp={Tenes que proveer al menos un \integrante{nombre}{lu}{email}.}\fi + \expandafter\ifsetuperror} + + +% ----- \maketitletxt correspondiente a la versión v0.2.1 (texto v0.2 + fecha ) --------- + +\def\maketitletxt{% + \ifsetuperror\errmessage{Faltan datos de la caratula! Ingresar 'h' para mas informacion.}\fi + \thispagestyle{empty} + \begin{center} + \vspace*{\stretch{2}} + {\LARGE\textbf{\Materia}}\\[1em] + \ifx\Submateria\relax\else{\Large \Submateria}\\[0.5em]\fi + \ifx\Fecha\relax\else{\Large \Fecha}\\[0.5em]\fi + \par\vspace{\stretch{1}} + {\large Departamento de Computaci\'on}\\[0.5em] + {\large Facultad de Ciencias Exactas y Naturales}\\[0.5em] + {\large Universidad de Buenos Aires} + \par\vspace{\stretch{3}} + {\Large \textbf{\Titulo}}\\[0.8em] + {\Large \Subtitulo} + \par\vspace{\stretch{3}} + \ifx\Grupo\relax\else\textbf{\Grupo}\par\bigskip\fi + \tablaIntegrantes + \end{center} + \vspace*{\stretch{3}} + \newpage} + +% ----- \maketitletxtlogo correspondiente v0.2.1 (texto con fecha y logo) --------- + +\def\maketitletxtlogo{% + \ifsetuperror\errmessage{Faltan datos de la caratula! Ingresar 'h' para mas informacion.}\fi + \thispagestyle{empty} + \begin{center} + \ifx\Logoimagefile\relax\else\includegraphics{\Logoimagefile}\fi \hfill \includegraphics{./figuras/logo_dc.jpg}\\[1em] + \vspace*{\stretch{2}} + {\LARGE\textbf{\Materia}}\\[1em] + \ifx\Submateria\relax\else{\Large \Submateria}\\[0.5em]\fi + \ifx\Fecha\relax\else{\large \Fecha}\\[0.5em]\fi + \par\vspace{\stretch{1}} + {\large Departamento de Computaci\'on}\\[0.5em] + {\large Facultad de Ciencias Exactas y Naturales}\\[0.5em] + {\large Universidad de Buenos Aires} + \par\vspace{\stretch{3}} + {\Large \textbf{\Titulo}}\\[0.8em] + {\Large \Subtitulo} + \par\vspace{\stretch{3}} + \ifx\Grupo\relax\else\textbf{\Grupo}\par\bigskip\fi + \tablaIntegrantes + \end{center} + \vspace*{\stretch{4}} + \newpage} + +% ----- \maketitlegraf correspondiente a la versión v0.3 (gráfica) ------------- + +\def\maketitlegraf{% + \ifsetuperror\errmessage{Faltan datos de la caratula! Ingresar 'h' para mas informacion.}\fi +% + \thispagestyle{empty} + + \ifx\Logoimagefile\relax\else\includegraphics{\Logoimagefile}\fi \hfill \includegraphics{./figuras/logo_dc.jpg} + + \vspace*{.12 \textheight} + + \noindent \textbf{\huge \Titulo} \medskip \\ + \ifx\Subtitulo\relax\else\noindent\textbf{\large \Subtitulo} \\ \fi% + \noindent \rule{\textwidth}{1 pt} + + {\noindent\large\Fecha \hspace*\fill \Materia} \\ + \ifx\Submateria\relax\else{\noindent \hspace*\fill \Submateria}\fi% + + \medskip% + \begin{center} + \ifx\Grupo\relax\else\textbf{\Grupo}\par\bigskip\fi + \tablaIntegrantes + + \tablaDirectores + \end{center}% + \vfill% + % \begin{abstract} + \small{\Resumen} + %\end{abstract} + + \begin{minipage}[t]{\textwidth} + \begin{minipage}[t]{.55 \textwidth} + \includegraphics{./figuras/logo_uba.jpg} + \end{minipage}%% + \begin{minipage}[b]{.5 \textwidth} + \textbf{\textsf{Facultad de Ciencias Exactas y Naturales}} \\ + \textsf{Universidad de Buenos Aires} \\ + {\scriptsize % + Ciudad Universitaria - (Pabell\'on I/Planta Baja) \\ + Intendente G\"uiraldes 2160 - C1428EGA \\ + Ciudad Aut\'onoma de Buenos Aires - Rep. Argentina \\ + Tel/Fax: (54 11) 4576-3359 \\ + http://www.fcen.uba.ar \\ + } + \end{minipage} + \end{minipage}% + + \newpage} + +% ----- Reemplazamos el comando \maketitle de LaTeX con el nuestro --------- +\renewcommand{\maketitle}{\maketitlegraf} + +% ----- Dependiendo de las opciones --------- +% +% opciones: +% txt : caratula solo texto. +% txtlogo : caratula txt con logo del DC y del grupo (opcional). +% graf : (default) caratula grafica con logo del DC, UBA y del grupo (opcional). +% +\@makeother\*% some package redefined it as a letter (as color.sty) +% +% Layout general de la caratula +% +\DeclareOption{txt}{\renewcommand{\maketitle}{\maketitletxt}} +\DeclareOption{txtlogo}{\renewcommand{\maketitle}{\maketitletxtlogo}} +\DeclareOption{graf}{\renewcommand{\maketitle}{\maketitlegraf}} +% +% Etiqueta Autores o Integrantes +% +\DeclareOption{integrante}{\renewcommand{\LabelIntegrantes}{Integrante}} +\DeclareOption{autor}{\renewcommand{\LabelIntegrantes}{Autor}} +% +% Formato tabla de integrantes +% +\DeclareOption{intVert}{\renewcommand{\tablaIntegrantes}{\tablaIntegrantesVertical}} +\DeclareOption{intHoriz}{\renewcommand{\tablaIntegrantes}{\tablaIntegrantesHorizontal}} +\DeclareOption{conLU}{\setboolean{showLU}{true}} +\DeclareOption{sinLU}{\setboolean{showLU}{false}} +\DeclareOption{showDirectores}{\setboolean{showDirectores}{true}} +\DeclareOption{hideDirectores}{\setboolean{showDirectores}{false}} +% +% Opciones predeterminadas +% +\ExecuteOptions{intVert}% +\ExecuteOptions{graf}% +\ExecuteOptions{integrante}% +\ExecuteOptions{conLU}% +\ExecuteOptions{hideDirectores}% +% +\ProcessOptions\relax diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/code_color.sty b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/code_color.sty new file mode 100644 index 0000000..413d147 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom 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0000000..a6c964d --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/informe.tex @@ -0,0 +1,112 @@ +%% SECCION documentclass %% +%%---------------------------------------------------------------------------%% +\documentclass{article} + +%%---------------------------------------------------------------------------%% +%% SECCION usepackage %% +%%---------------------------------------------------------------------------%% +\usepackage{amsmath, amsthm} +\usepackage[spanish,activeacute]{babel} +\usepackage{caratula} +\usepackage{a4wide} +\usepackage{hyperref} +\usepackage{fancyhdr} +% \usepackage{moreverb} +\usepackage{graphicx} % Para el logo magico! +\usepackage{capt-of} +\usepackage{afterpage} +\usepackage{float} +\usepackage{amssymb} +\usepackage{amsmath} +\usepackage[latin1]{inputenc} +\usepackage{subfigure} +\usepackage{algorithm} +\usepackage{algorithmic} +\usepackage[dvipsnames,usenames]{color} +\usepackage{amsfonts} +\usepackage{code_color} + +%%---------------------------------------------------------------------------%% +%% SECCION opciones %% +%%---------------------------------------------------------------------------%% +\parskip = 11 pt +\headheight = 13.1pt +\pagestyle {fancy} +\definecolor{orange}{rgb}{1,0.5,0} + +\addtolength{\headwidth}{1.0in} + +\addtolength{\oddsidemargin}{-0.5in} +\addtolength{\textwidth}{1.0in} +\addtolength{\topmargin}{-0.8in} +\addtolength{\textheight}{0.7in} + +%%%---------------------------------------------------------------------------%% +%%% SECCION listings %% +%%%---------------------------------------------------------------------------%% +%\usepackage{listings} +%\lstset{ +% language=C++, +% basicstyle=\ttfamily \small, +% keepspaces=true, +% flexiblecolumns=false, +% basewidth={0.5em,0.45em}, +% keywordstyle=\ttfamily \bfseries \hlkwa, +% tabsize=4 +%} + +%%---------------------------------------------------------------------------%% +%% SECCION document %% +%%---------------------------------------------------------------------------%% +\begin{document} +\renewcommand{\chaptername}{Parte } +\input{trans_algorithmic.tex} +%%---- Caratula -------------------------------------------------------------%% +\materia{Problemas, algoritmos y programación (2010)} +\titulo{Trabajo Pr'actico nº 1} + + +\integrante{Barenbaum, Pablo}{124/04}{pablo.barenbaum@gmail.com} +\integrante{Mart'inez, Federico}{17/06}{federicoemartinez@gmail.com} +\integrante{Sainz-Tr'apaga, Gonzalo}{454/06}{gonzalo@sainztrapaga.com.ar} +\grupo{Grupo 1} +\resumen{ +El siguiente informe presenta la resolución a los 4 problemas correspondientes al primer trabajo pr\'actico de la materia problemas, algoritmos y programación en el primer cuatrimestre del 2010. En el mismo se encuentra la explicación del algoritmo utilizado para resolver cada problema, así como también la implementación en C++ de los mismos. +} + +% TOC, usa estilos locos +\maketitle +\pagestyle{empty} +{ +\fancypagestyle{plain} + { + \fancyhead{} + \fancyfoot{} + \renewcommand{\headrulewidth}{0.0pt} + } % clear header and footer of plain page because of ToC +%\tableofcontents +} + +\newpage +% arreglos los estilos para el resto del documento, y +% reseteo los numeros de pagina para que queden bien +\pagenumbering{arabic} +\fancypagestyle{plain} { + \fancyhead[LO]{Barenbaum, Martínez, Sainz Trápaga} + \fancyhead[C]{} + \fancyhead[RO]{P\'agina \thepage\ de \pageref{LastPage}} + \fancyfoot{} + \renewcommand{\headrulewidth}{0.4pt} +} +\pagestyle{plain} + +\input{3nmas1} +\newpage +\input{bishops} +\newpage +\input{intervalos} +\newpage +\input{subsecuencias} +\label{LastPage} +\end{document} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/intervalos.tex b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/intervalos.tex new file mode 100644 index 0000000..d932581 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/intervalos.tex @@ -0,0 +1,187 @@ +\section{10020 - Minimal coverage} + +\textbf{Problema:} dado un conjunto de intervalos $[L_i,R_i)$, determinar +un subconjunto que cubra el segmento $[0,M)$ y que sea m\'inimo +(en el sentido de cardinalidad). En el enunciado los intervalos +se notan $[L,R]$, pero como los extremos son enteros y hay que +cubrir intervalos reales, los problemas son equivalentes. + +\subsection{Resolución} +Se resolvi\'o mediante una t\'ecnica golosa. La idea del algoritmo +es tomar en cada paso alguno de los intervalos cuyo borde izquierdo +ya se encuentre cubierto (o a lo sumo coincida con el punto m\'as chico +que todav\'ia no est\'e cubierto) y cuyo borde derecho sea lo mayor posible. + +\begin{algorithm}[H] +\begin{algorithmic} +\caption{Subconjunto de $A$ de cardinal m\'inimo que cubre a $[0,M)$} +\PARAMS{$A$: conjunto de intervalos $[L,R)$.} +\ENSURE{ $S$: un conjunto m\'inimo de intervalos de $A$ que cubren $[0,M)$.} +\STATE $A^\star :=$ intervalos no vac\'ios de $A$ ordenados crecientemente por $L$. +\STATE $final := 0$ +\STATE $S := [\,]$ +\WHILE {$final < M$} + \IF {$A^\star$ es vac\'ia $\lor$ \big($A^\star_0 = [L,R)$ con $L > final$\big)} + \STATE\COMMENT{No se puede cubrir el intervalo $[0,M)$} + \STATE Fallar. + \ELSE + \STATE $C := \{ [L,R) \gets A^\star \text{ tales que } L \leq final \}$ + \STATE\COMMENT{$C$ corresponde a un prefijo no vac\'io de $A^\star$} + \STATE $I := [L_I,R_I) \in C$ tal que $R_I = \max\{R : [L,R) \in C\}$ + \IF {$R_I \leq final$} + \STATE\COMMENT{No se puede cubrir el intervalo $[0,M)$} + \STATE Fallar. + \ENDIF + \STATE Agregar $I$ a $S$. + \STATE $A^\star := $ sufijo de $A^\star$ omitiendo los primeros $\#C$ elementos + \STATE $final := R_I$ + \ENDIF +\ENDWHILE +\end{algorithmic} +\end{algorithm} + +El algoritmo termina porque el conjunto $C$ nunca es vac\'io, y por lo tanto $A^\star$ +se va achicando. +El invariante del algoritmo es que los intervalos en $S$ cubren el +intervalo $[0,final)$. +Al entrar en una iteraci\'on, todav\'ia falta cubrir el intervalo +$[final, M)$. En la rama del {\bf then}, no se puede cubrir +$[final, M)$ y por lo tanto tampoco $[0,M)$. + +En la rama del {\bf else}, el conjunto $C$ no es vac\'io. +Corresponde a un prefijo de $A^\star$ porque los elementos de $A^\star$ +est\'an ordenados. Si hay soluci\'on, al menos un intervalo de $C$ debe +figurar en ella, porque todos los intervalos restantes de $A^\star$ no +cubren el punto $final$. Se puede encontrar una soluci\'on m\'inima +tomando $I$ como alguno de los intervalos de $C$ cuyo extremo +derecho sea mayor. +Al incluir $I$ en la soluci\'on, todos los dem\'as intervalos +de $C$ quedan cubiertos por el contenido de $S$ y por lo tanto +se pueden excluir de $A^\star$. + +Adem\'as, incluir $I$ en la soluci\'on no puede ser una mala +decisi\'on (que ``moleste'' en iteraciones posteriores), porque +el hecho de elegir un valor m\'as grande de $R_I$ hace que +en iteraciones posteriores el valor de $final$ sea mayor y +por lo tanto el conjunto $C$ incluya m\'as intervalos. + +Para una entrada de $n$ intervalos, la complejidad del algoritmo +es $O(n \log n)$ en peor caso. El paso m\'as costoso es ordenarlos. +El resto del algoritmo se reduce a +hacer una pasada sobre los intervalos ya ordenados\footnote{ +Eventualmente se podr\'ia mejorar la complejidad para que ordenarlos +fuera $O(n)$ haciendo bucket sort. El enunciado afirma que el valor +de los extremos $L_i, R_i$ es a lo sumo $50000$. Pueden ser negativos, +pero para este problema ser\'ia equivalente considerar los +intervalos $[\max(L_i,0),\max(R_i,0))$. +}. Al iterar los intervalos ordenados según su primera componente, no es +necesario construir los $C$ de forma expl\'icita. Simplemente se recorre hasta +que se obtiene el primer intervalo que cumple que $L_i > final$. El máximo +$R_i$ que actualiza a $final$ se puede obtener durante la recorrida. Luego +alcanza con seguir iterando desde donde se terminó, ya que los intervalos ya +revisados no son candidatos a tener en cuenta. Como la lista de intervalos se +recorre a lo sumo una sola vez, el ciclo itera $O(n)$ veces, +con lo cual el costo que domina es el de ordenar los intervalos. + +Las operaciones para manipular intervalos son $O(1)$ porque +los extremos se representan con enteros de 32 bits. + +En la implementaci\'on del algoritmo en C++ no se incluye el {\bf if} +cuya condici\'on es $R_I \leq final$. En ese caso, el +algoritmo falla en la siguiente iteraci\'on, porque si +$A^\star$ no es vac\'ia, el primer intervalo no puede ser +tal que $L \leq final$. + +\subsection{Implementación} + +\noindent +\ttfamily +\shorthandoff{"}\\ +\hlstd{}\hlline{\ 1\ }\hldir{\#include\ $<$stdio.h$>$}\\ +\hlline{\ 2\ }\hlstd{}\hldir{\#include\ $<$iostream$>$}\\ +\hlline{\ 3\ }\hlstd{}\hldir{\#include\ $<$list$>$}\\ +\hlline{\ 4\ }\hlstd{}\\ +\hlline{\ 5\ }\hlkwa{using\ namespace\ }\hlstd{std}\hlsym{;}\\ +\hlline{\ 6\ }\hlstd{}\\ +\hlline{\ 7\ }\hldir{\#define\ foreachin(it,s)\ for\ (typeof(s.begin())\ it\ =\ (s).begin();\ it\ !=\ (s).end();\ it++)}\\ +\hlline{\ 8\ }\hlstd{}\\ +\hlline{\ 9\ }\hlkwc{typedef\ }\hlstd{pair}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{,\ }\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$\ }\hlstd{Intervalo}\hlsym{;}\\ +\hlline{10\ }\hlstd{}\hlkwc{typedef\ }\hlstd{list}\hlsym{$<$}\hlstd{Intervalo}\hlsym{$>$\ }\hlstd{LIntervalo}\hlsym{;}\\ +\hlline{11\ }\hlstd{}\\ +\hlline{12\ }\hlkwb{bool\ }\hlstd{}\hlkwd{compararPorPrimeraComp}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ }\hlstd{Intervalo}\hlsym{\&\ }\hlstd{p1}\hlsym{,\ }\hlstd{}\hlkwb{const\ }\hlstd{Intervalo}\hlsym{\&\ }\hlstd{p2}\hlsym{)\{}\\ +\hlline{13\ }\hlstd{\ }\hlkwa{return\ }\hlstd{p1}\hlsym{.}\hlstd{first\ }\hlsym{$<$\ }\hlstd{p2}\hlsym{.}\hlstd{first}\hlsym{;}\\ +\hlline{14\ }\hlstd{}\hlsym{\}}\\ +\hlline{15\ }\hlstd{}\\ +\hlline{16\ }\hlkwb{bool\ }\hlstd{}\hlkwd{resolver}\hlstd{}\hlsym{(}\hlstd{LIntervalo}\hlsym{\&\ }\hlstd{intervalos}\hlsym{,\ }\hlstd{}\hlkwb{int\ }\hlstd{limite}\hlsym{,\ }\hlstd{LIntervalo}\hlsym{\&\ }\hlstd{solucion}\hlsym{)\ \{}\\ +\hlline{17\ }\hlstd{\ intervalos}\hlsym{.}\hlstd{}\hlkwd{sort}\hlstd{}\hlsym{(}\hlstd{compararPorPrimeraComp}\hlsym{);}\\ +\hlline{18\ }\hlstd{\ }\hlkwb{int\ }\hlstd{final\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;\ }\hlstd{}\hlslc{//\ mayor\ coordenada\ cubierta\ hasta\ ahora}\\ +\hlline{19\ }\hlstd{\ }\hlkwb{int\ }\hlstd{r\textunderscore i\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\hlstd{\ \ \ }\hlsym{}\hlstd{}\hlslc{//\ mayor\ coordenada\ hasta\ ahora\ alcanzada}\\ +\hlline{20\ }\hlstd{\ Intervalo\ parActual\ }\hlsym{=\ }\hlstd{}\hlkwd{Intervalo}\hlstd{}\hlsym{(}\hlstd{}\hlnum{0}\hlstd{}\hlsym{,\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{);\ }\hlstd{}\hlslc{//\ posible\ candidato\ a\ ser\ agregado}\\ +\hlline{21\ }\hlstd{\\ +\hlline{22\ }\ }\hlkwd{foreachin\ }\hlstd{}\hlsym{(}\hlstd{it}\hlsym{,\ }\hlstd{intervalos}\hlsym{)\ \{}\\ +\hlline{23\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlslc{//\ si\ la\ primera\ componente\ esta\ mayor\ que\ final,\ ya\ miramos}\\ +\hlline{24\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlslc{//\ todo\ el\ C,\ entonces\ hay\ que\ agregar\ el\ intervalo}\\ +\hlline{25\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{it}\hlsym{{-}$>$}\hlstd{first\ }\hlsym{$>$\ }\hlstd{final}\hlsym{)\ \{}\\ +\hlline{26\ }\hlstd{}\hlstd{\ \ \ }\hlstd{solucion}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{parActual}\hlsym{);}\\ +\hlline{27\ }\hlstd{}\hlstd{\ \ \ }\hlstd{final\ }\hlsym{=\ }\hlstd{r\textunderscore i}\hlsym{;\ }\hlstd{}\hlslc{//\ muevo\ el\ borde\ final}\\ +\hlline{28\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{29\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlslc{//\ si\ la\ primera\ componente\ es\ menor\ que\ final\ miro\ si\ el\ intervalo\ sirve}\\ +\hlline{30\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{it}\hlsym{{-}$>$}\hlstd{first\ }\hlsym{$<$=\ }\hlstd{final}\hlsym{)\ \{}\\ +\hlline{31\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlslc{//\ sirve\ si\ llega\ mas\ lejos\ que\ lo\ que\ hay\ hasta\ ahora}\\ +\hlline{32\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{it}\hlsym{{-}$>$}\hlstd{second\ }\hlsym{$>$\ }\hlstd{r\textunderscore i}\hlsym{)\ \{}\\ +\hlline{33\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{r\textunderscore i\ }\hlsym{=\ }\hlstd{it}\hlsym{{-}$>$}\hlstd{second}\hlsym{;}\\ +\hlline{34\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{parActual\ }\hlsym{=\ {*}}\hlstd{it}\hlsym{;}\\ +\hlline{35\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlslc{//\ si\ ademas\ ya\ llegue\ al\ limite,\ termine}\\ +\hlline{36\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{r\textunderscore i\ }\hlsym{$>$=\ }\hlstd{limite}\hlsym{)\ \{}\\ +\hlline{37\ }\hlstd{}\hlstd{\ \ \ \ \ }\hlstd{solucion}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{parActual}\hlsym{);}\\ +\hlline{38\ }\hlstd{}\hlstd{\ \ \ \ \ }\hlstd{}\hlkwa{break}\hlstd{}\hlsym{;}\\ +\hlline{39\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}\ }\\ +\hlline{40\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{41\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}\ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{42\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlslc{//\ hay\ un\ hueco\ que\ no\ puedo\ cubrir\ con\ ningun\ intervalo}\\ +\hlline{43\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwa{break}\hlstd{}\hlsym{;}\\ +\hlline{44\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{45\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{46\ }\hlstd{\\ +\hlline{47\ }\ }\hlkwa{return\ }\hlstd{r\textunderscore i\ }\hlsym{$>$=\ }\hlstd{limite}\hlsym{;}\\ +\hlline{48\ }\hlstd{}\hlsym{\}}\\ +\hlline{49\ }\hlstd{}\\ +\hlline{50\ }\hlkwb{int\ }\hlstd{}\hlkwd{main}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{int\ }\hlstd{argc}\hlsym{,\ }\hlstd{}\hlkwb{char\ }\hlstd{}\hlsym{{*}{*}}\hlstd{argv}\hlsym{)}\\ +\hlline{51\ }\hlstd{}\hlsym{\{}\\ +\hlline{52\ }\hlstd{\ }\hlkwb{int\ }\hlstd{casos}\hlsym{;}\\ +\hlline{53\ }\hlstd{\ cin\ }\hlsym{$>$$>$\ }\hlstd{casos}\hlsym{;}\\ +\hlline{54\ }\hlstd{\ }\hlkwa{while\ }\hlstd{}\hlsym{(}\hlstd{casos\ }\hlsym{$>$\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ \{}\\ +\hlline{55\ }\hlstd{}\hlstd{\ \ }\hlstd{casos}\hlsym{{-}{-};}\\ +\hlline{56\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwb{int\ }\hlstd{limite}\hlsym{,\ }\hlstd{x}\hlsym{,\ }\hlstd{y}\hlsym{;}\\ +\hlline{57\ }\hlstd{}\hlstd{\ \ }\hlstd{cin\ }\hlsym{$>$$>$\ }\hlstd{limite}\hlsym{;}\\ +\hlline{58\ }\hlstd{}\hlstd{\ \ }\hlstd{x\ }\hlsym{=\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{59\ }\hlstd{}\hlstd{\ \ }\hlstd{y\ }\hlsym{=\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{60\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlslc{//\ cargo\ intervalos}\\ +\hlline{61\ }\hlstd{}\hlstd{\ \ }\hlstd{LIntervalo\ intervalos}\hlsym{;}\\ +\hlline{62\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{while\ }\hlstd{}\hlsym{(}\hlstd{y\ }\hlsym{!=\ }\hlstd{}\hlnum{0\ }\hlstd{}\hlsym{\textbar \textbar \ }\hlstd{x\ }\hlsym{!=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ \{}\\ +\hlline{63\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwd{scanf\ }\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%d\ \%d"}\hlstd{}\hlsym{,\ \&}\hlstd{x}\hlsym{,\ \&}\hlstd{y}\hlsym{);}\\ +\hlline{64\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{x\ }\hlsym{!=\ }\hlstd{}\hlnum{0\ }\hlstd{}\hlsym{\textbar \textbar \ }\hlstd{y\ }\hlsym{!=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ \{}\\ +\hlline{65\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{x\ }\hlsym{$<$\ }\hlstd{y}\hlsym{)\ \{\ }\hlstd{}\hlslc{//para\ no\ cargar\ intervalos\ inutiles}\\ +\hlline{66\ }\hlstd{}\hlstd{\ \ \ \ \ }\hlstd{intervalos}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore front}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{Intervalo}\hlstd{}\hlsym{(}\hlstd{x}\hlsym{,}\hlstd{y}\hlsym{));}\\ +\hlline{67\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{68\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{69\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{70\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlslc{//\ resuelvo\ instancia}\\ +\hlline{71\ }\hlstd{}\hlstd{\ \ }\hlstd{LIntervalo\ solucion}\hlsym{;}\\ +\hlline{72\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwd{resolver}\hlstd{}\hlsym{(}\hlstd{intervalos}\hlsym{,\ }\hlstd{limite}\hlsym{,\ }\hlstd{solucion}\hlsym{))\ \{}\\ +\hlline{73\ }\hlstd{}\hlstd{\ \ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{solucion}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{()\ $<$$<$\ }\hlstd{endl}\hlsym{;}\\ +\hlline{74\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwd{foreachin\ }\hlstd{}\hlsym{(}\hlstd{it}\hlsym{,\ }\hlstd{solucion}\hlsym{)\ \{}\\ +\hlline{75\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{it}\hlsym{{-}$>$}\hlstd{first\ }\hlsym{$<$$<$\ }\hlstd{}\hlstr{"\ "}\hlstd{\ }\hlsym{$<$$<$\ }\hlstd{it}\hlsym{{-}$>$}\hlstd{second\ }\hlsym{$<$$<$\ }\hlstd{endl}\hlsym{;}\\ +\hlline{76\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{77\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}\ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{78\ }\hlstd{}\hlstd{\ \ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{}\hlnum{0\ }\hlstd{}\hlsym{$<$$<$\ }\hlstd{endl}\hlsym{;}\\ +\hlline{79\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{80\ }\hlstd{}\hlstd{\ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{endl}\hlsym{;}\\ +\hlline{81\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{82\ }\hlstd{}\hlsym{\}}\\ +\hlline{83\ }\hlstd{}\\ +\mbox{} +\normalfont +\shorthandon{"} + + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/main.tex b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/main.tex new file mode 100644 index 0000000..ad4899b --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/main.tex @@ -0,0 +1,165 @@ +\documentclass[10pt,a4paper,notitlepage]{article} +\usepackage[spanish]{babel} +\usepackage{amsmath,amssymb} +\usepackage{algorithmic} + +\begin{document} + +\section{100 - The $3n + 1$ problem} + +\section{861 - Little bishops} + +\section{10020 - Minimal coverage} + +Problema: dado un conjunto de intervalos $[L_i,R_i)$, determinar +un subconjunto que cubra el segmento $[0,M)$ y que sea m\'inimo +(en el sentido de cardinalidad). En el enunciado los intervalos +se notan $[L,R]$, pero como los extremos son enteros y hay que +cubrir intervalos reales, los problemas son equivalentes. + +Se resolvi\'o mediante una t\'ecnica golosa. La idea del algoritmo +es tomar en cada paso alguno de los intervalos cuyo borde izquierdo +ya se encuentre cubierto (o a lo sumo coincida con el punto m\'as chico +que todav\'ia no est\'e cubierto) y cuyo borde derecho sea lo mayor posible. + +\vspace{10pt} +\begin{algorithmic} +\STATE Entrada: $A$: conjunto de intervalos $[L,R)$. +\STATE Salida: $S$: un conjunto m\'inimo de intervalos de $A$ que cubren $[0,M)$. +\STATE $A^\star :=$ intervalos no vac\'ios de $A$ ordenados crecientemente por $L$. +\STATE $final := 0$ +\STATE $S := [\,]$ +\WHILE {$final < M$} + \IF {$A^\star$ es vac\'ia $\lor$ \big($A^\star_0 = [L,R)$ con $L > final$\big)} + \STATE --- No se puede cubrir el intervalo $[0,M)$ --- + \STATE Fallar. + \ELSE + \STATE $C := \{ [L,R) \gets A^\star \text{ tales que } L \leq final \}$ + \STATE --- $C$ corresponde a un prefijo no vac\'io de $A^\star$ --- + \STATE $I := [L_I,R_I) \in C$ tal que $R_I = \max\{R : [L,R) \in C\}$ + \IF {$R_I \leq final$} + \STATE --- No se puede cubrir el intervalo $[0,M)$ --- + \STATE Fallar. + \ENDIF + \STATE Agregar $I$ a $S$. + \STATE $A^\star := $ sufijo de $A^\star$ omitiendo los primeros $\#C$ elementos + \STATE $final := R_I$ + \ENDIF +\ENDWHILE +\end{algorithmic} +\vspace{10pt} + +El algoritmo termina porque en la rama del {\bf else} +el conjunto $C$ nunca es vac\'io, y por lo tanto $A^\star$ +se va achicando. + +El invariante del algoritmo es que los intervalos en $S$ cubren el +intervalo $[0,final)$. +Al entrar en una iteraci\'on, todav\'ia falta cubrir el intervalo +$[final, M)$. En la rama del {\bf then}, no se puede cubrir +$[final, M)$ y por lo tanto tampoco $[0,M)$. + +En la rama del {\bf else}, es claro que el conjunto $C$ no es vac\'io. +Corresponde a un prefijo de $A^\star$ porque los elementos de $A^\star$ +est\'an ordenados. Si hay soluci\'on, al menos un intervalo de $C$ debe +figurar en ella, porque todos los intervalos restantes de $A^\star$ no +cubren el punto $final$. Se puede encontrar una soluci\'on m\'inima +tomando $I$ como alguno de los intervalos de $C$ cuyo extremo +derecho sea mayor. +Al incluir $I$ en la soluci\'on, todos los dem\'as intervalos +de $C$ quedan cubiertos por el contenido de $S$ y por lo tanto +se pueden excluir de $A^\star$. + +Adem\'as, incluir $I$ en la soluci\'on no puede ser una mala +decisi\'on (que ``moleste'' en iteraciones posteriores), porque +el hecho de elegir un valor m\'as grande de $R_I$ hace que +en iteraciones posteriores el valor de $final$ sea mayor y +por lo tanto el conjunto $C$ incluya m\'as intervalos. + +Para una entrada de $n$ intervalos, la complejidad del algoritmo +es $O(n \log n)$ en peor caso. El paso m\'as costoso es ordenarlos. +Es claro que el resto del algoritmo se reduce a +hacer una pasada sobre los intervalos ya ordenados\footnote{ +Se podr\'ia mejorar la complejidad para que ordenarlos +fuera $O(n)$ haciendo bucket sort. El enunciado afirma que el valor +de los extremos $L_i, R_i$ es a lo sumo $50000$. Pueden ser negativos, +pero para este problema ser\'ia equivalente considerar los +intervalos $[\max(L_i,0),\max(R_i,0))$. +}. +Las operaciones para manipular intervalos son $O(1)$ porque +los extremos se representan con enteros de 32 bits. + +En la implementaci\'on del algoritmo en C++ no se incluye el {\bf if} +cuya condici\'on es $R_I \leq final$. En ese caso, el +algoritmo falla en la siguiente iteraci\'on, porque si +$A^\star$ no es vac\'ia, el primer intervalo no puede ser +tal que $L \leq final$. + +\section{10069 - Distinct subsequences} + +Problema: dadas dos strings $x = x_0 \hdots x_n$ y $z = z_0 \hdots z_m$, +determinar la cantidad de ocurrencias distintas de $z$ como subsecuencia de $x$. +(Dos ocurrencias son distintas si les corresponden distintas secuencias +de \'indices). + +Se resolvi\'o mediante un algoritmo de programaci\'on din\'amica. +Se define la siguiente funci\'on $M(i,j)$ para $i \in [0,n]$, $j \in [0,m]$: +$$M(i,j) = \text{cantidad de ocurrencias de $z[0..j)$ como subsecuencia de $x[0..i)$}$$ + +\noindent +Definida concretamente por las siguientes ecuaciones: + +\vspace{10pt} +\begin{tabular}{ll} +$M(i,0) = 1$ &\vspace{5pt}\\ +$M(0,j) = 0$ \text{ (para $j > 0$)}&\vspace{5pt}\\ +$M(i,j) = M(i - 1, j) + \begin{cases} +M(i - 1, j - 1) & \text{ si $x_{i - 1}$ = $z_{j - 1}$ }\\ +0 & \text{ si no} +\end{cases}$ +& (para $i, j > 0$) +\end{tabular} +\vspace{10pt} + +La primera ecuaci\'on afirma que la cadena vac\'ia ocurre una vez en cualquier otra cadena +(la secuencia de \'indices de la cadena vac\'ia es una secuencia vac\'ia). +La segunda ecuaci\'on afirma que cualquier cadena no vac\'ia no ocurre en la cadena vac\'ia. +En la tercera ecuaci\'on se afirma que: +\begin{itemize} +\item Todas las ocurrencias de $z[0..j)$ en $x[0..i-1)$ + son ocurrencias de $z[0..j)$ en $x[0..i)$. +\item Adem\'as, si $x_{i - 1} = z_{j - 1}$, cada una de las ocurrencias de + $z[0..j-1)$ en $x[0..i-1)$ tiene asociada una ocurrencia de + $z[0..j)$ en $x[0..i)$. +\item Es claro que no puede haber otras ocurrencias de $z[0..j)$ en $x[0..i)$ + y que los dos tipos de ocurrencias descriptos son disjuntos, + de modo que alcanza con sumarlos. +\end{itemize} + +El algoritmo se implementa computando la matriz de la funci\'on $M$, +visitando una vez cada posici\'on de la matriz. S\'olo se necesita el +resultado, $M(n,m) = $ cantidad de ocurrencias de $z$ en $x$. Alcanza +con mantener en memoria s\'olo las dos \'ultimas columnas de $M(i,j)$. +La complejidad temporal es $O(n \cdot m)$ en peor caso. + +\subsection{Aritm\'etica de n\'umeros grandes} + +El enunciado afirma que $|x| \leq 10000$, $|z| \leq 100$ y que la cantidad de +ocurrencias de $z$ en $x$ es a lo sumo $10^{100}$, que obviamente no cabe en registros +de 64 bits. Adem\'as, la afirmaci\'on no es espuria porque {\em pueden} darse +situaciones en las que el n\'umero de ocurrencias sea mucho mayor que $10^{100}$. +Por ejemplo, tomando $x = a^{10000}$ y $z = a^{100}$, hay +$10000 \choose 100$ ocurrencias de $z$ en $x$. + +La \'unica operaci\'on requerida por el algoritmo es la suma de n\'umeros +grandes. Se program\'o una clase \texttt{BigInt} que representa +un n\'umero natural con un vector de 16 d\'igitos en base +$10^8$. Esto permite representar enteros en $[0,10^{128})$ +e imprimir la salida en base 10 sin recurrir a divisiones. + +La suma de n\'umeros grandes es $O(1)$ porque est\'an representados +con un arreglo que siempre tiene exactamente 16 d\'igitos. La +implementaci\'on de la suma con carry es la usual. + +\end{document} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/subsecuencias.tex b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/subsecuencias.tex new file mode 100644 index 0000000..f03ea89 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/subsecuencias.tex @@ -0,0 +1,237 @@ +\section{10069 - Distinct subsequences} + +\textbf{Problema:} dadas dos strings $x = x_0 \hdots x_n$ y $z = z_0 \hdots z_m$, +determinar la cantidad de ocurrencias distintas de $z$ como subsecuencia de $x$. +(Dos ocurrencias son distintas si les corresponden distintas secuencias +de \'indices). + +\subsection{Resolución} + +Se resolvi\'o mediante un algoritmo de programaci\'on din\'amica. +Se define la siguiente funci\'on $M(i,j)$ para $i \in [0,n]$, $j \in [0,m]$: +$$M(i,j) = \text{cantidad de ocurrencias de $z[0..j)$ como subsecuencia de $x[0..i)$}$$ + +\noindent +Definida concretamente por las siguientes ecuaciones: + +\vspace{10pt} +\begin{tabular}{ll} +$M(i,0) = 1$ &\vspace{5pt}\\ +$M(0,j) = 0$ \text{ (para $j > 0$)}&\vspace{5pt}\\ +$M(i,j) = M(i - 1, j) + \begin{cases} +M(i - 1, j - 1) & \text{ si $x_{i - 1}$ = $z_{j - 1}$ }\\ +0 & \text{ si no} +\end{cases}$ +& (para $i, j > 0$) +\end{tabular} +\vspace{10pt} + +La primera ecuaci\'on afirma que la cadena vac\'ia ocurre una vez en cualquier otra cadena +(la secuencia de \'indices de la cadena vac\'ia es una secuencia vac\'ia). +La segunda ecuaci\'on afirma que cualquier cadena no vac\'ia no ocurre en la cadena vac\'ia. +En la tercera ecuaci\'on se afirma que: +\begin{itemize} +\item Todas las ocurrencias de $z[0..j)$ en $x[0..i-1)$ + son ocurrencias de $z[0..j)$ en $x[0..i)$. + +\item Adem\'as, si $x_{i - 1} = z_{j - 1}$, cada una de las ocurrencias de + $z' = z[0..j-1)$ en $x' = x[0..i-1)$ tiene asociada una ocurrencia de + $z'' = z[0..j)$ en $x'' = x[0..i)$. Esto es porque si $z'$ ocurre en $x'$ + con la secuencia de \'indices $\langle p_1, \hdots, p_{j-1} \rangle$, entonces + $z''$ ocurre en $x''$ con la secuencia de \'indices $\langle p_1, \hdots, p_{j-1}, i - 1 \rangle$. + +\item No puede haber otras ocurrencias de $z[0..j)$ en $x[0..i)$ + (por simple an\'alisis de casos) + y adem\'as los dos tipos de ocurrencias descriptos son disjuntos + (porque en el primer caso la secuencia de \'indices nunca termina en $i - 1$). + Por lo tanto, la cantidad total de ocurrencias es la suma de estos + dos tipos de ocurrencias. +\end{itemize} + +El algoritmo se implementa computando la matriz de la funci\'on $M$, +visitando una vez cada posici\'on de la matriz. S\'olo se necesita el +resultado, $M(n,m) = $ cantidad de ocurrencias de $z$ en $x$. Alcanza +con mantener en memoria s\'olo las dos \'ultimas columnas de $M(i,j)$. + +\begin{algorithm}[H] +\begin{algorithmic} +\caption{Cantidad de ocurrencias de $z$ como subsecuencia de $x$} +\PARAMS{$z$: string cuyas ocurrencias se quieren contar, $x$: string donde se buscan las ocurrencias de $z$} +\STATE $M :=$ matriz de 2 filas por $largo(z) + 1$ columnas%%, tal que $m_{i,j}=0$ +\STATE $M_{i,0} := 1$ para $i \in \{1,2\}$ +\STATE $M_{0,j} := 0$ para $j > 0$ +\STATE $fila actual := 1$ +\STATE $otra fila := 0$ +\FOR{cada $i$ en $[1,largo(x)]$} + \FOR{cada $j$ en $[1,largo(z)]$} + \IF{$x_{i-1}$ es igual a $z_{j-1}$} + \STATE $M_{filaactual, j} = M_{otrafila, j} + M_{otrafila, j-1}$ + \ELSE + \STATE $M_{filaactual, j} = M_{otrafila, j}$ + \ENDIF + \ENDFOR + \STATE intercambiar $fila actual$ y $otra fila$ +\ENDFOR +\RETURN $M_{otra fila, largo(z)}$ +\end{algorithmic} +\end{algorithm} + +Como vemos a partir del pseudoc\'odigo, si $largo(x)=n$ y $largo(z)=m$, la +complejidad temporal es $O(n \cdot m)$ en peor caso, y es el costo del llenado +de la matriz. La memoria usada son las dos filas de la matriz, es decir $O(m)$. + +\subsubsection{Aritm\'etica de n\'umeros grandes} + +El enunciado afirma que $|x| \leq 10000$, $|z| \leq 100$ y que la cantidad de +ocurrencias de $z$ en $x$ es a lo sumo $10^{100}$, que obviamente no cabe en registros +de 64 bits. Adem\'as, la afirmaci\'on no es irrelevante porque {\em pueden} darse +situaciones en las que el n\'umero de ocurrencias sea mucho mayor que $10^{100}$. +Por ejemplo, tomando $x = a^{10000}$ y $z = a^{100}$, hay +$10000 \choose 100$ ocurrencias de $z$ en $x$. + +La \'unica operaci\'on requerida por el algoritmo es la suma de n\'umeros +grandes. Se program\'o una clase \texttt{BigInt} que representa +un n\'umero natural con un vector de 16 d\'igitos en base +$10^8$. Esto permite representar enteros en $[0,10^{128})$ +e imprimir la salida en base 10 sin recurrir a divisiones. + +La suma de n\'umeros grandes es $O(1)$ porque est\'an representados +con un arreglo que siempre tiene exactamente 16 d\'igitos. La +implementaci\'on de la suma con carry es la usual. + +\subsection{Implementación} +\noindent +\ttfamily +\shorthandoff{"}\\ +\hlstd{}\hlline{\ 1\ }\hldir{\#include\ $<$vector$>$}\\ +\hlline{\ 2\ }\hlstd{}\hldir{\#include\ $<$string$>$}\\ +\hlline{\ 3\ }\hlstd{}\hldir{\#include\ $<$iostream$>$}\\ +\hlline{\ 4\ }\hlstd{}\hldir{\#include\ $<$cassert$>$}\\ +\hlline{\ 5\ }\hlstd{}\hldir{\#include\ $<$cstdio$>$}\\ +\hlline{\ 6\ }\hlstd{}\\ +\hlline{\ 7\ }\hlkwa{using\ namespace\ }\hlstd{std}\hlsym{;}\\ +\hlline{\ 8\ }\hlstd{}\\ +\hlline{\ 9\ }\hlkwc{typedef\ }\hlstd{}\hlkwb{unsigned\ int\ }\hlstd{uint32}\hlsym{;}\\ +\hlline{10\ }\hlstd{}\\ +\hlline{11\ }\hldir{\#define\ forsn(i,\ s,\ n)\ for\ (uint32\ i\ =\ (s);\ i\ $<$\ (n);\ i++)}\\ +\hlline{12\ }\hlstd{}\hldir{\#define\ forn(i,\ n)\ forsn\ (i,\ 0,\ n)}\\ +\hlline{13\ }\hlstd{}\hldir{\#define\ dforn(i,\ n)\ for\ (uint32\ i\ =\ (n);\ i{-}{-}\ $>$\ 0;)}\\ +\hlline{14\ }\hlstd{}\\ +\hlline{15\ }\hlslc{//\ BigInt}\\ +\hlline{16\ }\hlstd{}\hlslc{//\ Represents\ a\ number\ in\ 0\ $<$=\ n\ $<$\ 10\ {*}{*}\ 128}\\ +\hlline{17\ }\hlstd{}\\ +\hlline{18\ }\hldir{\#define\ BigInt\textunderscore NDIGITS\ 16}\\ +\hlline{19\ }\hlstd{}\hldir{\#define\ BigInt\textunderscore BASE\ 100000000}\\ +\hlline{20\ }\hlstd{}\hlkwc{class\ }\hlstd{BigInt\ }\hlsym{\{}\\ +\hlline{21\ }\hlstd{}\hlkwc{public}\hlstd{}\hlsym{:}\\ +\hlline{22\ }\hlstd{\ }\hlkwd{BigInt}\hlstd{}\hlsym{()\ :\ }\hlstd{}\hlkwd{\textunderscore digits}\hlstd{}\hlsym{(}\hlstd{BigInt\textunderscore NDIGITS}\hlsym{,\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ \{\}}\\ +\hlline{23\ }\hlstd{\\ +\hlline{24\ }\ }\hlkwd{BigInt}\hlstd{}\hlsym{(}\hlstd{uint32\ n}\hlsym{)\ :\ }\hlstd{}\hlkwd{\textunderscore digits}\hlstd{}\hlsym{(}\hlstd{BigInt\textunderscore NDIGITS}\hlsym{,\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ \{}\\ +\hlline{25\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{assert}\hlstd{}\hlsym{(}\hlstd{n\ }\hlsym{$<$\ }\hlstd{BigInt\textunderscore BASE}\hlsym{);}\\ +\hlline{26\ }\hlstd{}\hlstd{\ \ }\hlstd{\textunderscore digits}\hlsym{{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}\ =\ }\hlstd{n}\hlsym{;}\\ +\hlline{27\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{28\ }\hlstd{\\ +\hlline{29\ }\ }\hlslc{//\ For\ testing}\\ +\hlline{30\ }\hlstd{\ }\hlkwd{BigInt}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ }\hlstd{string}\hlsym{\&\ }\hlstd{s}\hlsym{)\ :\ }\hlstd{}\hlkwd{\textunderscore digits}\hlstd{}\hlsym{(}\hlstd{BigInt\textunderscore NDIGITS}\hlsym{,\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ \{}\\ +\hlline{31\ }\hlstd{}\hlstd{\ \ }\hlstd{uint32\ pow\ }\hlsym{=\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{32\ }\hlstd{}\hlstd{\ \ }\hlstd{uint32\ digit\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{33\ }\hlstd{}\hlstd{\ \ }\hlstd{uint32\ j\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{34\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{dforn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{s}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{())\ \{}\\ +\hlline{35\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwd{assert}\hlstd{}\hlsym{(}\hlstd{}\hlstr{'0´}\hlstd{\ }\hlsym{$<$=\ }\hlstd{s}\hlsym{{[}}\hlstd{i}\hlsym{{]}\ \&\&\ }\hlstd{s}\hlsym{{[}}\hlstd{i}\hlsym{{]}\ $<$=\ }\hlstd{}\hlstr{`9´}\hlstd{}\hlsym{);}\\ +\hlline{36\ }\hlstd{}\hlstd{\ \ \ }\hlstd{digit\ }\hlsym{+=\ }\hlstd{pow\ }\hlsym{{*}\ (}\hlstd{s}\hlsym{{[}}\hlstd{i}\hlsym{{]}\ {-}\ }\hlstd{}\hlstr{'0´}\hlstd{}\hlsym{);}\\ +\hlline{37\ }\hlstd{\\ +\hlline{38\ }}\hlstd{\ \ \ }\hlstd{pow\ }\hlsym{{*}=\ }\hlstd{}\hlnum{10}\hlstd{}\hlsym{;}\\ +\hlline{39\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{pow\ }\hlsym{==\ }\hlstd{BigInt\textunderscore BASE}\hlsym{)\ \{}\\ +\hlline{40\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{\textunderscore digits}\hlsym{{[}}\hlstd{j}\hlsym{++{]}\ =\ }\hlstd{digit}\hlsym{;}\\ +\hlline{41\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{digit\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{42\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{pow\ }\hlsym{=\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{43\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{44\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{45\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{assert}\hlstd{}\hlsym{(}\hlstd{j\ }\hlsym{$<$\ }\hlstd{BigInt\textunderscore NDIGITS\ }\hlsym{\textbar \textbar \ }\hlstd{digit\ }\hlsym{==\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{);}\\ +\hlline{46\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{j\ }\hlsym{$<$\ }\hlstd{BigInt\textunderscore NDIGITS}\hlsym{)\ \{}\\ +\hlline{47\ }\hlstd{}\hlstd{\ \ \ }\hlstd{\textunderscore digits}\hlsym{{[}}\hlstd{j}\hlsym{{]}\ =\ }\hlstd{digit}\hlsym{;}\\ +\hlline{48\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{49\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{50\ }\hlstd{\\ +\hlline{51\ }\ BigInt\ }\hlkwc{operator}\hlstd{}\hlsym{+(}\hlstd{}\hlkwb{const\ }\hlstd{BigInt}\hlsym{\&\ }\hlstd{n}\hlsym{)\ \{}\\ +\hlline{52\ }\hlstd{}\hlstd{\ \ }\hlstd{BigInt\ res}\hlsym{;}\\ +\hlline{53\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwb{bool\ }\hlstd{carry\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{54\ }\hlstd{\\ +\hlline{55\ }}\hlstd{\ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{BigInt\textunderscore NDIGITS}\hlsym{)\ \{}\\ +\hlline{56\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwb{const\ }\hlstd{uint32\ r\ }\hlsym{=\ }\hlstd{\textunderscore digits}\hlsym{{[}}\hlstd{i}\hlsym{{]}\ +\ }\hlstd{n}\hlsym{.}\hlstd{\textunderscore digits}\hlsym{{[}}\hlstd{i}\hlsym{{]}\ +\ }\hlstd{carry}\hlsym{;}\\ +\hlline{57\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{r\ }\hlsym{$>$=\ }\hlstd{BigInt\textunderscore BASE}\hlsym{)\ \{}\\ +\hlline{58\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{res}\hlsym{.}\hlstd{\textunderscore digits}\hlsym{{[}}\hlstd{i}\hlsym{{]}\ =\ }\hlstd{r\ }\hlsym{\%\ }\hlstd{BigInt\textunderscore BASE}\hlsym{;}\\ +\hlline{59\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{carry\ }\hlsym{=\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{60\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}\ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{61\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{res}\hlsym{.}\hlstd{\textunderscore digits}\hlsym{{[}}\hlstd{i}\hlsym{{]}\ =\ }\hlstd{r}\hlsym{;}\\ +\hlline{62\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{carry\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{63\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{64\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{65\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{assert}\hlstd{}\hlsym{(}\hlstd{carry\ }\hlsym{==\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{);}\\ +\hlline{66\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{return\ }\hlstd{res}\hlsym{;}\\ +\hlline{67\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{68\ }\hlstd{\\ +\hlline{69\ }\ }\hlkwb{void\ }\hlstd{}\hlkwd{print}\hlstd{}\hlsym{()\ \{}\\ +\hlline{70\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwb{bool\ }\hlstd{zero\ }\hlsym{=\ }\hlstd{}\hlkwa{true}\hlstd{}\hlsym{;\ }\\ +\hlline{71\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{dforn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{BigInt\textunderscore NDIGITS}\hlsym{)\ \{}\\ +\hlline{72\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{zero}\hlsym{)\ \{}\\ +\hlline{73\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{\textunderscore digits}\hlsym{{[}}\hlstd{i}\hlsym{{]}\ ==\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ }\hlstd{}\hlkwa{continue}\hlstd{}\hlsym{;}\\ +\hlline{74\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{printf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%u"}\hlstd{}\hlsym{,\ }\hlstd{\textunderscore digits}\hlsym{{[}}\hlstd{i}\hlsym{{]});}\\ +\hlline{75\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{zero\ }\hlsym{=\ }\hlstd{}\hlkwa{false}\hlstd{}\hlsym{;}\\ +\hlline{76\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}\ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{77\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{printf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%.8u"}\hlstd{}\hlsym{,\ }\hlstd{\textunderscore digits}\hlsym{{[}}\hlstd{i}\hlsym{{]});}\\ +\hlline{78\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{79\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{80\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{zero}\hlsym{)\ \{}\\ +\hlline{81\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwd{printf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"0"}\hlstd{}\hlsym{);}\\ +\hlline{82\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{83\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{84\ }\hlstd{}\\ +\hlline{85\ }\hlkwc{private}\hlstd{}\hlsym{:}\\ +\hlline{86\ }\hlstd{\ }\hlslc{//\ Least\ significant\ digit\ first.}\\ +\hlline{87\ }\hlstd{\ }\hlslc{//\ Digits\ are\ in\ 0\ $<$=\ d\ $<$\ BigInt\textunderscore BASE}\\ +\hlline{88\ }\hlstd{\ vector}\hlsym{$<$}\hlstd{uint32}\hlsym{$>$\ }\hlstd{\textunderscore digits}\hlsym{;}\\ +\hlline{89\ }\hlstd{}\hlsym{\};}\\ +\hlline{90\ }\hlstd{}\\ +\hlline{91\ }\hldir{\#define\ print\textunderscore bigint(x)\ (x).print()}\\ +\hlline{92\ }\hlstd{}\\ +\hlline{93\ }\hlkwc{typedef\ }\hlstd{vector}\hlsym{$<$}\hlstd{BigInt}\hlsym{$>$\ }\hlstd{vBigInt}\hlsym{;}\\ +\hlline{94\ }\hlstd{}\hlkwc{typedef\ }\hlstd{vector}\hlsym{$<$}\hlstd{vBigInt}\hlsym{$>$\ }\hlstd{vvBigInt}\hlsym{;}\\ +\hlline{95\ }\hlstd{BigInt\ }\hlkwd{distinct\textunderscore subsequences}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ }\hlstd{string}\hlsym{\&\ }\hlstd{x}\hlsym{,\ }\hlstd{}\hlkwb{const\ }\hlstd{string}\hlsym{\&\ }\hlstd{z}\hlsym{)\ \{}\\ +\hlline{96\ }\hlstd{\ vvBigInt\ }\hlkwd{m}\hlstd{}\hlsym{(}\hlstd{}\hlnum{2}\hlstd{}\hlsym{,\ }\hlstd{}\hlkwd{vBigInt}\hlstd{}\hlsym{(}\hlstd{z}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{()\ +\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{,\ }\hlstd{}\hlkwd{BigInt}\hlstd{}\hlsym{(}\hlstd{}\hlnum{0}\hlstd{}\hlsym{)));}\\ +\hlline{97\ }\hlstd{\\ +\hlline{98\ }\ m}\hlsym{{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}\ =\ }\hlstd{}\hlkwd{BigInt}\hlstd{}\hlsym{(}\hlstd{}\hlnum{1}\hlstd{}\hlsym{);}\\ +\hlline{99\ }\hlstd{\ m}\hlsym{{[}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]}{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}\ =\ }\hlstd{}\hlkwd{BigInt}\hlstd{}\hlsym{(}\hlstd{}\hlnum{1}\hlstd{}\hlsym{);}\\ +\hlline{100\ }\hlstd{\ }\hlkwb{bool\ }\hlstd{row\ }\hlsym{=\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{101\ }\hlstd{\ }\hlkwd{forsn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{,\ }\hlstd{x}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{()\ +\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ \{}\\ +\hlline{102\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{forsn\ }\hlstd{}\hlsym{(}\hlstd{j}\hlsym{,\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{,\ }\hlstd{z}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{()\ +\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ \{}\\ +\hlline{103\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{x}\hlsym{{[}}\hlstd{i\ }\hlsym{{-}\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]}\ ==\ }\hlstd{z}\hlsym{{[}}\hlstd{j\ }\hlsym{{-}\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]})\ \{}\\ +\hlline{104\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{m}\hlsym{{[}}\hlstd{row}\hlsym{{]}{[}}\hlstd{j}\hlsym{{]}\ =\ }\hlstd{m}\hlsym{{[}!}\hlstd{row}\hlsym{{]}{[}}\hlstd{j}\hlsym{{]}\ +\ }\hlstd{m}\hlsym{{[}!}\hlstd{row}\hlsym{{]}{[}}\hlstd{j\ }\hlsym{{-}\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]};}\\ +\hlline{105\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}\ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{106\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{m}\hlsym{{[}}\hlstd{row}\hlsym{{]}{[}}\hlstd{j}\hlsym{{]}\ =\ }\hlstd{m}\hlsym{{[}!}\hlstd{row}\hlsym{{]}{[}}\hlstd{j}\hlsym{{]};}\\ +\hlline{107\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{108\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{109\ }\hlstd{}\hlstd{\ \ }\hlstd{row\ }\hlsym{=\ !}\hlstd{row}\hlsym{;}\\ +\hlline{110\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{111\ }\hlstd{\ }\hlkwa{return\ }\hlstd{m}\hlsym{{[}!}\hlstd{row}\hlsym{{]}{[}}\hlstd{z}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{(){]};}\\ +\hlline{112\ }\hlstd{}\hlsym{\}}\\ +\hlline{113\ }\hlstd{}\\ +\hlline{114\ }\hlkwb{int\ }\hlstd{}\hlkwd{main}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{int\ }\hlstd{argc}\hlsym{,\ }\hlstd{}\hlkwb{char\ }\hlstd{}\hlsym{{*}{*}}\hlstd{argv}\hlsym{)\ \{}\\ +\hlline{115\ }\hlstd{\ uint32\ n}\hlsym{;}\\ +\hlline{116\ }\hlstd{\ cin\ }\hlsym{$>$$>$\ }\hlstd{n}\hlsym{;}\\ +\hlline{117\ }\hlstd{\ }\hlkwb{char\ }\hlstd{c}\hlsym{;}\\ +\hlline{118\ }\hlstd{\ cin}\hlsym{.}\hlstd{}\hlkwd{get}\hlstd{}\hlsym{(}\hlstd{c}\hlsym{);}\\ +\hlline{119\ }\hlstd{\ }\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{n}\hlsym{)\ \{}\\ +\hlline{120\ }\hlstd{}\hlstd{\ \ }\hlstd{string\ x}\hlsym{,\ }\hlstd{z}\hlsym{;}\\ +\hlline{121\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{getline}\hlstd{}\hlsym{(}\hlstd{cin}\hlsym{,\ }\hlstd{x}\hlsym{);}\\ +\hlline{122\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{getline}\hlstd{}\hlsym{(}\hlstd{cin}\hlsym{,\ }\hlstd{z}\hlsym{);}\\ +\hlline{123\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{print\textunderscore bigint}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{distinct\textunderscore subsequences}\hlstd{}\hlsym{(}\hlstd{x}\hlsym{,\ }\hlstd{z}\hlsym{));}\\ +\hlline{124\ }\hlstd{}\hlstd{\ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{endl}\hlsym{;}\\ +\hlline{125\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{126\ }\hlstd{\ }\hlkwa{return\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{127\ }\hlstd{}\hlsym{\}}\\ +\hlline{128\ }\hlstd{}\\ +\mbox{} +\normalfont +\shorthandon{"} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/trans_algorithmic.tex b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/trans_algorithmic.tex new file mode 100644 index 0000000..9ce8c65 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/doc/trans_algorithmic.tex @@ -0,0 +1,15 @@ +\renewcommand{\algorithmicrequire}{\textcolor{blue}{\textbf{Requiere:}}} +\renewcommand{\algorithmicensure}{\textbf{Devuelve:}} +\renewcommand{\algorithmicend}{\textbf{Fin}} +\renewcommand{\algorithmicif}{\textcolor{blue}{\textbf{Si}}} +\renewcommand{\algorithmicthen}{\textcolor{blue}{}} %%\textbf{entonces}}} +\renewcommand{\algorithmicelse}{\textcolor{red}{\textbf{Si no}}} +\renewcommand{\algorithmicelsif }{\textcolor{blue}{\textbf{Si no y}}} +\renewcommand{\algorithmicendif}{\textcolor{blue}{\textbf{Fin si}}} +\renewcommand{\algorithmicfor}{\textcolor{ForestGreen}{\textbf{Para}}} +\renewcommand{\algorithmicendfor}{\textcolor{ForestGreen}{\textbf{Fin para}}} +\renewcommand{\algorithmicwhile}{\textcolor{ForestGreen}{\textbf{Mientras}}} +\renewcommand{\algorithmicendwhile}{\textcolor{ForestGreen}{\textbf{Fin mientras}}} +\renewcommand{\algorithmicdo}{\textcolor{ForestGreen}{}} %%\textbf{hacer}}} +\renewcommand{\algorithmicreturn}{\textbf{Devolver}} +\floatname{algorithm}{Algoritmo} diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/minimal-coverage/main.cpp b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/minimal-coverage/main.cpp new file mode 100644 index 0000000..f2fa45d --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/minimal-coverage/main.cpp @@ -0,0 +1,83 @@ +#include +#include +#include + +using namespace std; + +#define foreachin(it,s) for (typeof(s.begin()) it = (s).begin(); it != (s).end(); it++) + +typedef pair Intervalo; +typedef list LIntervalo; + +bool compararPorPrimeraComp(const Intervalo& p1, const Intervalo& p2){ + return p1.first < p2.first; +} + +bool resolver(LIntervalo& intervalos, int limite, LIntervalo& solucion) { + intervalos.sort(compararPorPrimeraComp); + int final = 0; // mayor coordenada cubierta hasta ahora + int r_i = 0; // mayor coordenada hasta ahora alcanzada + Intervalo parActual = Intervalo(0, 0); // posible candidato a ser agregado + + foreachin (it, intervalos) { + // si la primera componente esta mayor que final, ya miramos + // todo el C, entonces hay que agregar el intervalo + if (it->first > final) { + solucion.push_back(parActual); + final = r_i; // muevo el borde final + } + // si la primera componente es menor que final miro si el intervalo sirve + if (it->first <= final) { + // sirve si llega mas lejos que lo que hay hasta ahora + if (it->second > r_i) { + r_i = it->second; + parActual = *it; + // si ademas ya llegue al limite, termine + if (r_i >= limite) { + solucion.push_back(parActual); + break; + } + } + } else { + // hay un hueco que no puedo cubrir con ningun intervalo + break; + } + } + + return r_i >= limite; +} + +int main(int argc, char **argv) +{ + int casos; + cin >> casos; + while (casos > 0) { + casos--; + int limite, x, y; + cin >> limite; + x = 1; + y = 1; + // cargo intervalos + LIntervalo intervalos; + while (y != 0 || x != 0) { + scanf ("%d %d", &x, &y); + if (x != 0 || y != 0) { + if (x < y) { //para no cargar intervalos inutiles + intervalos.push_front(Intervalo(x,y)); + } + } + } + // resuelvo instancia + LIntervalo solucion; + if (resolver(intervalos, limite, solucion)) { + cout << solucion.size() << endl; + foreachin (it, solucion) { + cout << it->first << " " << it->second << endl; + } + } else { + cout << 0 << endl; + } + cout << endl; + } +} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/subseq/main.cpp b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/subseq/main.cpp new file mode 100644 index 0000000..1743ed9 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/subseq/main.cpp @@ -0,0 +1,128 @@ +#include +#include +#include +#include +#include + +using namespace std; + +typedef unsigned int uint32; + +#define forsn(i, s, n) for (uint32 i = (s); i < (n); i++) +#define forn(i, n) forsn (i, 0, n) +#define dforn(i, n) for (uint32 i = (n); i-- > 0;) + +// BigInt +// Represents a number in 0 <= n < 10 ** 128 + +#define BigInt_NDIGITS 16 +#define BigInt_BASE 100000000 +class BigInt { +public: + BigInt() : _digits(BigInt_NDIGITS, 0) {} + + BigInt(uint32 n) : _digits(BigInt_NDIGITS, 0) { + assert(n < BigInt_BASE); + _digits[0] = n; + } + + // For testing + BigInt(const string& s) : _digits(BigInt_NDIGITS, 0) { + uint32 pow = 1; + uint32 digit = 0; + uint32 j = 0; + dforn (i, s.size()) { + assert('0' <= s[i] && s[i] <= '9'); + digit += pow * (s[i] - '0'); + + pow *= 10; + if (pow == BigInt_BASE) { + _digits[j++] = digit; + digit = 0; + pow = 1; + } + } + assert(j < BigInt_NDIGITS || digit == 0); + if (j < BigInt_NDIGITS) { + _digits[j] = digit; + } + } + + BigInt operator+(const BigInt& n) { + BigInt res; + bool carry = 0; + + forn (i, BigInt_NDIGITS) { + const uint32 r = _digits[i] + n._digits[i] + carry; + if (r >= BigInt_BASE) { + res._digits[i] = r % BigInt_BASE; + carry = 1; + } else { + res._digits[i] = r; + carry = 0; + } + } + assert(carry == 0); + return res; + } + + void print() { + bool zero = true; + dforn (i, BigInt_NDIGITS) { + if (zero) { + if (_digits[i] == 0) continue; + printf("%u", _digits[i]); + zero = false; + } else { + printf("%.8u", _digits[i]); + } + } + if (zero) { + printf("0"); + } + } + +private: + // Least significant digit first. + // Digits are in 0 <= d < BigInt_BASE + vector _digits; +}; + +#define print_bigint(x) (x).print() + +typedef vector vBigInt; +typedef vector vvBigInt; +BigInt distinct_subsequences(const string& x, const string& z) { + vvBigInt m(2, vBigInt(z.size() + 1, BigInt(0))); + + m[0][0] = BigInt(1); + m[1][0] = BigInt(1); + bool row = 1; + forsn (i, 1, x.size() + 1) { + forsn (j, 1, z.size() + 1) { + if (x[i - 1] == z[j - 1]) { + m[row][j] = m[!row][j] + m[!row][j - 1]; + } else { + m[row][j] = m[!row][j]; + } + } + row = !row; + } + return m[!row][z.size()]; +} + +int main(int argc, char **argv) { + uint32 n; + cin >> n; + char c; + cin.get(c); + forn (i, n) { + string x, z; + getline(cin, x); + getline(cin, z); + print_bigint(distinct_subsequences(x, z)); + cout << endl; + } + return 0; +} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/subseq/test.cpp b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/subseq/test.cpp new file mode 100644 index 0000000..39550fc --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpa/subseq/test.cpp @@ -0,0 +1,202 @@ +#include +#include +#include +#include +#include + +using namespace std; + +typedef unsigned int uint32; + +#define forsn(i, s, n) for (uint32 i = (s); i < (n); i++) +#define forn(i, n) forsn (i, 0, n) +#define fordn(i, n) for (uint32 i = (n); i-- > 0;) + +// BigInt +// Represents a number in 0 <= n < 10 ** 128 + +#define BigInt_NDIGITS 16 +#define BigInt_BASE 100000000 +class BigInt { +public: + BigInt() : _digits(BigInt_NDIGITS, 0) {} + + BigInt(uint32 n) : _digits(BigInt_NDIGITS, 0) { + assert(n < BigInt_BASE); + _digits[0] = n; + } + +#if 0 + // Test BigInt + BigInt(const string& s) : _digits(BigInt_NDIGITS, 0) { + uint32 pow = 1; + uint32 digit = 0; + uint32 j = 0; + fordn (i, s.size()) { + assert('0' <= s[i] && s[i] <= '9'); + digit += pow * (s[i] - '0'); + + pow *= 10; + if (pow == BigInt_BASE) { + _digits[j++] = digit; + digit = 0; + pow = 1; + } + } + assert(j < BigInt_NDIGITS || digit == 0); + if (j < BigInt_NDIGITS) { + _digits[j] = digit; + } + } +#endif + + BigInt operator+(const BigInt& n) { + BigInt res; + bool carry = 0; + + forn (i, BigInt_NDIGITS) { + const uint32 r = _digits[i] + n._digits[i] + carry; + if (r >= BigInt_BASE) { + res._digits[i] = r % BigInt_BASE; + assert(r / BigInt_BASE == 1); + carry = 1; + } else { + res._digits[i] = r; + carry = 0; + } + } + assert(carry == 0); + return res; + } + + void print() { + bool zero = true; + fordn (i, BigInt_NDIGITS) { + if (zero) { + if (_digits[i] == 0) continue; + printf("%u", _digits[i]); + zero = false; + } else { + printf("%.8u", _digits[i]); + } + } + if (zero) { + printf("0"); + } + } + +private: + // Least significant digit first. + // Digits are in 0 <= d < BigInt_BASE + vector _digits; +}; + +#define print_bigint(x) (x).print() + +typedef vector vBigInt; +typedef vector vvBigInt; +BigInt distinct_subsequences(const string& x, const string& z) { + vvBigInt m(2, vBigInt(z.size() + 1, BigInt(0))); + + m[0][0] = BigInt(1); + m[1][0] = BigInt(1); + bool row = 1; + forsn (i, 1, x.size() + 1) { + forsn (j, 1, z.size() + 1) { + if (x[i - 1] == z[j - 1]) { + m[row][j] = m[!row][j] + m[!row][j - 1]; + } else { + m[row][j] = m[!row][j]; + } + } + row = !row; + } + return m[!row][z.size()]; +} + + +struct Prefijo{ + BigInt cantidad; + Prefijo* previo; +}; + +void contar_substrings(string x, string z){ + + // Diccionario para poder acceder en O(1) a los prefijos que terminan en cierta letra + list diccionario[26]; + + // Inicializamos el diccionario + int i = 0; + while(i < 26){ + diccionario[i] = list(); + i++; + } + + string::iterator it; + Prefijo * anterior = 0; + /* + Idea: para guardar un prefijo me alcanza conocer cual era el prefijo anterior (una letra menos) y cual es su ultima letra + */ + foreachin(it,z){ + Prefijo* aux = new Prefijo; + aux->cantidad = BigInt(0); + aux-> previo = anterior; + diccionario[*it-97].push_front(aux); + anterior = aux; + + } + + foreachin(it,x){ + list::iterator it2; + + foreachin(it2,(diccionario[*it-97])){ + // Si es el prefijo de una sola letra, encontre uno mas + if((*it2)->previo == 0)(*it2)->cantidad=(*it2)->cantidad + BigInt(1); + // Sino, tengo tantos como tenia mas la cantidad de prefijos de una letra menos, que ahora se completan + else (*it2)->cantidad= (*it2)->cantidad + (*it2)->previo->cantidad; + } + } + + char ultimo = *(--z.end()); + print_bigint((*(diccionario[ultimo - 97].begin()))->cantidad); + + + foreachin(it,z){ + list::iterator it2; + Prefijo* aux = diccionario[*it-97].front(); + diccionario[*it-97].pop_front(); + delete aux; + } + +} + +int main(int argc, char **argv) { +#if 0 + // Test BigInt + if (argc == 2) { + BigInt a(argv[1]); + a.print(); + printf("\n"); + } else if (argc == 3) { + BigInt a(argv[1]); + BigInt b(argv[2]); + BigInt c = a + b; + c.print(); + printf("\n"); + } +#endif + uint32 n; + cin >> n; + char c; + cin.get(c); + forn (i, n) { + string x, z; + getline(cin, x); + getline(cin, z); + //print_bigint(distinct_subsequences(x, z)); + contar_substrings(x,z); + cout << endl; + } + return 0; +} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/acm/CppApplication_1/main.cpp b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/acm/CppApplication_1/main.cpp new file mode 100644 index 0000000..ffc0376 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/acm/CppApplication_1/main.cpp @@ -0,0 +1,220 @@ +#include +#include +#include +#include +#include +#include + +using namespace std; +#define foreachin(it,s) for (typeof(s.begin()) it = (s).begin(); it != (s).end(); it++) +#define forn(i,n) for(unsigned short i = 0; i < (n); i++) + + +class uf_node{ +public: +unsigned short name; +unsigned short rank; +uf_node *parent; +}; + + +class union_find{ + public : + uf_node* S; + inline union_find(unsigned short n){ + S =new uf_node[n]; + for(unsigned short i=0;irank; + rankb=S[b].parent->rank; + if(ranka>rankb){ + (S[b].parent)->parent=S[a].parent; + S[a].rank=ranka+rankb; + } + else{ + (S[a].parent)->parent=S[b].parent; + S[b].rank=ranka+rankb; + } + } + + inline void compress_path(uf_node* temp, uf_node* aux, uf_node* stop_point){ + temp=aux->parent; + aux->parent=stop_point; + aux=temp; + while(aux!=stop_point){ + temp=aux->parent; + aux->parent=stop_point; + aux=temp; + } + } + + inline unsigned short Find(unsigned short a){ + uf_node* temp; + uf_node* aux; + unsigned short result; + aux=&S[a]; + temp=S[a].parent; + while(aux!=temp){ + aux=temp; + temp=(*aux).parent; + } + result=aux->name; + uf_node* stop_point; + stop_point=aux; + aux=&S[a]; + compress_path(temp,aux,stop_point); + + return result; + } +}; + +class edge{ +public : + unsigned short start,end; + unsigned short cost; + inline edge(unsigned short start, unsigned short end, unsigned short cost){ + this->start=start; + this->end=end; + this->cost=cost; + } +}; + + +inline bool compare(const edge& a,const edge& b ){ + return a.cost < b.cost; + +} + +inline void bucket_sort(list& e,unsigned short max_cost){ + vector > v(max_cost+1); + while(!e.empty()){ + const edge& ed = e.front(); + v[ed.cost].push_back(ed); + e.pop_front(); + } + forn(i, max_cost+1){ + while(!v[i].empty()){ + e.push_back(v[i].back()); + v[i].pop_back(); + } + } + +} + +inline unsigned short kruskal(list& e,unsigned short n, vector >& adj,list& rejected, unsigned short max_cost, unsigned short m){ + union_find list(n); + unsigned short res=0; + if (m > max_cost) + bucket_sort(e,max_cost); + else + e.sort(compare); + + foreachin(it,e){ + unsigned short s,f; + s=it->start; + f=it->end; + + if(list.Find(s)==list.Find(f)){ + + rejected.push_back(*it); + continue; + } + else{ + list.Union(s,f); + res += it->cost; + adj[s].push_back(*it); + adj[f].push_back(edge(it->end,it->start,it->cost)); + } + } + + return res; + +} + + +inline void dfs_fill_max(unsigned short u, unsigned short x,vector >& mst_adjacency, vector >& max){ + foreachin(v,(mst_adjacency[x])){ + if( max[u][v->end] == NULL && v->end != u){ + if(x==u || v->cost > max[u][x]->cost){ + max[u][v->end] = &(*v); + } + else{ + max[u][v->end] = max[u][x]; + } + dfs_fill_max(u,v->end,mst_adjacency,max); + } + + } +} + +inline unsigned short second_mst(unsigned short n, vector >& mst_adjacency, list& rejected,unsigned short minimum_cost){ + vector > max(n,vector(n,NULL)); + list::iterator it = rejected.begin(); + unsigned short start = it->start; + unsigned short end = it->end; + dfs_fill_max(start,start,mst_adjacency, max); + unsigned short old_cost=max[start][end]->cost; + unsigned short new_cost=it->cost; + unsigned short minimum= new_cost - old_cost; + it++; + for(it;it != rejected.end();it++ ){ + start = it->start; + end = it->end; + if(max[start][end] == NULL)dfs_fill_max(start,start,mst_adjacency, max); + + unsigned short aux=it->cost- max[start][end]->cost; + if(aux < minimum){ + if(aux == 0)return minimum_cost; + minimum= aux; + new_cost = it->cost; + old_cost = max[start][end]->cost; + } + + } + return minimum_cost - old_cost + new_cost; +} + + +int main(){ +int cases; +cin>>cases; +unsigned short n; +unsigned short m; +unsigned short from,to,cost; + + +while(cases > 0){ + scanf("%hu %hu",&n,&m); + vector > mst_adjacency(n); + list rejected; + list l; + unsigned short cant_edges=0; + unsigned short max_cost = 0; + while(cant_edges < m){ + scanf("%hu %hu %hu",&from,&to,&cost); + if(cost > max_cost)max_cost = cost; + l.push_back(edge(from-1,to-1,cost)); + cant_edges++; + } + unsigned short k =kruskal(l,n,mst_adjacency,rejected,max_cost,m); + //unsigned short k =kruskal(l,n,mst_adjacency,rejected); + cout << k<<" "; + cout << second_mst(n,mst_adjacency,rejected,k)< +#include +#include +#include +#include + +using namespace std; + +typedef long long int int64; + +#define forsn(i, s, n) for (int64 i = (s); i < (n); i++) +#define forn(i, n) forsn (i, 0, n) +#define forall(x, s) for (typeof((s).begin()) x = (s).begin(); x != (s).end(); x++) + +typedef vector vint; +typedef vector vvint; + +int64 n; +int64 capacidad_eje0; +int64 capacidad_enlace; +vvint grafo; // listas de adyacencia +vvint costo; // matriz +vvint flujo; // matriz + +#define agregar(u, v, c) { \ + grafo[u].push_back(v); \ + costo[u][v] = (c); \ + grafo[v].push_back(u); \ + costo[v][u] = (c); \ +} + +#define capacidad(v, w) (((v) == 0 || (w) == 0) ? capacidad_eje0 : capacidad_enlace) + +void print_grafo_residual() { + cout << "---------------" << endl; + forn (v, n) { + cout << v << endl; + forall (vecino, grafo[v]) { + cout << "--> "; + cout << *vecino; + cout << " costo = " << costo[v][*vecino]; + cout << " flujo = " << flujo[v][*vecino] << " / " << capacidad(v, *vecino); + cout << endl; + } + cout << endl; + } +} + +#define INF 0x7fffffff +#define No_hay_camino -1 +#define signo(x) ((x) < 0 ? -1 : 1) +int64 caumento(vint& camino) { + // buscar el camino de aumento de costo minimo usando Bellman-Ford + vint dist(n, INF); + vint ant(n, -1); + + dist[0] = 0; + + forn (it, n - 1) { + // para cada arista del grafo residual + bool cambio = false; + forn (v, n) forall (vecino, grafo[v]) { + const int64 w = *vecino; + if (capacidad(v, w) - flujo[v][w] <= 0) continue; + if (dist[v] == INF) continue; + int64 ndist = dist[v] + signo(flujo[v][w]) * costo[v][w]; + if (ndist < dist[w]) { + dist[w] = ndist; + ant[w] = v; + cambio = true; + } + } + if (!cambio) break; + } + + // armar el camino + int64 costo_camino = 0; + int64 actual = n - 1; + while (true) { + camino.push_back(actual); + int64 anterior = ant[actual]; + if (anterior == -1) break; + costo_camino += signo(flujo[anterior][actual]) * costo[anterior][actual]; + actual = anterior; + } + if (actual == 0) { + return costo_camino; + } else { + return No_hay_camino; + } +} + +int64 resolver() { + int64 flujo_total = 0; + int64 costo_total = 0; + while (flujo_total < capacidad_eje0) { + //print_grafo_residual(); + vint camino_aumento; + int64 costo_camino = caumento(camino_aumento); + if (costo_camino == No_hay_camino) return No_hay_camino; + // saturar el camino de aumento + int64 mn = INF; + + forn (i, camino_aumento.size() - 1) { + const int64 v = camino_aumento[i + 1], w = camino_aumento[i]; + if (flujo[v][w] < 0) { + mn = min(mn, -flujo[v][w]); + } else { + mn = min(mn, capacidad(v, w) - flujo[v][w]); + } + } + forn (i, camino_aumento.size() - 1) { + const int64 v = camino_aumento[i + 1], w = camino_aumento[i]; + flujo[v][w] += mn; + flujo[w][v] -= mn; + } + if (mn == 0) return No_hay_camino; + flujo_total += mn; + costo_total += costo_camino * mn; + } + + return costo_total; +} + +int main() { + int64 m; + while (cin >> n >> m) { + n++; + grafo = vvint(n, vint()); + costo = vvint(n, vint(n, 0)); + flujo = vvint(n, vint(n, 0)); + + agregar(0, 1, 0); + forn (i, m) { + int64 v1, v2, c; + cin >> v1 >> v2 >> c; + agregar(v1, v2, c); + } + cin >> capacidad_eje0 >> capacidad_enlace; + int64 r = resolver(); + if (r == No_hay_camino) { + cout << "Impossible." << endl; + } else { + cout << r << endl; + } + } + return 0; +} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/acm.tex b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/acm.tex new file mode 100644 index 0000000..fdd7365 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/acm.tex @@ -0,0 +1,438 @@ +\newcommand{\tq}{\ensuremath{\ |\ }} +\section{10600-ACM Contest and Blackout} +\textbf{Problema:} Dado un conjunto de escuelas, y posibles conexiones entre ellas, cada una con un costo, encontrar los dos costos m\'as baratos para conectarlos. + +\subsection{Resolución} +El problema se modela como un problema de grafos. El grafo tiene un nodo por cada escuela y existe un eje entre dos nodos por cada forma de conectar las escuelas representadas por esos nodos. El costo del eje es el costo de la conexión. En este modelo la respuesta consiste en buscar el costo de los dos árboles m\'as baratos. M\'as formalmente, si $g$ es el grafo, consideramos el siguiente conjunto $A$: + +$A=\{ T \tq T$ es árbol generador de $g$$\}$ + +lo que buscamos es $costo(T_1),costo(T_2)$ tal que: + +$T_1 \in A \wedge T_2 \in A \wedge T_1 \neq T_2 \wedge T_1$ es árbol generador mínimo $\wedge \forall T_3 \in A, T_1 \neq T_3 \implies costo(T_2) \leq costo(T_3)$ + +Dado que el problema nos dice que podemos encontrar los costos, podemos asumir que el grafo tiene m\'as de una forma de conectar a todos los nodos. + +Si tenemos la forma m\'as barata de conectar a todas las escuelas y miramos +esta solución en el grafo, vemos que tiene que ser un árbol generador mínimo: +es un \'arbol porque no puede haber escuelas ``sueltas'' (es conexo) y +no puede haber ciclos, ya que las +conexiones tienen un costo positivo (por lo cual eliminar una de esas +conexiones abaratar\'ia el costo). Adem\'as, tiene +que ser mínimo, ya que se busca que sea el de mínimo costo. La segunda forma +m\'as barata de conectar a las escuelas tiene que ser también un árbol generador, +ya que, por los mismos motivos de antes, el grafo correspondiente debe ser +conexo y sin ciclos. Por lo tanto, si hay una solución al problema, sus costos +tienen que coincidir con los costos de $T_1$ y $T_2$. + +Por otro lado es simple ver que los costos de $T_1$ y de $T_2$ son solución al +problema, ya que si alguno de los dos no fuera es porque hay una forma m\'as +barata de conectarlos; pero eso es absurdo por la definición de $T_1$ y de +$T_2$. + +Encontrar $T_1$ es simple, se puede usar el algoritmo de Kruskal para hallar un +árbol generador mínimo. +Para encontrar $T_2$ podría sacarse uno a uno los ejes que están en $T_1$ de $g$, +y buscar el árbol generador mínimo de los sucesivos $g'$ hasta hallar el mas +chico de todos ellos. Sin embargo esto es muy costoso y puede hacerse mejor. +Para ello, usamos el Teorema~\ref{t1} demostrado abajo, que nos permite +asegurar que se puede encontrar un $T_2$ cambiando a lo sumo un eje de $T_1$. + +Sean dos ejes $(u,v) \in T_1$, $(x,y) \notin T_1$ tales que $T_1\cup \{(x,y)\}$ +tiene un ciclo en que tambi\'en est\'a el eje $(u,v)$. Sea adem\'as +$T_2=T_1-\{(u,v)\}\cup\{(x,y)\}$, entonces: + +%TODO: esto les parece que hay que justificarlo mas? +%RESPUESTA: naaah +$costo(T_2) = costo(T_1) - costo((u,v)) + costo((x,y))$ + +Si queremos minimizar el costo de $T_2$ dado un $(x,y)$ fijo, debemos buscar cual es +el $(u,v)$ que minimiza $- costo((u,v)) + costo((x,y))$. Este $(u,v)$ es el eje +m\'as pesado del único camino que existe en $T_1$ entre $x$ e $y$. Una forma de +resolver el problema es, para cada eje $(x,y)$ que ocurr\'ia en el grafo original +pero qued\'o excluido de $T_1$, calcular cu\'al es el eje $(u,v)$ que le corresponde. +Una vez hecho esto, se tienen los posibles mínimos incrementos que genera agregar +un eje a $T_1$. El \'arbol $T_2$ buscado es el que minimiza este incremento. + +%los posibles mínimos incrementos que genera agregar +%un eje a $T_1$. El costo que buscamos es el de $T_1$ mas el mínimo de estos incrementos. + +Una forma de hacer esto es encontrar, usando DFS, el eje m\'as caro del +camino entre $u$ y $v$ para todo par de nodos $u,v$. El camino es \'unico +porque $T_1$ es un árbol. + +\begin{algorithm}[H] +\begin{algorithmic} +\caption{Encontrar el eje m\'as caro en el camino que existe en un árbol para cada par de nodos $u$, $v$} +\PARAMS{árbol sobre el que buscar} +\STATE $M_{v,w} :=$ no calculado $\forall v, w$ nodos del árbol +\FOR{cada nodo $v$ en el árbol} + \STATE \texttt{llenar\_con\_dfs\_m\'ax}($v$, $v$, $max$) +\ENDFOR +\end{algorithmic} +\end{algorithm} + +\begin{algorithm}[H] +\begin{algorithmic} +\caption{\texttt{llenar\_con\_dfs\_m\'ax:} Encontrar los ejes m\'as caros para los caminos que empiezan en un nodo} +\PARAMS{nodo inicial $u$, otro nodo $x$, matriz ($max$) donde guardar los resultados} +\FOR{cada nodo $v$ adyacente a $x$} +\IF{$M_{u,v}$ es no calculado y $v\neq u$} + \IF{$x=u$ $\lor$ $peso(u,v) > M_{u,x}$} + \STATE $M_{u,v} := (x,v)$ + \ELSE + \STATE $M_{u,v} := M_{u,x}$ + \ENDIF + \STATE \texttt{llenar\_con\_dfs\_m\'ax}($u$, $v$, $max$) +\ENDIF +\ENDFOR +\end{algorithmic} +\end{algorithm} + +Para obtener el árbol generador mínimo se utilizó el algoritmo de Kruskal, con una estructura auxiliar para {\em union-find} +representada con un bosque de conjuntos disjuntos, de manera tal que cada nodo mantiene un puntero al representante de su +clase. El algoritmo para la resolución del problema fue: + +\begin{algorithm}[H] +\begin{algorithmic} +\caption{Costo de los dos \'arboles generadores m\'as baratos} +\PARAMS{un grafo $g$ con peso en los ejes} +\STATE ordenar los ejes según su peso +\STATE obtener el árbol generador mínimo $T_1$ y su costo mediante el algoritmo de Kruskal +\STATE $M_{u,v}$ := eje m\'as caro en el camino desde $u$ hasta $v$ en $T_1$ +\STATE costo nuevo $:= \infty$ +\FOR{cada eje $(u,v)$ que quedo fuera del árbol generador mínimo} + \IF{costo nuevo $>$ $costo(T_1) - costo(M_{u,v}) + costo(u,v)$} + \STATE costo nuevo := $costo(T_1) - costo(M_{u,v}) + costo(u,v)$ + \ENDIF +\ENDFOR +\RETURN $\langle$ $costo(T_1)$, costo nuevo $\rangle$ +\end{algorithmic} +\end{algorithm} + +Podemos analizar la complejidad en base al pseudoc\'odigo antes presentado. +Lo primero que hacemos es ordenar los ejes, lo cual toma $O(E \log E)$\footnote{Eventualmente se podría mejorar la complejidad utilizando bucket sort, ya que el costo de cada eje es a lo sumo 300.}, que es igual a $O(E \log V$). Luego obtenemos el árbol generador mínimo. Como usamos Kruskal con {\em union-find} y los ejes ya están ordenados, la complejidad es $O(E \alpha(V))$. + +Luego llenamos la matriz $M$, que como vimos antes, se logra haciendo DFS desde +cada nodo, lo cual nos da un costo $O(V^2)$, ya que se hacen $V$ recorridos sobre el +árbol, cada uno de los cuales cuesta $O(V)$ porque, como es un árbol, tiene $V-1$ ejes. En +la implementación, no se llenan todas las posiciones $M_{u,v}$ al inicio, sino que +se hace cada DFS a medida que se necesita su resultado. Esto no cambia la +complejidad en peor caso, pero mejora los casos en los que hay pocos ejes. +Finalmente, recorremos los ejes que no est\'an en el árbol, buscando cu\'al es el +incremento mínimo que se produce al agregarlo; esto se hace en $O(E)$. +Por lo tanto, la complejidad temporal es $O(V^2 + E \log V)$. + +\newtheorem{theorem}{Teorema} +\begin{theorem} +\label{t1} +Sea $g$ un grafo tal que posee por lo menos dos árboles generadores. Entonces +existe un árbol generador $T'$ tal que si $T$ es un árbol generador mínimo, +entonces $T'$ difiere de $T$ en exactamente un eje y para todo otro árbol +generador $T''$ ($T'' \neq T$), $costo(T') \leq costo(T'')$. +\end{theorem} +\begin{proof} +Veamos primero que existe un \'arbol generador que difiere de $T$ en exactamente un +eje. + +Sabemos que $g$ tiene por lo menos dos árboles generadores, por lo cual existe +por lo menos un eje en g que no pertenece a $T$. Sea $e$ un eje de $g$ que no +est\'a en $T$. Si se agrega $e$ a $T$, este pasa a tener un ciclo. Si se saca +un eje de ese ciclo, que no sea $e$, se obtiene otro árbol generador que +difiere de $T$ en exactamente un eje. + +Sea $T'$ un árbol generador que difiere de $T$ en exactamente un eje y cuyo +costo es mínimo entre todos los que se diferencian de $T$ en exactamente un +eje. Es decir: + +$A =\{t \tq t \text{ es árbol generador} \land \exists e \in E . T - t = \{e\}\}$ (difieren de $T$ en un eje) + +$T' \in \{ t \tq t \in A \wedge \forall t_1 \in A, costo(t) \leq costo(t_1)\}$ + +Veamos que $costo(T') \leq costo(T'')$ para todo \'arbol generador $T'' \neq T$. + +Por la elecci\'on de $T'$, s\'olo falta considerar aquellos \'arboles generadores +$T''$ que difieran de $T$ en dos o m\'as ejes. +Supongamos que existe $T''$ que difiere de $T$ en dos o m\'as ejes y que +$costo(T') > costo(T'')$. +Considerar alg\'un $T''$ de costo mínimo y, dentro de los de costo m\'inimo, +el que difiera de $T$ en la menor cantidad de ejes. M\'as formalmente: +%$B =\{t \tq t $ es árbol generador,$ \#(T-t) \geq 2\}$ + +$C =\{t \tq t \text{ es \'arbol generador }\land \#(T - t) \geq 2 \land costo(t) < costo(T')\}$ (difieren de $T$ en 2 o m\'as ejes) + +\noindent queremos ver que $C=\emptyset$. Consideramos: + +$C' = \{ t \tq t \in C \wedge \forall t_1 \in C, costo(t) \leq costo(t_1)\}$ (de costo m\'inimo) + +$C'' = \{ t \tq t \in C' \wedge \forall t_1 \in C', \#(T-t) \leq \#(T-t_1)\}$ (difieren de $T$ en m\'inima cantidad de ejes) + +Probar que $C=\emptyset$ es equivalente a probar que $C''=\emptyset$. Supongamos que $C'' \neq \emptyset$, entonces, sea $T'' \in C''$. + +Existe un eje $(u,v) \in T-T''$ que adem\'as tiene costo mínimo entre todos los que pertenecen a $T-T''$. Si agregamos $(u,v)$ a $T''$ obtenemos un ciclo, y en este ciclo hay un eje $(x,y)\in T''-T$ (porque si no habr\'ia un ciclo en $T$). + +\begin{itemize} +\item Si $peso((u,v)) > peso((x,y))$, agregamos $(x,y)$ a $T$ y obtenemos un ciclo. Hay un eje $(u',v')$ +en este ciclo que cumple que $(u',v') \in T-T''$ (porque si no habr\'ia un ciclo en $T''$). +Como $(u,v)$ era el mínimo de todos los ejes de $T-T''$, vale que $peso((u,v))\leq peso((u',v'))$. + +Si $peso((u,v)) \leq peso((u',v'))$ y consideramos $T^\star=T-\{(u',v')\}\cup\{(x,y)\}$ obtenemos un árbol generador que tiene un costo mayor o igual que el de $T$. + +En verdad, no puede ser igual, porque $T^\star$ difiere de $T$ en exactamente +un eje, y tendríamos que $costo(T) = costo(T^\star) \geq costo(T') > costo(T'')$ +y esto es absurdo ya que $T$ tiene costo mínimo. + +Entonces $T^\star$ tiene un costo mayor, por lo cual tiene que valer que +$peso((u',v')) < peso((x,y))$, entonces $peso((u',v')) < peso((x,y)) < peso((u,v))$. Esto es absurdo, ya que $(u,v)$ era un eje de peso mínimo en $T-T''$ + +%Vemos entonces que $peso((u,v))\leq peso((x,y))$. + +\item +Si $peso((u,v)) = peso((x,y))$, resulta que existe $T^\star = T''-\{(x,y)\}\cup \{(u,v) \}$ +que tiene el mismo costo que $T''$ pero difiere de $T$ en menos ejes. +Entonces, o bien $T^\star$ difiere en exactamente un eje de $T$, lo cual +es absurdo porque $costo(T'') < costo(T') \leq costo(T^\star) = costo(T'')$, +o bien difiere en m\'as de un eje, +pero esto no puede ser porque, dentro de los de m\'inimo costo, $T''$ difer\'ia +de $T$ en m\'inima cantidad de ejes. +%pero esto no puede ser porque entonces $T^\star$ diferir\'ia en un eje menos de $T$ que $T''$. + +\item Por \'ultimo, si $peso((u,v)) < peso((x,y))$, entonces $T''-\{(x,y)\}\cup \{(u,v) \}$ pesa +menos que $T''$ y difiere de $T$ en menos ejes, lo cual es nuevamente absurdo por +las asunciones hechas sobre $T''$. +\end{itemize} + +En todos los casos, el absurdo provino de suponer que existía $T''$. +\end{proof} + + +\subsection{Implementación} +\noindent +\ttfamily +\shorthandoff{"}\\ +\hlstd{}\hlline{\ 1\ }\hldir{\#include$<$iostream$>$}\\ +\hlline{\ 2\ }\hlstd{}\hldir{\#include\ $<$stdio.h$>$}\\ +\hlline{\ 3\ }\hlstd{}\hldir{\#include\ $<$stdlib.h$>$}\\ +\hlline{\ 4\ }\hlstd{}\hldir{\#include\ $<$vector$>$}\\ +\hlline{\ 5\ }\hlstd{}\hldir{\#include\ $<$algorithm$>$}\\ +\hlline{\ 6\ }\hlstd{}\hldir{\#include\ $<$list$>$}\\ +\hlline{\ 7\ }\hlstd{}\\ +\hlline{\ 8\ }\hlkwa{using\ namespace\ }\hlstd{std}\hlsym{;}\\ +\hlline{\ 9\ }\hlstd{}\hldir{\#define\ foreachin(it,s)\ for\ (typeof(s.begin())\ it\ =\ (s).begin();\ it\ !=\ (s).end();\ it++)}\\ +\hlline{10\ }\hlstd{}\hldir{\#define\ forn(i,n)\ for(unsigned\ short\ i\ =\ 0;\ i\ $<$\ (n);\ i++)}\\ +\hlline{11\ }\hlstd{}\\ +\hlline{12\ }\\ +\hlline{13\ }\hlkwc{class\ }\hlstd{uf\textunderscore node}\hlsym{\{}\\ +\hlline{14\ }\hlstd{}\hlkwc{public}\hlstd{}\hlsym{:}\\ +\hlline{15\ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{name}\hlsym{;}\\ +\hlline{16\ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{rank}\hlsym{;}\\ +\hlline{17\ }\hlstd{uf\textunderscore node\ }\hlsym{{*}}\hlstd{parent}\hlsym{;}\\ +\hlline{18\ }\hlstd{}\hlsym{\};}\\ +\hlline{19\ }\hlstd{}\\ +\hlline{20\ }\\ +\hlline{21\ }\hlkwc{class\ }\hlstd{union\textunderscore find}\hlsym{\{}\\ +\hlline{22\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwc{public\ }\hlstd{}\hlsym{:}\\ +\hlline{23\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{uf\textunderscore node}\hlsym{{*}\ }\hlstd{S}\hlsym{;}\\ +\hlline{24\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwc{inline\ }\hlstd{}\hlkwd{union\textunderscore find}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{n}\hlsym{)\{}\\ +\hlline{25\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{S\ }\hlsym{=}\hlstd{}\hlkwa{new\ }\hlstd{uf\textunderscore node}\hlsym{{[}}\hlstd{n}\hlsym{{]};}\\ +\hlline{26\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{for}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{i}\hlsym{=}\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\hlstd{i}\hlsym{$<$}\hlstd{n}\hlsym{;}\hlstd{i}\hlsym{++)\{}\\ +\hlline{27\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{S}\hlsym{{[}}\hlstd{i}\hlsym{{]}.}\hlstd{rank}\hlsym{=}\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{28\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{S}\hlsym{{[}}\hlstd{i}\hlsym{{]}.}\hlstd{name}\hlsym{=}\hlstd{i}\hlsym{;}\\ +\hlline{29\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{S}\hlsym{{[}}\hlstd{i}\hlsym{{]}.}\hlstd{parent}\hlsym{=\&}\hlstd{S}\hlsym{{[}}\hlstd{i}\hlsym{{]};}\\ +\hlline{30\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{31\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{32\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{$\sim$}\hlstd{}\hlkwd{union\textunderscore find}\hlstd{}\hlsym{()\{}\hlstd{}\hlkwa{delete}\hlstd{}\hlsym{{[}{]}\ }\hlstd{S}\hlsym{;\}}\\ +\hlline{33\ }\hlstd{\\ +\hlline{34\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwc{inline\ }\hlstd{}\hlkwb{void\ }\hlstd{}\hlkwd{Union}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{a}\hlsym{,\ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{b}\hlsym{)\{\ }\hlstd{}\hlslc{//use\ Union\ because\ union\ is\ a\ keyword\ :P}\\ +\hlline{35\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{ranka}\hlsym{,}\hlstd{rankb}\hlsym{;}\\ +\hlline{36\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{ranka}\hlsym{=}\hlstd{S}\hlsym{{[}}\hlstd{a}\hlsym{{]}.}\hlstd{parent}\hlsym{{-}$>$}\hlstd{rank}\hlsym{;}\\ +\hlline{37\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{rankb}\hlsym{=}\hlstd{S}\hlsym{{[}}\hlstd{b}\hlsym{{]}.}\hlstd{parent}\hlsym{{-}$>$}\hlstd{rank}\hlsym{;}\\ +\hlline{38\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if}\hlstd{}\hlsym{(}\hlstd{ranka}\hlsym{$>$}\hlstd{rankb}\hlsym{)\{}\\ +\hlline{39\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{(}\hlstd{S}\hlsym{{[}}\hlstd{b}\hlsym{{]}.}\hlstd{parent}\hlsym{){-}$>$}\hlstd{parent}\hlsym{=}\hlstd{S}\hlsym{{[}}\hlstd{a}\hlsym{{]}.}\hlstd{parent}\hlsym{;}\\ +\hlline{40\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{S}\hlsym{{[}}\hlstd{a}\hlsym{{]}.}\hlstd{rank}\hlsym{=}\hlstd{ranka}\hlsym{+}\hlstd{rankb}\hlsym{;}\\ +\hlline{41\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{42\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{else}\hlstd{}\hlsym{\{}\\ +\hlline{43\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{(}\hlstd{S}\hlsym{{[}}\hlstd{a}\hlsym{{]}.}\hlstd{parent}\hlsym{){-}$>$}\hlstd{parent}\hlsym{=}\hlstd{S}\hlsym{{[}}\hlstd{b}\hlsym{{]}.}\hlstd{parent}\hlsym{;}\\ +\hlline{44\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{S}\hlsym{{[}}\hlstd{b}\hlsym{{]}.}\hlstd{rank}\hlsym{=}\hlstd{ranka}\hlsym{+}\hlstd{rankb}\hlsym{;}\\ +\hlline{45\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{46\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{47\ }\hlstd{\\ +\hlline{48\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwc{inline\ }\hlstd{}\hlkwb{void\ }\hlstd{}\hlkwd{compress\textunderscore path}\hlstd{}\hlsym{(}\hlstd{uf\textunderscore node}\hlsym{{*}\ }\hlstd{temp}\hlsym{,\ }\hlstd{uf\textunderscore node}\hlsym{{*}\ }\hlstd{aux}\hlsym{,\ }\hlstd{uf\textunderscore node}\hlsym{{*}\ }\hlstd{stop\textunderscore point}\hlsym{)\{}\\ +\hlline{49\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{temp}\hlsym{=}\hlstd{aux}\hlsym{{-}$>$}\hlstd{parent}\hlsym{;}\\ +\hlline{50\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{aux}\hlsym{{-}$>$}\hlstd{parent}\hlsym{=}\hlstd{stop\textunderscore point}\hlsym{;}\\ +\hlline{51\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{aux}\hlsym{=}\hlstd{temp}\hlsym{;}\\ +\hlline{52\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{while}\hlstd{}\hlsym{(}\hlstd{aux}\hlsym{!=}\hlstd{stop\textunderscore point}\hlsym{)\{}\\ +\hlline{53\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{temp}\hlsym{=}\hlstd{aux}\hlsym{{-}$>$}\hlstd{parent}\hlsym{;}\\ +\hlline{54\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{aux}\hlsym{{-}$>$}\hlstd{parent}\hlsym{=}\hlstd{stop\textunderscore point}\hlsym{;}\\ +\hlline{55\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{aux}\hlsym{=}\hlstd{temp}\hlsym{;}\\ +\hlline{56\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{57\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{58\ }\hlstd{\\ +\hlline{59\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwc{inline\ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{}\hlkwd{Find}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{a}\hlsym{)\{}\\ +\hlline{60\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{uf\textunderscore node}\hlsym{{*}\ }\hlstd{temp}\hlsym{;}\\ +\hlline{61\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{uf\textunderscore node}\hlsym{{*}\ }\hlstd{aux}\hlsym{;}\\ +\hlline{62\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{result}\hlsym{;}\\ +\hlline{63\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{aux}\hlsym{=\&}\hlstd{S}\hlsym{{[}}\hlstd{a}\hlsym{{]};}\\ +\hlline{64\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{temp}\hlsym{=}\hlstd{S}\hlsym{{[}}\hlstd{a}\hlsym{{]}.}\hlstd{parent}\hlsym{;}\\ +\hlline{65\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{while}\hlstd{}\hlsym{(}\hlstd{aux}\hlsym{!=}\hlstd{temp}\hlsym{)\{}\\ +\hlline{66\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{aux}\hlsym{=}\hlstd{temp}\hlsym{;}\\ +\hlline{67\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{temp}\hlsym{=({*}}\hlstd{aux}\hlsym{).}\hlstd{parent}\hlsym{;}\\ +\hlline{68\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{69\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{result}\hlsym{=}\hlstd{aux}\hlsym{{-}$>$}\hlstd{name}\hlsym{;}\\ +\hlline{70\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{uf\textunderscore node}\hlsym{{*}\ }\hlstd{stop\textunderscore point}\hlsym{;}\\ +\hlline{71\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{stop\textunderscore point}\hlsym{=}\hlstd{aux}\hlsym{;}\\ +\hlline{72\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{aux}\hlsym{=\&}\hlstd{S}\hlsym{{[}}\hlstd{a}\hlsym{{]};}\\ +\hlline{73\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{compress\textunderscore path}\hlstd{}\hlsym{(}\hlstd{temp}\hlsym{,}\hlstd{aux}\hlsym{,}\hlstd{stop\textunderscore point}\hlsym{);}\\ +\hlline{74\ }\hlstd{\\ +\hlline{75\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{result}\hlsym{;}\\ +\hlline{76\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{77\ }\hlstd{}\hlsym{\};}\\ +\hlline{78\ }\hlstd{}\\ +\hlline{79\ }\hlkwc{class\ }\hlstd{edge}\hlsym{\{}\\ +\hlline{80\ }\hlstd{}\hlkwc{public\ }\hlstd{}\hlsym{:}\\ +\hlline{81\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{start}\hlsym{,}\hlstd{end}\hlsym{;}\\ +\hlline{82\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{cost}\hlsym{;}\\ +\hlline{83\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwc{inline\ }\hlstd{}\hlkwd{edge}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{start}\hlsym{,\ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{end}\hlsym{,\ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{cost}\hlsym{)\{}\\ +\hlline{84\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{this}\hlstd{}\hlsym{{-}$>$}\hlstd{start}\hlsym{=}\hlstd{start}\hlsym{;}\\ +\hlline{85\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{this}\hlstd{}\hlsym{{-}$>$}\hlstd{end}\hlsym{=}\hlstd{end}\hlsym{;}\\ +\hlline{86\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{this}\hlstd{}\hlsym{{-}$>$}\hlstd{cost}\hlsym{=}\hlstd{cost}\hlsym{;}\\ +\hlline{87\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{88\ }\hlstd{}\hlsym{\};}\\ +\hlline{89\ }\hlstd{}\\ +\hlline{90\ }\\ +\hlline{91\ }\hlkwc{inline\ }\hlstd{}\hlkwb{bool\ }\hlstd{}\hlkwd{compare}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ }\hlstd{edge}\hlsym{\&\ }\hlstd{a}\hlsym{,}\hlstd{}\hlkwb{const\ }\hlstd{edge}\hlsym{\&\ }\hlstd{b\ }\hlsym{)\{}\\ +\hlline{92\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{a}\hlsym{.}\hlstd{cost\ }\hlsym{$<$\ }\hlstd{b}\hlsym{.}\hlstd{cost}\hlsym{;}\\ +\hlline{93\ }\hlstd{}\\ +\hlline{94\ }\hlsym{\}}\\ +\hlline{95\ }\hlstd{}\\ +\hlline{96\ }\hlkwc{inline\ }\hlstd{}\hlkwb{void\ }\hlstd{}\hlkwd{bucket\textunderscore sort}\hlstd{}\hlsym{(}\hlstd{list}\hlsym{$<$}\hlstd{edge}\hlsym{$>$\&\ }\hlstd{e}\hlsym{,}\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{max\textunderscore cost}\hlsym{)\{}\\ +\hlline{97\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{vector}\hlsym{$<$}\hlstd{list}\hlsym{$<$}\hlstd{edge}\hlsym{$>$\ $>$\ }\hlstd{}\hlkwd{v}\hlstd{}\hlsym{(}\hlstd{max\textunderscore cost}\hlsym{+}\hlstd{}\hlnum{1}\hlstd{}\hlsym{);}\\ +\hlline{98\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{while}\hlstd{}\hlsym{(!}\hlstd{e}\hlsym{.}\hlstd{}\hlkwd{empty}\hlstd{}\hlsym{())\{}\\ +\hlline{99\ }\hlstd{\ }\hlkwb{const\ }\hlstd{edge}\hlsym{\&\ }\hlstd{ed\ }\hlsym{=\ }\hlstd{e}\hlsym{.}\hlstd{}\hlkwd{front}\hlstd{}\hlsym{();}\\ +\hlline{100\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{v}\hlsym{{[}}\hlstd{ed}\hlsym{.}\hlstd{cost}\hlsym{{]}.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{ed}\hlsym{);}\\ +\hlline{101\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{e}\hlsym{.}\hlstd{}\hlkwd{pop\textunderscore front}\hlstd{}\hlsym{();}\\ +\hlline{102\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{103\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{forn}\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{max\textunderscore cost}\hlsym{+}\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\{}\\ +\hlline{104\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{while}\hlstd{}\hlsym{(!}\hlstd{v}\hlsym{{[}}\hlstd{i}\hlsym{{]}.}\hlstd{}\hlkwd{empty}\hlstd{}\hlsym{())\{}\\ +\hlline{105\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{e}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{v}\hlsym{{[}}\hlstd{i}\hlsym{{]}.}\hlstd{}\hlkwd{back}\hlstd{}\hlsym{());}\\ +\hlline{106\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{v}\hlsym{{[}}\hlstd{i}\hlsym{{]}.}\hlstd{}\hlkwd{pop\textunderscore back}\hlstd{}\hlsym{();}\\ +\hlline{107\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{108\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{109\ }\hlstd{}\\ +\hlline{110\ }\hlsym{\}}\\ +\hlline{111\ }\hlstd{}\\ +\hlline{112\ }\hlkwc{inline\ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{}\hlkwd{kruskal}\hlstd{}\hlsym{(}\hlstd{list}\hlsym{$<$}\hlstd{edge}\hlsym{$>$\&\ }\hlstd{e}\hlsym{,}\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{n}\hlsym{,\ }\hlstd{vector}\hlsym{$<$}\hlstd{list}\hlsym{$<$}\hlstd{edge}\hlsym{$>$\ $>$\&\ }\hlstd{adj}\hlsym{, }\hlstd{list}\hlsym{$<$}\hlstd{edge}\hlsym{$>$\&\ }\Righttorque\\ +\hlline{113\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{rejected}\hlsym{,\ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{max\textunderscore cost}\hlsym{,\ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{m}\hlsym{)\{}\\ +\hlline{114\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{union\textunderscore find\ }\hlkwd{list}\hlstd{}\hlsym{(}\hlstd{n}\hlsym{);}\\ +\hlline{115\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{res}\hlsym{=}\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{116\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{m\ }\hlsym{$>$\ }\hlstd{max\textunderscore cost}\hlsym{)}\\ +\hlline{117\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{bucket\textunderscore sort}\hlstd{}\hlsym{(}\hlstd{e}\hlsym{,}\hlstd{max\textunderscore cost}\hlsym{);}\\ +\hlline{118\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{else}\\ +\hlline{119\ }\hlstd{\ e}\hlsym{.}\hlstd{}\hlkwd{sort}\hlstd{}\hlsym{(}\hlstd{compare}\hlsym{);}\\ +\hlline{120\ }\hlstd{\\ +\hlline{121\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{foreachin}\hlstd{}\hlsym{(}\hlstd{it}\hlsym{,}\hlstd{e}\hlsym{)\{}\\ +\hlline{122\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{s}\hlsym{,}\hlstd{f}\hlsym{;}\\ +\hlline{123\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{s}\hlsym{=}\hlstd{it}\hlsym{{-}$>$}\hlstd{start}\hlsym{;}\\ +\hlline{124\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{f}\hlsym{=}\hlstd{it}\hlsym{{-}$>$}\hlstd{end}\hlsym{;}\\ +\hlline{125\ }\hlstd{\\ +\hlline{126\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if}\hlstd{}\hlsym{(}\hlstd{list}\hlsym{.}\hlstd{}\hlkwd{Find}\hlstd{}\hlsym{(}\hlstd{s}\hlsym{)==}\hlstd{list}\hlsym{.}\hlstd{}\hlkwd{Find}\hlstd{}\hlsym{(}\hlstd{f}\hlsym{))\{}\\ +\hlline{127\ }\hlstd{\\ +\hlline{128\ }}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{rejected}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{({*}}\hlstd{it}\hlsym{);}\\ +\hlline{129\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{continue}\hlstd{}\hlsym{;}\\ +\hlline{130\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{131\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{else}\hlstd{}\hlsym{\{}\\ +\hlline{132\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{list}\hlsym{.}\hlstd{}\hlkwd{Union}\hlstd{}\hlsym{(}\hlstd{s}\hlsym{,}\hlstd{f}\hlsym{);}\\ +\hlline{133\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{res\ }\hlsym{+=\ }\hlstd{it}\hlsym{{-}$>$}\hlstd{cost}\hlsym{;}\\ +\hlline{134\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{adj}\hlsym{{[}}\hlstd{s}\hlsym{{]}.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{({*}}\hlstd{it}\hlsym{);}\\ +\hlline{135\ }\hlstd{}\hlstd{\ \ \ \ \ }\hlstd{adj}\hlsym{{[}}\hlstd{f}\hlsym{{]}.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{edge}\hlstd{}\hlsym{(}\hlstd{it}\hlsym{{-}$>$}\hlstd{end}\hlsym{,}\hlstd{it}\hlsym{{-}$>$}\hlstd{start}\hlsym{,}\hlstd{it}\hlsym{{-}$>$}\hlstd{cost}\hlsym{));}\\ +\hlline{136\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{137\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{138\ }\hlstd{\\ +\hlline{139\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{res}\hlsym{;}\\ +\hlline{140\ }\hlstd{}\\ +\hlline{141\ }\hlsym{\}}\\ +\hlline{142\ }\hlstd{}\\ +\hlline{143\ }\\ +\hlline{144\ }\hlkwc{inline\ }\hlstd{}\hlkwb{void\ }\hlstd{}\hlkwd{dfs\textunderscore fill\textunderscore max}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{u}\hlsym{,\ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{x}\hlsym{,}\hlstd{vector}\hlsym{$<$}\hlstd{list}\hlsym{$<$}\hlstd{edge}\hlsym{$>$\ $>$\&\ }\hlstd{mst\textunderscore adjacency}\hlsym{,\ }\Righttorque\\ +\hlline{145\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{vector}\hlsym{$<$}\hlstd{vector}\hlsym{$<$}\hlstd{edge}\hlsym{{*}$>$\ $>$\&\ }\hlstd{max}\hlsym{)\{}\\ +\hlline{146\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{foreachin}\hlstd{}\hlsym{(}\hlstd{v}\hlsym{,(}\hlstd{mst\textunderscore adjacency}\hlsym{{[}}\hlstd{x}\hlsym{{]}))\{}\\ +\hlline{147\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ }\hlstd{}\hlkwa{if}\hlstd{}\hlsym{(\ }\hlstd{max}\hlsym{{[}}\hlstd{u}\hlsym{{]}{[}}\hlstd{v}\hlsym{{-}$>$}\hlstd{end}\hlsym{{]}\ ==\ }\hlstd{NULL\ }\hlsym{\&\&\ }\hlstd{v}\hlsym{{-}$>$}\hlstd{end\ }\hlsym{!=\ }\hlstd{u}\hlsym{)\{}\\ +\hlline{148\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if}\hlstd{}\hlsym{(}\hlstd{x}\hlsym{==}\hlstd{u\ }\hlsym{\textbar \textbar \ }\hlstd{v}\hlsym{{-}$>$}\hlstd{cost\ }\hlsym{$>$\ }\hlstd{max}\hlsym{{[}}\hlstd{u}\hlsym{{]}{[}}\hlstd{x}\hlsym{{]}{-}$>$}\hlstd{cost}\hlsym{)\{}\\ +\hlline{149\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{max}\hlsym{{[}}\hlstd{u}\hlsym{{]}{[}}\hlstd{v}\hlsym{{-}$>$}\hlstd{end}\hlsym{{]}\ =\ \&({*}}\hlstd{v}\hlsym{);}\\ +\hlline{150\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{151\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{else}\hlstd{}\hlsym{\{}\\ +\hlline{152\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{max}\hlsym{{[}}\hlstd{u}\hlsym{{]}{[}}\hlstd{v}\hlsym{{-}$>$}\hlstd{end}\hlsym{{]}\ =\ }\hlstd{max}\hlsym{{[}}\hlstd{u}\hlsym{{]}{[}}\hlstd{x}\hlsym{{]};}\\ +\hlline{153\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{154\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{dfs\textunderscore fill\textunderscore max}\hlstd{}\hlsym{(}\hlstd{u}\hlsym{,}\hlstd{v}\hlsym{{-}$>$}\hlstd{end}\hlsym{,}\hlstd{mst\textunderscore adjacency}\hlsym{,}\hlstd{max}\hlsym{);}\\ +\hlline{155\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{156\ }\hlstd{\\ +\hlline{157\ }}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{158\ }\hlstd{}\hlsym{\}}\\ +\hlline{159\ }\hlstd{}\\ +\hlline{160\ }\hlkwc{inline\ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{}\hlkwd{second\textunderscore mst}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{n}\hlsym{,\ }\hlstd{vector}\hlsym{$<$}\hlstd{list}\hlsym{$<$}\hlstd{edge}\hlsym{$>$\ $>$\&\ }\hlstd{mst\textunderscore adjacency}\hlsym{,\ }\hlstd{list}\hlsym{$<$}\hlstd{edge}\hlsym{$>$\&\ }\Righttorque\\ +\hlline{161\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{rejected}\hlsym{,}\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{minimum\textunderscore cost}\hlsym{)\{}\\ +\hlline{162\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{vector}\hlsym{$<$}\hlstd{vector}\hlsym{$<$}\hlstd{edge}\hlsym{{*}$>$\ $>$\ }\hlstd{}\hlkwd{max}\hlstd{}\hlsym{(}\hlstd{n}\hlsym{,}\hlstd{vector}\hlsym{$<$}\hlstd{edge}\hlsym{{*}$>$(}\hlstd{n}\hlsym{,}\hlstd{NULL}\hlsym{));}\\ +\hlline{163\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{list}\hlsym{$<$}\hlstd{edge}\hlsym{$>$::}\hlstd{iterator\ it\ }\hlsym{=\ }\hlstd{rejected}\hlsym{.}\hlstd{}\hlkwd{begin}\hlstd{}\hlsym{();}\\ +\hlline{164\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{start\ }\hlsym{=\ }\hlstd{it}\hlsym{{-}$>$}\hlstd{start}\hlsym{;}\\ +\hlline{165\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{end\ }\hlsym{=\ }\hlstd{it}\hlsym{{-}$>$}\hlstd{end}\hlsym{;}\\ +\hlline{166\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{dfs\textunderscore fill\textunderscore max}\hlstd{}\hlsym{(}\hlstd{start}\hlsym{,}\hlstd{start}\hlsym{,}\hlstd{mst\textunderscore adjacency}\hlsym{,\ }\hlstd{max}\hlsym{);}\\ +\hlline{167\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{old\textunderscore cost}\hlsym{=}\hlstd{max}\hlsym{{[}}\hlstd{start}\hlsym{{]}{[}}\hlstd{end}\hlsym{{]}{-}$>$}\hlstd{cost}\hlsym{;}\\ +\hlline{168\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{new\textunderscore cost}\hlsym{=}\hlstd{it}\hlsym{{-}$>$}\hlstd{cost}\hlsym{;}\\ +\hlline{169\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{minimum}\hlsym{=\ }\hlstd{new\textunderscore cost\ }\hlsym{{-}\ }\hlstd{old\textunderscore cost}\hlsym{;}\\ +\hlline{170\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{it}\hlsym{++;}\\ +\hlline{171\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{for}\hlstd{}\hlsym{(}\hlstd{it}\hlsym{;}\hlstd{it\ }\hlsym{!=\ }\hlstd{rejected}\hlsym{.}\hlstd{}\hlkwd{end}\hlstd{}\hlsym{();}\hlstd{it}\hlsym{++\ )\{}\\ +\hlline{172\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{start\ }\hlsym{=\ }\hlstd{it}\hlsym{{-}$>$}\hlstd{start}\hlsym{;}\\ +\hlline{173\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{end\ }\hlsym{=\ }\hlstd{it}\hlsym{{-}$>$}\hlstd{end}\hlsym{;}\\ +\hlline{174\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if}\hlstd{}\hlsym{(}\hlstd{max}\hlsym{{[}}\hlstd{start}\hlsym{{]}{[}}\hlstd{end}\hlsym{{]}\ ==\ }\hlstd{NULL}\hlsym{)}\hlstd{}\hlkwd{dfs\textunderscore fill\textunderscore max}\hlstd{}\hlsym{(}\hlstd{start}\hlsym{,}\hlstd{start}\hlsym{,}\hlstd{mst\textunderscore adjacency}\hlsym{,\ }\hlstd{max}\hlsym{);}\\ +\hlline{175\ }\hlstd{\\ +\hlline{176\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{aux}\hlsym{=}\hlstd{it}\hlsym{{-}$>$}\hlstd{cost}\hlsym{{-}\ }\hlstd{max}\hlsym{{[}}\hlstd{start}\hlsym{{]}{[}}\hlstd{end}\hlsym{{]}{-}$>$}\hlstd{cost}\hlsym{;}\\ +\hlline{177\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if}\hlstd{}\hlsym{(}\hlstd{aux\ }\hlsym{$<$\ }\hlstd{minimum}\hlsym{)\{}\\ +\hlline{178\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if}\hlstd{}\hlsym{(}\hlstd{aux\ }\hlsym{==\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)}\hlstd{}\hlkwa{return\ }\hlstd{minimum\textunderscore cost}\hlsym{;}\\ +\hlline{179\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{minimum}\hlsym{=\ }\hlstd{aux}\hlsym{;}\\ +\hlline{180\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{new\textunderscore cost\ }\hlsym{=}\hlstd{\ \ }\hlsym{}\hlstd{it}\hlsym{{-}$>$}\hlstd{cost}\hlsym{;}\\ +\hlline{181\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{old\textunderscore cost\ }\hlsym{=\ }\hlstd{max}\hlsym{{[}}\hlstd{start}\hlsym{{]}{[}}\hlstd{end}\hlsym{{]}{-}$>$}\hlstd{cost}\hlsym{;}\\ +\hlline{182\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{183\ }\hlstd{\\ +\hlline{184\ }}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{185\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{minimum\textunderscore cost\ }\hlsym{{-}\ }\hlstd{old\textunderscore cost\ }\hlsym{+\ }\hlstd{new\textunderscore cost}\hlsym{;}\\ +\hlline{186\ }\hlstd{}\hlsym{\}}\\ +\hlline{187\ }\hlstd{}\\ +\hlline{188\ }\\ +\hlline{189\ }\hlkwb{int\ }\hlstd{}\hlkwd{main}\hlstd{}\hlsym{()\{}\\ +\hlline{190\ }\hlstd{}\hlkwb{int\ }\hlstd{cases}\hlsym{;}\\ +\hlline{191\ }\hlstd{cin}\hlsym{$>$$>$}\hlstd{cases}\hlsym{;}\\ +\hlline{192\ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{n}\hlsym{;}\\ +\hlline{193\ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{m}\hlsym{;}\\ +\hlline{194\ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{from}\hlsym{,}\hlstd{to}\hlsym{,}\hlstd{cost}\hlsym{;}\\ +\hlline{195\ }\hlstd{}\\ +\hlline{196\ }\\ +\hlline{197\ }\hlkwa{while}\hlstd{}\hlsym{(}\hlstd{cases\ }\hlsym{$>$\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\{}\\ +\hlline{198\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{scanf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{``\%hu\ \%hu''}\hlstd{}\hlsym{,\&}\hlstd{n}\hlsym{,\&}\hlstd{m}\hlsym{);}\\ +\hlline{199\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{vector}\hlsym{$<$}\hlstd{list}\hlsym{$<$}\hlstd{edge}\hlsym{$>$\ $>$\ }\hlstd{}\hlkwd{mst\textunderscore adjacency}\hlstd{}\hlsym{(}\hlstd{n}\hlsym{);}\\ +\hlline{200\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{list}\hlsym{$<$}\hlstd{edge}\hlsym{$>$\ }\hlstd{rejected}\hlsym{;}\\ +\hlline{201\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{list}\hlsym{$<$}\hlstd{edge}\hlsym{$>$\ }\hlstd{l}\hlsym{;}\\ +\hlline{202\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{cant\textunderscore edges}\hlsym{=}\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{203\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{max\textunderscore cost\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{204\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{while}\hlstd{}\hlsym{(}\hlstd{cant\textunderscore edges\ }\hlsym{$<$\ }\hlstd{m}\hlsym{)\{}\\ +\hlline{205\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{scanf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{``\%hu\ \%hu\ \%hu''}\hlstd{}\hlsym{,\&}\hlstd{from}\hlsym{,\&}\hlstd{to}\hlsym{,\&}\hlstd{cost}\hlsym{);}\\ +\hlline{206\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if}\hlstd{}\hlsym{(}\hlstd{cost\ }\hlsym{$>$\ }\hlstd{max\textunderscore cost}\hlsym{)}\hlstd{max\textunderscore cost\ }\hlsym{=\ }\hlstd{cost}\hlsym{;}\\ +\hlline{207\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{l}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{edge}\hlstd{}\hlsym{(}\hlstd{from}\hlsym{{-}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{,}\hlstd{to}\hlsym{{-}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{,}\hlstd{cost}\hlsym{));}\\ +\hlline{208\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{cant\textunderscore edges}\hlsym{++;}\\ +\hlline{209\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{210\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{unsigned\ short\ }\hlstd{k\ }\hlsym{=}\hlstd{}\hlkwd{kruskal}\hlstd{}\hlsym{(}\hlstd{l}\hlsym{,}\hlstd{n}\hlsym{,}\hlstd{mst\textunderscore adjacency}\hlsym{,}\hlstd{rejected}\hlsym{,}\hlstd{max\textunderscore cost}\hlsym{,}\hlstd{m}\hlsym{);}\\ +\hlline{211\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlslc{//unsigned\ short\ k\ =kruskal(l,n,mst\textunderscore adjacency,rejected);}\\ +\hlline{212\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{k}\hlsym{$<$$<$}\hlstd{}\hlstr{``\ ''}\hlstd{}\hlsym{;}\\ +\hlline{213\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{}\hlkwd{second\textunderscore mst}\hlstd{}\hlsym{(}\hlstd{n}\hlsym{,}\hlstd{mst\textunderscore adjacency}\hlsym{,}\hlstd{rejected}\hlsym{,}\hlstd{k}\hlsym{)$<$$<$}\hlstd{endl}\hlsym{;}\\ +\hlline{214\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{cases}\hlsym{{-}{-};}\\ +\hlline{215\ }\hlstd{}\hlsym{\}}\\ +\hlline{216\ }\hlstd{}\hlkwa{return\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{217\ }\hlstd{}\hlsym{\}}\\ +\hlline{218\ }\hlstd{}\\ +\hlline{219\ }\\ +\hlline{220\ }\\ +\hlline{221\ }\\ +\hlline{222\ }\\ +\hlline{223\ }\\ +\mbox{} +\normalfont +\shorthandon{"} diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/algorithm.sty b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/algorithm.sty new file mode 100644 index 0000000..34e1f1f --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/algorithm.sty @@ -0,0 +1,96 @@ +% ALGORITHM STYLE -- Released 8 April 1996 +% for LaTeX-2e +% Copyright -- 1994 Peter Williams +% +% E-mail pwil3058@bigpond.net.au +% +% This style file is free software; you can redistribute it and/or +% modify it under the terms of the GNU Lesser General Public +% License as published by the Free Software Foundation; either +% version 2 of the License, or (at your option) any later version. +% +% This style file is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +% Lesser General Public License for more details. +% +% You should have received a copy of the GNU Lesser General Public +% License along with this style file; if not, write to the +% Free Software Foundation, Inc., 59 Temple Place - Suite 330, +% Boston, MA 02111-1307, USA. +% +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{algorithm} +\typeout{Document Style `algorithm' - floating environment} + +\RequirePackage{float} +\RequirePackage{ifthen} +\newcommand{\ALG@within}{nothing} +\newboolean{ALG@within} +\setboolean{ALG@within}{false} +\newcommand{\ALG@floatstyle}{ruled} +\newcommand{\ALG@name}{Algorithm} +\newcommand{\listalgorithmname}{List of \ALG@name s} + +% Declare Options +% first appearance +\DeclareOption{plain}{ + \renewcommand{\ALG@floatstyle}{plain} +} +\DeclareOption{ruled}{ + \renewcommand{\ALG@floatstyle}{ruled} +} +\DeclareOption{boxed}{ + \renewcommand{\ALG@floatstyle}{boxed} +} +% then numbering convention +\DeclareOption{part}{ + \renewcommand{\ALG@within}{part} + \setboolean{ALG@within}{true} +} +\DeclareOption{chapter}{ + \renewcommand{\ALG@within}{chapter} + \setboolean{ALG@within}{true} +} +\DeclareOption{section}{ + \renewcommand{\ALG@within}{section} + \setboolean{ALG@within}{true} +} +\DeclareOption{subsection}{ + \renewcommand{\ALG@within}{subsection} + \setboolean{ALG@within}{true} +} +\DeclareOption{subsubsection}{ + \renewcommand{\ALG@within}{subsubsection} + \setboolean{ALG@within}{true} +} +\DeclareOption{nothing}{ + \renewcommand{\ALG@within}{nothing} + \setboolean{ALG@within}{true} +} +\DeclareOption*{\edef\ALG@name{\CurrentOption}} + +% ALGORITHM +% +\ProcessOptions +\floatstyle{\ALG@floatstyle} +\ifthenelse{\boolean{ALG@within}}{ + \ifthenelse{\equal{\ALG@within}{part}} + {\newfloat{algorithm}{htbp}{loa}[part]}{} + \ifthenelse{\equal{\ALG@within}{chapter}} + {\newfloat{algorithm}{htbp}{loa}[chapter]}{} + \ifthenelse{\equal{\ALG@within}{section}} + {\newfloat{algorithm}{htbp}{loa}[section]}{} + \ifthenelse{\equal{\ALG@within}{subsection}} + {\newfloat{algorithm}{htbp}{loa}[subsection]}{} + \ifthenelse{\equal{\ALG@within}{subsubsection}} + {\newfloat{algorithm}{htbp}{loa}[subsubsection]}{} + \ifthenelse{\equal{\ALG@within}{nothing}} + {\newfloat{algorithm}{htbp}{loa}}{} +}{ + \newfloat{algorithm}{htbp}{loa} +} +\floatname{algorithm}{\ALG@name} + +\newcommand{\listofalgorithms}{\listof{algorithm}{\listalgorithmname}} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/algorithmic.sty b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/algorithmic.sty new file mode 100644 index 0000000..4dcaa7c --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/algorithmic.sty @@ -0,0 +1,194 @@ +% ALGORITHMIC STYLE for LaTeX version 2e +% +% This style file is free software; you can redistribute it and/or +% modify it under the terms of the GNU Lesser General Public +% License as published by the Free Software Foundation; either +% version 2 of the License, or (at your option) any later version. +% +% This style file is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +% Lesser General Public License for more details. +% +% You should have received a copy of the GNU Lesser General Public +% License along with this style file; if not, write to the +% Free Software Foundation, Inc., 59 Temple Place - Suite 330, +% Boston, MA 02111-1307, USA. +% +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{algorithmic}[2006/06/02] +\typeout{Document Style `algorithmic' - environment} +% +\RequirePackage{ifthen} +\RequirePackage{calc} +\RequirePackage{keyval} +\newboolean{ALC@noend} +\setboolean{ALC@noend}{false} +\newcounter{ALC@line} +\newcounter{ALC@rem} +\newcounter{ALC@depth} +\newlength{\ALC@tlm} +% +\DeclareOption{noend}{\setboolean{ALC@noend}{true}} +% +\ProcessOptions +% +% For keyval-style options +\def\algsetup{\setkeys{ALG}} +% +% For indentation of algorithms +\newlength{\algorithmicindent} +\setlength{\algorithmicindent}{0pt} +\define@key{ALG}{indent}{\setlength{\algorithmicindent}{#1}} +\ifthenelse{\lengthtest{\algorithmicindent=0pt}}% + {\setlength{\algorithmicindent}{1em}}{} +% +% For line numbers' delimiters +\newcommand{\ALC@linenodelimiter}{:} +\define@key{ALG}{linenodelimiter}{\renewcommand{\ALC@linenodelimiter}{#1}} + +% +% For line numbers' size +\newcommand{\ALC@linenosize}{\footnotesize} +\define@key{ALG}{linenosize}{\renewcommand{\ALC@linenosize}{#1}} + +% +% ALGORITHMIC +\newcommand{\algorithmicrequire}{\textbf{Require:}} +\newcommand{\algorithmicensure}{\textbf{Ensure:}} +\newcommand{\algorithmicparams}[1]{\textcolor{RawSienna}{\textbf{Entrada:}} #1} +\newcommand{\algorithmiccomment}[1]{\textcolor{Purple}{\{#1\}}} +\newcommand{\algorithmicend}{\textbf{end}} +\newcommand{\algorithmicif}{\textbf{if}} +\newcommand{\algorithmicthen}{\textbf{then}} +\newcommand{\algorithmicelse}{\textbf{else}} +\newcommand{\algorithmicelsif}{\algorithmicelse\ \algorithmicif} +\newcommand{\algorithmicendif}{\algorithmicend\ \algorithmicif} +\newcommand{\algorithmicfor}{\textbf{for}} +\newcommand{\algorithmicforall}{\textbf{for all}} +\newcommand{\algorithmicdo}{\textbf{do}} +\newcommand{\algorithmicendfor}{\algorithmicend\ \algorithmicfor} +\newcommand{\algorithmicwhile}{\textbf{while}} +\newcommand{\algorithmicendwhile}{\algorithmicend\ \algorithmicwhile} +\newcommand{\algorithmicloop}{\textbf{loop}} +\newcommand{\algorithmicendloop}{\algorithmicend\ \algorithmicloop} +\newcommand{\algorithmicrepeat}{\textbf{repeat}} +\newcommand{\algorithmicuntil}{\textbf{until}} +\newcommand{\algorithmicprint}{\textbf{print}} +\newcommand{\algorithmicreturn}{\textbf{return}} +\newcommand{\algorithmictrue}{\textbf{true}} +\newcommand{\algorithmicfalse}{\textbf{false}} +\def\ALC@setref{% + \def\@currentlabel{\theALC@line}% +} +\def\ALC@item[#1]{% +\if@noparitem \@donoparitem + \else \if@inlabel \indent \par \fi + \ifhmode \unskip\unskip \par \fi + \if@newlist \if@nobreak \@nbitem \else + \addpenalty\@beginparpenalty + \addvspace\@topsep \addvspace{-\parskip}\fi + \else \addpenalty\@itempenalty \addvspace\itemsep + \fi + \global\@inlabeltrue +\fi +\everypar{\global\@minipagefalse\global\@newlistfalse + \if@inlabel\global\@inlabelfalse \hskip -\parindent \box\@labels + \penalty\z@ \fi + \everypar{}}\global\@nobreakfalse +\if@noitemarg \@noitemargfalse \if@nmbrlist \refstepcounter{\@listctr}\fi \fi +\sbox\@tempboxa{\makelabel{#1}}% +\global\setbox\@labels + \hbox{\unhbox\@labels \hskip \itemindent + \hskip -\labelwidth \hskip -\ALC@tlm + \ifdim \wd\@tempboxa >\labelwidth + \box\@tempboxa + \else \hbox to\labelwidth {\unhbox\@tempboxa}\fi + \hskip \ALC@tlm}\ignorespaces} +% +\newenvironment{algorithmic}[1][0]{ +\setcounter{ALC@depth}{\@listdepth}% +\let\@listdepth\c@ALC@depth% +\let\@item\ALC@item% + \newcommand{\ALC@lno}{% +\ifthenelse{\equal{\arabic{ALC@rem}}{0}} +{{\ALC@linenosize \arabic{ALC@line}\ALC@linenodelimiter}}{}% +} +\let\@listii\@listi +\let\@listiii\@listi +\let\@listiv\@listi +\let\@listv\@listi +\let\@listvi\@listi +\let\@listvii\@listi + \newenvironment{ALC@g}{ + \begin{list}{\ALC@lno}{ \itemsep\z@ \itemindent\z@ + \listparindent\z@ \rightmargin\z@ + \topsep\z@ \partopsep\z@ \parskip\z@\parsep\z@ + \leftmargin \algorithmicindent%1em + \addtolength{\ALC@tlm}{\leftmargin} + } + } + {\end{list}} + \newcommand{\ALC@it}{\refstepcounter{ALC@rem}\refstepcounter{ALC@line}\ifthenelse{\equal{\arabic{ALC@rem}}{#1}}{\setcounter{ALC@rem}{0}}{}\item\ALC@setref} + \newcommand{\ALC@com}[1]{\ifthenelse{\equal{##1}{default}}% +{}{\ \algorithmiccomment{##1}}} + \newcommand{\REQUIRE}{\item[\algorithmicrequire]} + \newcommand{\ENSURE}{\item[\algorithmicensure]} + \newcommand{\PRINT}{\ALC@it\algorithmicprint{}\ \ } + \newcommand{\RETURN}{\ALC@it\algorithmicreturn{}\ \ } + \newcommand{\TRUE}{\algorithmictrue{}} + \newcommand{\FALSE}{\algorithmicfalse{}} + \newcommand{\STATE}{\ALC@it} + \newcommand{\STMT}{\ALC@it} + \newcommand{\PARAMS}[1]{\item[\algorithmicparams{##1}]} + \newcommand{\COMMENT}[1]{\algorithmiccomment{##1}} + \newenvironment{ALC@if}{\begin{ALC@g}}{\end{ALC@g}} + \newenvironment{ALC@for}{\begin{ALC@g}}{\end{ALC@g}} + \newenvironment{ALC@whl}{\begin{ALC@g}}{\end{ALC@g}} + \newenvironment{ALC@loop}{\begin{ALC@g}}{\end{ALC@g}} + \newenvironment{ALC@rpt}{\begin{ALC@g}}{\end{ALC@g}} + \renewcommand{\\}{\@centercr} + \newcommand{\IF}[2][default]{\ALC@it\algorithmicif\ ##2\ \algorithmicthen% +\ALC@com{##1}\begin{ALC@if}} + \newcommand{\ELSE}[1][default]{\end{ALC@if}\ALC@it\algorithmicelse% +\ALC@com{##1}\begin{ALC@if}} + \newcommand{\ELSIF}[2][default]% +{\end{ALC@if}\ALC@it\algorithmicelsif\ ##2\ \algorithmicthen% +\ALC@com{##1}\begin{ALC@if}} + \newcommand{\FOR}[2][default]{\ALC@it\algorithmicfor\ ##2\ \algorithmicdo% +\ALC@com{##1}\begin{ALC@for}} + \newcommand{\FORALL}[2][default]{\ALC@it\algorithmicforall\ ##2\ % +\algorithmicdo% +\ALC@com{##1}\begin{ALC@for}} + \newcommand{\WHILE}[2][default]{\ALC@it\algorithmicwhile\ ##2\ % +\algorithmicdo% +\ALC@com{##1}\begin{ALC@whl}} + \newcommand{\LOOP}[1][default]{\ALC@it\algorithmicloop% +\ALC@com{##1}\begin{ALC@loop}} + \newcommand{\REPEAT}[1][default]{\ALC@it\algorithmicrepeat% +\ALC@com{##1}\begin{ALC@rpt}} + \newcommand{\UNTIL}[1]{\end{ALC@rpt}\ALC@it\algorithmicuntil\ ##1} + \ifthenelse{\boolean{ALC@noend}}{ + \newcommand{\ENDIF}{\end{ALC@if}} + \newcommand{\ENDFOR}{\end{ALC@for}} + \newcommand{\ENDWHILE}{\end{ALC@whl}} + \newcommand{\ENDLOOP}{\end{ALC@loop}} + }{ + \newcommand{\ENDIF}{\end{ALC@if}\ALC@it\algorithmicendif} + \newcommand{\ENDFOR}{\end{ALC@for}\ALC@it\algorithmicendfor} + \newcommand{\ENDWHILE}{\end{ALC@whl}\ALC@it\algorithmicendwhile} + \newcommand{\ENDLOOP}{\end{ALC@loop}\ALC@it\algorithmicendloop} + } + \renewcommand{\@toodeep}{} + \begin{list}{\ALC@lno}{\setcounter{ALC@rem}{0}\setcounter{ALC@line}{0}% + \itemsep\z@ \itemindent\z@ \listparindent\z@% + \partopsep\z@ \parskip\z@ \parsep\z@% + \labelsep 0.5em \topsep 0.2em% +\ifthenelse{\equal{#1}{0}} + {\labelwidth 0.5em } + {\labelwidth 1.2em } +\leftmargin\labelwidth \addtolength{\leftmargin}{\labelsep} + \ALC@tlm\labelsep + } +} +{\end{list}} diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/caratula.sty b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/caratula.sty new file mode 100644 index 0000000..7d4a979 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/caratula.sty @@ -0,0 +1,290 @@ +% ************************************************************************** +% +% Package 'caratula', version 0.3 (para componer caratulas de TPs del DC). +% +% En caso de dudas, problemas o sugerencias sobre este package escribir a +% Brian J. Cardiff (bcardif arroba gmail.com). +% Nico Rosner (nrosner arroba dc.uba.ar). +% +% ************************************************************************** + +% ----- Informacion sobre el package para el sistema ----------------------- + +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{caratula}[2005/08/09 v0.4 Para componer caratulas de TPs del DC] +\RequirePackage{ifthen} +\usepackage[pdftex]{graphicx} + +% ----- Imprimir un mensajito al procesar un .tex que use este package ----- + +\typeout{Cargando package 'caratula' v0.4 (2006/09/29)} + +% ----- Algunas variables -------------------------------------------------- + +\let\Materia\relax +\let\Submateria\relax +\let\Titulo\relax +\let\Subtitulo\relax +\let\Grupo\relax +\let\Fecha\relax +\let\Logoimagefile\relax +\let\Resumen\relax +\newcommand{\LabelIntegrantes}{} +\newboolean{showLU} +\newboolean{showDirectores} + +% ----- Comandos para que el usuario defina las variables ------------------ + +\def\materia#1{\def\Materia{#1}} +\def\submateria#1{\def\Submateria{#1}} +\def\titulo#1{\def\Titulo{#1}} +\def\subtitulo#1{\def\Subtitulo{#1}} +\def\grupo#1{\def\Grupo{#1}} +\def\fecha#1{\def\Fecha{#1}} +\def\logoimagefile#1{\def\Logoimagefile{#1}} +\def\resumen#1{\def\Resumen{#1}} + +% ----- Token list para los integrantes ------------------------------------ + +\newtoks\intlist\intlist={} + +\newtoks\intlistSinLU\intlistSinLU={} + +\newcounter{integrantesCount} +\setcounter{integrantesCount}{0} +\newtoks\intTabNombre\intTabNombre={} +\newtoks\intTabLU\intTabLU={} +\newtoks\intTabEmail\intTabEmail={} + +\newcounter{directoresCount} +\setcounter{directoresCount}{0} +\newtoks\direcTabNombre\direcTabNombre={} +\newtoks\direcTabEmail\direcTabEmail={} + +% ----- Comando para que el usuario agregue integrantes -------------------- + +\def\integrante#1#2#3{% + \intlist=\expandafter{\the\intlist\rule{0pt}{1.2em}#1&\tt #3\\[0.2em]}% + \intlistSinLU=\expandafter{\the\intlistSinLU\rule{0pt}{1.2em}#1 & \tt #3\\[0.2em]}% + % + \ifthenelse{\value{integrantesCount} > 0}{% + \intTabNombre=\expandafter{\the\intTabNombre & #1}% + \intTabLU=\expandafter{\the\intTabLU & #2}% + \intTabEmail=\expandafter{\the\intTabEmail & \tt #3}% + }{ + \intTabNombre=\expandafter{\the\intTabNombre #1}% + \intTabLU=\expandafter{\the\intTabLU #2}% + \intTabEmail=\expandafter{\the\intTabEmail \tt #3}% + }% + \addtocounter{integrantesCount}{1}% +} + +\def\director#1#2{% + \ifthenelse{\value{directoresCount} > 0}{% + \direcTabNombre=\expandafter{\the\direcTabNombre & #1}% + \direcTabEmail=\expandafter{\the\direcTabEmail & \tt #2}% + }{ + \direcTabNombre=\expandafter{\the\direcTabNombre #1}% + \direcTabEmail=\expandafter{\the\direcTabEmail \tt #2}% + }% + \addtocounter{directoresCount}{1}% +} + +% ----- Macro para generar la tabla de integrantes ------------------------- + +\newcommand{\tablaIntegrantes}{\ } + +\newcommand{\tablaIntegrantesVertical}{% +\ifthenelse{\boolean{showLU}}{% + \begin{tabular}[t]{| l @{\hspace{4ex}} c @{\hspace{4ex}} l|} + \hline + \multicolumn{1}{|c}{\rule{0pt}{1.2em} \LabelIntegrantes} & LU & \multicolumn{1}{c|}{Correo electr\'onico} \\[0.2em] + \hline \hline + \the\intlist + \hline + \end{tabular} +}{ + \begin{tabular}[t]{| l @{\hspace{4ex}} @{\hspace{4ex}} l|} + \hline + \multicolumn{1}{|c}{\rule{0pt}{1.2em} \LabelIntegrantes} & \multicolumn{1}{c|}{Correo electr\'onico} \\[0.2em] + \hline \hline + \the\intlistSinLU + \hline + \end{tabular} + }% +} + +\newcommand{\tablaIntegrantesHorizontal}{% + \begin{tabular}[t]{ *{\value{integrantesCount}}{c} } + \the\intTabNombre \\% +\ifthenelse{\boolean{showLU}}{ + \the\intTabLU \\% +}{} + \the\intTabEmail % + \end{tabular}% +} + +\newcommand{\tablaDirectores}{% +\ifthenelse{\boolean{showDirectores}}{% + \bigskip + Directores + + \smallskip + \begin{tabular}[t]{ *{\value{directoresCount}}{c} } + \the\direcTabNombre \\% + \the\direcTabEmail % + \end{tabular}% +}{}% +} + +% ----- Codigo para manejo de errores -------------------------------------- + +\def\se{\let\ifsetuperror\iftrue} +\def\ifsetuperror{% + \let\ifsetuperror\iffalse + \ifx\Materia\relax\se\errhelp={Te olvidaste de proveer una \materia{}.}\fi + \ifx\Titulo\relax\se\errhelp={Te olvidaste de proveer un \titulo{}.}\fi + \edef\mlist{\the\intlist}\ifx\mlist\empty\se% + \errhelp={Tenes que proveer al menos un \integrante{nombre}{lu}{email}.}\fi + \expandafter\ifsetuperror} + + +% ----- \maketitletxt correspondiente a la versión v0.2.1 (texto v0.2 + fecha ) --------- + +\def\maketitletxt{% + \ifsetuperror\errmessage{Faltan datos de la caratula! Ingresar 'h' para mas informacion.}\fi + \thispagestyle{empty} + \begin{center} + \vspace*{\stretch{2}} + {\LARGE\textbf{\Materia}}\\[1em] + \ifx\Submateria\relax\else{\Large \Submateria}\\[0.5em]\fi + \ifx\Fecha\relax\else{\Large \Fecha}\\[0.5em]\fi + \par\vspace{\stretch{1}} + {\large Departamento de Computaci\'on}\\[0.5em] + {\large Facultad de Ciencias Exactas y Naturales}\\[0.5em] + {\large Universidad de Buenos Aires} + \par\vspace{\stretch{3}} + {\Large \textbf{\Titulo}}\\[0.8em] + {\Large \Subtitulo} + \par\vspace{\stretch{3}} + \ifx\Grupo\relax\else\textbf{\Grupo}\par\bigskip\fi + \tablaIntegrantes + \end{center} + \vspace*{\stretch{3}} + \newpage} + +% ----- \maketitletxtlogo correspondiente v0.2.1 (texto con fecha y logo) --------- + +\def\maketitletxtlogo{% + \ifsetuperror\errmessage{Faltan datos de la caratula! Ingresar 'h' para mas informacion.}\fi + \thispagestyle{empty} + \begin{center} + \ifx\Logoimagefile\relax\else\includegraphics{\Logoimagefile}\fi \hfill \includegraphics{./figuras/logo_dc.jpg}\\[1em] + \vspace*{\stretch{2}} + {\LARGE\textbf{\Materia}}\\[1em] + \ifx\Submateria\relax\else{\Large \Submateria}\\[0.5em]\fi + \ifx\Fecha\relax\else{\large \Fecha}\\[0.5em]\fi + \par\vspace{\stretch{1}} + {\large Departamento de Computaci\'on}\\[0.5em] + {\large Facultad de Ciencias Exactas y Naturales}\\[0.5em] + {\large Universidad de Buenos Aires} + \par\vspace{\stretch{3}} + {\Large \textbf{\Titulo}}\\[0.8em] + {\Large \Subtitulo} + \par\vspace{\stretch{3}} + \ifx\Grupo\relax\else\textbf{\Grupo}\par\bigskip\fi + \tablaIntegrantes + \end{center} + \vspace*{\stretch{4}} + \newpage} + +% ----- \maketitlegraf correspondiente a la versión v0.3 (gráfica) ------------- + +\def\maketitlegraf{% + \ifsetuperror\errmessage{Faltan datos de la caratula! Ingresar 'h' para mas informacion.}\fi +% + \thispagestyle{empty} + + \ifx\Logoimagefile\relax\else\includegraphics{\Logoimagefile}\fi \hfill \includegraphics{./figuras/logo_dc.jpg} + + \vspace*{.12 \textheight} + + \noindent \textbf{\huge \Titulo} \medskip \\ + \ifx\Subtitulo\relax\else\noindent\textbf{\large \Subtitulo} \\ \fi% + \noindent \rule{\textwidth}{1 pt} + + {\noindent\large\Fecha \hspace*\fill \Materia} \\ + \ifx\Submateria\relax\else{\noindent \hspace*\fill \Submateria}\fi% + + \medskip% + \begin{center} + \ifx\Grupo\relax\else\textbf{\Grupo}\par\bigskip\fi + \tablaIntegrantes + + \tablaDirectores + \end{center}% + \vfill% + % \begin{abstract} + \small{\Resumen} + %\end{abstract} + + \begin{minipage}[t]{\textwidth} + \begin{minipage}[t]{.55 \textwidth} + \includegraphics{./figuras/logo_uba.jpg} + \end{minipage}%% + \begin{minipage}[b]{.5 \textwidth} + \textbf{\textsf{Facultad de Ciencias Exactas y Naturales}} \\ + \textsf{Universidad de Buenos Aires} \\ + {\scriptsize % + Ciudad Universitaria - (Pabell\'on I/Planta Baja) \\ + Intendente G\"uiraldes 2160 - C1428EGA \\ + Ciudad Aut\'onoma de Buenos Aires - Rep. Argentina \\ + Tel/Fax: (54 11) 4576-3359 \\ + http://www.fcen.uba.ar \\ + } + \end{minipage} + \end{minipage}% + + \newpage} + +% ----- Reemplazamos el comando \maketitle de LaTeX con el nuestro --------- +\renewcommand{\maketitle}{\maketitlegraf} + +% ----- Dependiendo de las opciones --------- +% +% opciones: +% txt : caratula solo texto. +% txtlogo : caratula txt con logo del DC y del grupo (opcional). +% graf : (default) caratula grafica con logo del DC, UBA y del grupo (opcional). +% +\@makeother\*% some package redefined it as a letter (as color.sty) +% +% Layout general de la caratula +% +\DeclareOption{txt}{\renewcommand{\maketitle}{\maketitletxt}} +\DeclareOption{txtlogo}{\renewcommand{\maketitle}{\maketitletxtlogo}} +\DeclareOption{graf}{\renewcommand{\maketitle}{\maketitlegraf}} +% +% Etiqueta Autores o Integrantes +% +\DeclareOption{integrante}{\renewcommand{\LabelIntegrantes}{Integrante}} +\DeclareOption{autor}{\renewcommand{\LabelIntegrantes}{Autor}} +% +% Formato tabla de integrantes +% +\DeclareOption{intVert}{\renewcommand{\tablaIntegrantes}{\tablaIntegrantesVertical}} +\DeclareOption{intHoriz}{\renewcommand{\tablaIntegrantes}{\tablaIntegrantesHorizontal}} +\DeclareOption{conLU}{\setboolean{showLU}{true}} +\DeclareOption{sinLU}{\setboolean{showLU}{false}} +\DeclareOption{showDirectores}{\setboolean{showDirectores}{true}} +\DeclareOption{hideDirectores}{\setboolean{showDirectores}{false}} +% +% Opciones predeterminadas +% +\ExecuteOptions{intVert}% +\ExecuteOptions{graf}% +\ExecuteOptions{integrante}% +\ExecuteOptions{conLU}% +\ExecuteOptions{hideDirectores}% +% +\ProcessOptions\relax diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/code_color.sty b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/code_color.sty new file mode 100644 index 0000000..b030e31 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/code_color.sty @@ -0,0 +1,20 @@ +% Style definition file generated by highlight 2.16, http://www.andre-simon.de/ + +% Highlighting theme definition: + +\newcommand{\hlstd}[1]{\textcolor[rgb]{0,0,0}{#1}} +\newcommand{\hlnum}[1]{\textcolor[rgb]{0,0,0}{#1}} +\newcommand{\hlesc}[1]{\textcolor[rgb]{0,0,0}{#1}} +\newcommand{\hlstr}[1]{\textcolor[rgb]{0,0,0}{#1}} +\newcommand{\hldstr}[1]{\textcolor[rgb]{0,0,0}{#1}} +\newcommand{\hlslc}[1]{\textcolor[rgb]{0.4,0.4,0.4}{\it{#1}}} +\newcommand{\hlcom}[1]{\textcolor[rgb]{0.4,0.4,0.4}{\it{#1}}} +\newcommand{\hldir}[1]{\textcolor[rgb]{0,0,0}{\bf{#1}}} +\newcommand{\hlsym}[1]{\textcolor[rgb]{0,0,0}{\bf{#1}}} +\newcommand{\hlline}[1]{\textcolor[rgb]{0.53,0.53,0.53}{#1}} +\newcommand{\hlkwa}[1]{\textcolor[rgb]{0,0,0}{\bf{#1}}} +\newcommand{\hlkwb}[1]{\textcolor[rgb]{0,0,0}{\bf{#1}}} +\newcommand{\hlkwc}[1]{\textcolor[rgb]{0,0,0}{\bf{#1}}} +\newcommand{\hlkwd}[1]{\textcolor[rgb]{0,0,0}{\bf{#1}}} +\definecolor{bgcolor}{rgb}{1,1,1} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/data-flow.tex b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/data-flow.tex new file mode 100644 index 0000000..75f821c --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/data-flow.tex @@ -0,0 +1,283 @@ +\section{10594 - Data Flow} + +\textbf{Problema:} +Dada una red en la que cada enlace tiene asociado un +tiempo de transferencia (por unidad de datos), y todos +los enlaces permiten transferir una cantidad m\'axima +de datos fija $k$, determinar la manera de enviar una cierta +cantidad de datos $m$ desde un nodo $v_A$ a un nodo $v_B$ +de manera tal que el tiempo de transferencia sea m\'inimo. + +\subsection{Resoluci\'on} + +Se modela como un problema de flujo m\'aximo de costo m\'inimo. +Se considera un grafo donde todas las conexiones dadas en la entrada +son ejes de capacidad $k$, y el costo de un eje es el tiempo de +transferencia por unidad. +Para convertir el problema original en un problema de flujo m\'aximo, +se agrega un nodo inicial $v_0$ y un eje $(v_0,v_A)$ con capacidad +$m$ y costo $0$. + +El problema de buscar el flujo m\'aximo de costo m\'inimo desde $v_0$ hasta $v_B$ +es equivalente al problema original, porque +si el flujo m\'aximo de $v_0$ a $v_B$ es igual a $m$, +en particular es posible enviar $m$ unidades de $v_A$ a $v_B$. +Inversamente, si el flujo m\'aximo de $v_0$ a $v_B$ es menor que $m$, +no es posible enviar m\'as de $m$ unidades en la red original, ya +que el eje agregado entre $v_0$ a $v_A$ no est\'a saturado, y por +lo tanto el corte m\'inimo se da en ejes de la red original. + +El algoritmo utilizado es Ford-Fulkerson, donde en cada paso +el camino de aumento elegido es el de costo m\'inimo. El +camino de aumento de costo m\'inimo se busca con Bellman-Ford. +Como en el grafo original los ejes tienen costos no negativos, +nunca hay ciclos de costo negativo en el grafo residual. + +El hecho de que todos los ejes de la red original (antes de +agregar $v_0$) tengan la misma capacidad, permite acotar la +cantidad de pasos de Ford-Fulkerson de la siguiente manera. + +La capacidad del eje $(v_0,v_A)$ en el grafo residual +representa el flujo remanente, es decir, la cantidad de +unidades de informaci\'on que todav\'ia no fueron asignadas +a ejes. +Todos los ejes del grafo, exceptuando el eje $(v_0,v_A)$, +tienen la misma capacidad $k$. Como en la red del problema los +ejes no son orientados, cada eje $(v,w)$ tiene asociado +un eje reverso $(w,v)$ de igual capacidad. +Cada eje y su eje reverso pueden encontrarse en $2k + 1$ estados +posibles: o bien ambos tienen asignado flujo $0$, o bien el flujo +es una cantidad de datos $1 \leq c \leq k$ en un sentido, +o bien en el sentido opuesto. + +En cada paso de Ford-Fulkerson, si hay un camino de aumento +desde $v_0$ hasta $v_B$, este camino debe ser de la forma +$v_0, v_A, ..., v_B$. +Adem\'as, como no hay ciclos de costo negativo y el camino +es m\'inimo, el camino debe ser simple en nodos (si repitiera +un nodo $v_i$, habr\'ia un ciclo de costo positivo y se +podr\'ia sacar). +Por lo tanto, en un camino de aumento no se vuelve a utilizar +el eje $(v_0,v_A)$ (ni su reverso). Como adem\'as los caminos +de aumento tienen capacidad positiva por definici\'on, la capacidad +residual del eje $(v_0,v_A)$ va disminuyendo a lo largo de las +iteraciones del algoritmo. + +Por inducci\'on, se puede ver que mientras el flujo remanente +sea mayor que $k$ (es decir, en todos los pasos excepto en el \'ultimo) +y mientras haya un camino de aumento, +la capacidad del camino de aumento encontrado entre $v_A$ y $v_B$ +es $k$, y adem\'as el flujo asignado a cada uno de los restantes ejes +del grafo (exceptuando el eje $(v_0,v_A)$) es o bien $0$ o bien $k$ +(es decir, si se pasa flujo por un eje, esto se hace hasta saturar +la capacidad). + +En el caso base, el flujo es $0$ y la capacidad del camino de +aumento es $k$. En una iteraci\'on $i > 0$, la capacidad del +camino de aumento entre $v_A$ y $v_B$ est\'a dada por el m\'inimo +de las capacidades de los ejes en el grafo residual. Si un eje +tiene asignado flujo $k$, su capacidad residual es $0$ y la +capacidad residual del eje reverso es $2k$. Si un eje tiene +asignado flujo $0$, su capacidad residual y la de su eje reverso +son ambas $k$. + +Despu\'es de la primera iteraci\'on, hay al menos un camino $C_1$ +desde $v_A$ hasta $v_B$ cuyos ejes tienen asignado flujo positivo +(esto es porque el algoritmo de Ford-Fulkerson en todo +momento mantiene un conjunto de caminos disjuntos desde $v_0$ +hasta $v_B$). +Por lo tanto, en la iteraci\'on $i > 0$, no puede ocurrir que haya +un camino de aumento $C_2$ desde $v_A$ hasta $v_B$ que tenga +capacidad $2k$ (es decir, tomando siempre ejes con flujo +en un sentido y satur\'andolos en el sentido opuesto), +porque si esto ocurriera se podr\'ia construir un ciclo de costo negativo +combinando los caminos $C_1$ y $C_2$. Esto es así porque se puede +pasar flujo por $C_2$ en la dirección opuesta sin aumentar el costo, +ya que el costo se estaba pagando antes, pero pasando flujo en la otra +dirección, y luego dejar de pasar flujo por $C_1$, lo cual disminuye el costo, +ya que los costos de los ejes son positivos, por lo cual son mayores a $0$. + +Por lo tanto, el camino de aumento tiene capacidad $k$. +Una vez determinado esto, los flujos de los ejes se +actualizan restando o sumando $k$ en el eje y en el eje +reverso, de tal manera que cada uno sigue teniendo +correspondientemente flujo $0$ o $k$. + +Por \'ultimo, si en alguna iteraci\'on la capacidad residual +de $(v_0,v_A)$ es menor que $k$, el algoritmo termina en esa +iteraci\'on. Dado que todos los caminos de aumento tienen +capacidad $k$, la capacidad residual del eje $(v_0,v_A)$ debe +ser $m\mod k$. Despu\'es de esta \'ultima iteraci\'on, deja de +valer la propiedad sobre el flujo asignado a cada uno de los ejes, +pero la capacidad residual del eje $(v_0,v_A)$ queda en $0$ +y por lo tanto el algoritmo termina. + +Este razonamiento permite acotar la cantidad de iteraciones +de Ford-Fulkerson por $\lceil\frac{m}{k}\rceil$. +Adem\'as, el costo de encontrar el camino de aumento de costo m\'inimo +con Bellman-Ford es el de hacer a lo sumo $N - 1$ iteraciones +(donde $N$ es la cantidad de nodos del grafo) en las que se +recorren las $M$ aristas del grafo, +representado con listas de adyacencia. +La complejidad del algoritmo resulta entonces de las +$O(\frac{m}{k})$ iteraciones, cada una con un costo de +$O(N M)$, es decir $O(\frac{m}{k} N M)$. + +\subsection{Implementación} +\noindent +\ttfamily +\shorthandoff{"}\\ +\hlstd{}\hlline{\ 1\ }\\ +\hlline{\ 2\ }\hldir{\#include\ $<$iostream$>$}\\ +\hlline{\ 3\ }\hlstd{}\hldir{\#include\ $<$map$>$}\\ +\hlline{\ 4\ }\hlstd{}\hldir{\#include\ $<$vector$>$}\\ +\hlline{\ 5\ }\hlstd{}\hldir{\#include\ $<$list$>$}\\ +\hlline{\ 6\ }\hlstd{}\hldir{\#include\ $<$cassert$>$}\\ +\hlline{\ 7\ }\hlstd{}\\ +\hlline{\ 8\ }\hlkwa{using\ namespace\ }\hlstd{std}\hlsym{;}\\ +\hlline{\ 9\ }\hlstd{}\\ +\hlline{10\ }\hlkwc{typedef\ }\hlstd{}\hlkwb{long\ long\ int\ }\hlstd{int64}\hlsym{;}\\ +\hlline{11\ }\hlstd{}\\ +\hlline{12\ }\hldir{\#define\ forsn(i,\ s,\ n)\ for\ (int64\ i\ =\ (s);\ i\ $<$\ (n);\ i++)}\\ +\hlline{13\ }\hlstd{}\hldir{\#define\ forn(i,\ n)\ forsn\ (i,\ 0,\ n)}\\ +\hlline{14\ }\hlstd{}\hldir{\#define\ forall(x,\ s)\ for\ (typeof((s).begin())\ x\ =\ (s).begin();\ x\ !=\ (s).end();\ x++)}\\ +\hlline{15\ }\hlstd{}\\ +\hlline{16\ }\hlkwc{typedef\ }\hlstd{vector}\hlsym{$<$}\hlstd{int64}\hlsym{$>$\ }\hlstd{vint}\hlsym{;}\\ +\hlline{17\ }\hlstd{}\hlkwc{typedef\ }\hlstd{vector}\hlsym{$<$}\hlstd{vint}\hlsym{$>$\ }\hlstd{vvint}\hlsym{;}\\ +\hlline{18\ }\hlstd{\\ +\hlline{19\ }int64\ n}\hlsym{;}\\ +\hlline{20\ }\hlstd{int64\ capacidad\textunderscore eje0}\hlsym{;}\\ +\hlline{21\ }\hlstd{int64\ capacidad\textunderscore enlace}\hlsym{;}\\ +\hlline{22\ }\hlstd{vvint\ grafo}\hlsym{;}\hlstd{\ \ }\hlsym{}\hlstd{}\hlslc{//\ listas\ de\ adyacencia}\\ +\hlline{23\ }\hlstd{vvint\ costo}\hlsym{;}\hlstd{\ \ }\hlsym{}\hlstd{}\hlslc{//\ matriz}\\ +\hlline{24\ }\hlstd{vvint\ flujo}\hlsym{;}\hlstd{\ \ }\hlsym{}\hlstd{}\hlslc{//\ matriz}\\ +\hlline{25\ }\hlstd{}\\ +\hlline{26\ }\hldir{\#define\ agregar(u,\ v,\ c)\ \{\ $\backslash$}\\ +\hlline{27\ }\hldir{\ grafo{[}u{]}.push\textunderscore back(v);\ $\backslash$}\\ +\hlline{28\ }\hldir{\ costo{[}u{]}{[}v{]}\ =\ (c);\ $\backslash$}\\ +\hlline{29\ }\hldir{\ grafo{[}v{]}.push\textunderscore back(u);\ $\backslash$}\\ +\hlline{30\ }\hldir{\ costo{[}v{]}{[}u{]}\ =\ (c);\ $\backslash$}\\ +\hlline{31\ }\hldir{\}}\\ +\hlline{32\ }\hlstd{}\\ +\hlline{33\ }\hldir{\#define\ capacidad(v,\ w)\ (((v)\ ==\ 0\ \textbar \textbar \ (w)\ ==\ 0)\ ?\ capacidad\textunderscore eje0\ :\ capacidad\textunderscore enlace)}\\ +\hlline{34\ }\hlstd{}\\ +\hlline{35\ }\hlkwb{void\ }\hlstd{}\hlkwd{print\textunderscore grafo\textunderscore residual}\hlstd{}\hlsym{()\ \{}\\ +\hlline{36\ }\hlstd{\ cout\ }\hlsym{$<$$<$\ }\hlstd{}\hlstr{"{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}"}\hlstd{\ }\hlsym{$<$$<$\ }\hlstd{endl}\hlsym{;}\\ +\hlline{37\ }\hlstd{\ }\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{v}\hlsym{,\ }\hlstd{n}\hlsym{)\ \{}\\ +\hlline{38\ }\hlstd{}\hlstd{\ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{v\ }\hlsym{$<$$<$\ }\hlstd{endl}\hlsym{;}\\ +\hlline{39\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{forall\ }\hlstd{}\hlsym{(}\hlstd{vecino}\hlsym{,\ }\hlstd{grafo}\hlsym{{[}}\hlstd{v}\hlsym{{]})\ \{}\\ +\hlline{40\ }\hlstd{}\hlstd{\ \ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{}\hlstr{"{-}{-}$>$\ "}\hlstd{}\hlsym{;}\\ +\hlline{41\ }\hlstd{}\hlstd{\ \ \ }\hlstd{cout\ }\hlsym{$<$$<$\ {*}}\hlstd{vecino}\hlsym{;}\\ +\hlline{42\ }\hlstd{}\hlstd{\ \ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{}\hlstr{"\ costo\ =\ "}\hlstd{\ }\hlsym{$<$$<$\ }\hlstd{costo}\hlsym{{[}}\hlstd{v}\hlsym{{]}{[}{*}}\hlstd{vecino}\hlsym{{]};}\\ +\hlline{43\ }\hlstd{}\hlstd{\ \ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{}\hlstr{"\ flujo\ =\ "}\hlstd{\ }\hlsym{$<$$<$\ }\hlstd{flujo}\hlsym{{[}}\hlstd{v}\hlsym{{]}{[}{*}}\hlstd{vecino}\hlsym{{]}\ $<$$<$\ }\hlstd{}\hlstr{"\ /\ "}\hlstd{\ }\hlsym{$<$$<$\ }\hlstd{}\hlkwd{capacidad}\hlstd{}\hlsym{(}\hlstd{v}\hlsym{,\ {*}}\hlstd{vecino}\hlsym{);}\\ +\hlline{44\ }\hlstd{}\hlstd{\ \ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{endl}\hlsym{;}\\ +\hlline{45\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{46\ }\hlstd{}\hlstd{\ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{endl}\hlsym{;}\\ +\hlline{47\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{48\ }\hlstd{}\hlsym{\}}\\ +\hlline{49\ }\hlstd{}\\ +\hlline{50\ }\hldir{\#define\ INF\ 0x7fffffff}\\ +\hlline{51\ }\hlstd{}\hldir{\#define\ No\textunderscore hay\textunderscore camino\ {-}1}\\ +\hlline{52\ }\hlstd{}\hldir{\#define\ signo(x)\ ((x)\ $<$\ 0\ ?\ {-}1\ :\ 1)}\\ +\hlline{53\ }\hlstd{int64\ }\hlkwd{caumento}\hlstd{}\hlsym{(}\hlstd{vint}\hlsym{\&\ }\hlstd{camino}\hlsym{)\ \{}\\ +\hlline{54\ }\hlstd{\ }\hlslc{//\ buscar\ el\ camino\ de\ aumento\ de\ costo\ minimo\ usando\ Bellman{-}Ford}\\ +\hlline{55\ }\hlstd{\ vint\ }\hlkwd{dist}\hlstd{}\hlsym{(}\hlstd{n}\hlsym{,\ }\hlstd{INF}\hlsym{);}\\ +\hlline{56\ }\hlstd{\ vint\ }\hlkwd{ant}\hlstd{}\hlsym{(}\hlstd{n}\hlsym{,\ {-}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{);}\\ +\hlline{57\ }\hlstd{\\ +\hlline{58\ }\ dist}\hlsym{{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}\ =\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{59\ }\hlstd{\\ +\hlline{60\ }\ }\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{it}\hlsym{,\ }\hlstd{n\ }\hlsym{{-}\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ \{}\\ +\hlline{61\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlslc{//\ para\ cada\ arista\ del\ grafo\ residual}\\ +\hlline{62\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwb{bool\ }\hlstd{cambio\ }\hlsym{=\ }\hlstd{}\hlkwa{false}\hlstd{}\hlsym{;}\\ +\hlline{63\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{v}\hlsym{,\ }\hlstd{n}\hlsym{)\ }\hlstd{}\hlkwd{forall\ }\hlstd{}\hlsym{(}\hlstd{vecino}\hlsym{,\ }\hlstd{grafo}\hlsym{{[}}\hlstd{v}\hlsym{{]})\ \{}\\ +\hlline{64\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwb{const\ }\hlstd{int64\ w\ }\hlsym{=\ {*}}\hlstd{vecino}\hlsym{;}\\ +\hlline{65\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwd{capacidad}\hlstd{}\hlsym{(}\hlstd{v}\hlsym{,\ }\hlstd{w}\hlsym{)\ {-}\ }\hlstd{flujo}\hlsym{{[}}\hlstd{v}\hlsym{{]}{[}}\hlstd{w}\hlsym{{]}\ $<$=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ }\hlstd{}\hlkwa{continue}\hlstd{}\hlsym{;}\\ +\hlline{66\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{dist}\hlsym{{[}}\hlstd{v}\hlsym{{]}\ ==\ }\hlstd{INF}\hlsym{)\ }\hlstd{}\hlkwa{continue}\hlstd{}\hlsym{;}\\ +\hlline{67\ }\hlstd{}\hlstd{\ \ \ }\hlstd{int64\ ndist\ }\hlsym{=\ }\hlstd{dist}\hlsym{{[}}\hlstd{v}\hlsym{{]}\ +\ }\hlstd{}\hlkwd{signo}\hlstd{}\hlsym{(}\hlstd{flujo}\hlsym{{[}}\hlstd{v}\hlsym{{]}{[}}\hlstd{w}\hlsym{{]})\ {*}\ }\hlstd{costo}\hlsym{{[}}\hlstd{v}\hlsym{{]}{[}}\hlstd{w}\hlsym{{]};}\\ +\hlline{68\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{ndist\ }\hlsym{$<$\ }\hlstd{dist}\hlsym{{[}}\hlstd{w}\hlsym{{]})\ \{}\\ +\hlline{69\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{dist}\hlsym{{[}}\hlstd{w}\hlsym{{]}\ =\ }\hlstd{ndist}\hlsym{;}\\ +\hlline{70\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{ant}\hlsym{{[}}\hlstd{w}\hlsym{{]}\ =\ }\hlstd{v}\hlsym{;}\\ +\hlline{71\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{cambio\ }\hlsym{=\ }\hlstd{}\hlkwa{true}\hlstd{}\hlsym{;}\\ +\hlline{72\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{73\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{74\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(!}\hlstd{cambio}\hlsym{)\ }\hlstd{}\hlkwa{break}\hlstd{}\hlsym{;}\\ +\hlline{75\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{76\ }\hlstd{\\ +\hlline{77\ }\ }\hlslc{//\ armar\ el\ camino}\\ +\hlline{78\ }\hlstd{\ int64\ costo\textunderscore camino\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{79\ }\hlstd{\ int64\ actual\ }\hlsym{=\ }\hlstd{n\ }\hlsym{{-}\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{80\ }\hlstd{\ }\hlkwa{while\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwa{true}\hlstd{}\hlsym{)\ \{}\\ +\hlline{81\ }\hlstd{}\hlstd{\ \ }\hlstd{camino}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{actual}\hlsym{);}\\ +\hlline{82\ }\hlstd{}\hlstd{\ \ }\hlstd{int64\ anterior\ }\hlsym{=\ }\hlstd{ant}\hlsym{{[}}\hlstd{actual}\hlsym{{]};}\\ +\hlline{83\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{anterior\ }\hlsym{==\ {-}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ }\hlstd{}\hlkwa{break}\hlstd{}\hlsym{;}\\ +\hlline{84\ }\hlstd{}\hlstd{\ \ }\hlstd{costo\textunderscore camino\ }\hlsym{+=\ }\hlstd{}\hlkwd{signo}\hlstd{}\hlsym{(}\hlstd{flujo}\hlsym{{[}}\hlstd{anterior}\hlsym{{]}{[}}\hlstd{actual}\hlsym{{]})\ {*}\ }\hlstd{costo}\hlsym{{[}}\hlstd{anterior}\hlsym{{]}{[}}\hlstd{actual}\hlsym{{]};}\\ +\hlline{85\ }\hlstd{}\hlstd{\ \ }\hlstd{actual\ }\hlsym{=\ }\hlstd{anterior}\hlsym{;}\\ +\hlline{86\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{87\ }\hlstd{\ }\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{actual\ }\hlsym{==\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ \{}\\ +\hlline{88\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{return\ }\hlstd{costo\textunderscore camino}\hlsym{;}\\ +\hlline{89\ }\hlstd{\ }\hlsym{\}\ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{90\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{return\ }\hlstd{No\textunderscore hay\textunderscore camino}\hlsym{;}\\ +\hlline{91\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{92\ }\hlstd{}\hlsym{\}}\\ +\hlline{93\ }\hlstd{\\ +\hlline{94\ }int64\ }\hlkwd{resolver}\hlstd{}\hlsym{()\ \{}\\ +\hlline{95\ }\hlstd{\ int64\ flujo\textunderscore total\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{96\ }\hlstd{\ int64\ costo\textunderscore total\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{97\ }\hlstd{\ }\hlkwa{while\ }\hlstd{}\hlsym{(}\hlstd{flujo\textunderscore total\ }\hlsym{$<$\ }\hlstd{capacidad\textunderscore eje0}\hlsym{)\ \{}\\ +\hlline{98\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlslc{//print\textunderscore grafo\textunderscore residual();}\\ +\hlline{99\ }\hlstd{}\hlstd{\ \ }\hlstd{vint\ camino\textunderscore aumento}\hlsym{;}\\ +\hlline{100\ }\hlstd{}\hlstd{\ \ }\hlstd{int64\ costo\textunderscore camino\ }\hlsym{=\ }\hlstd{}\hlkwd{caumento}\hlstd{}\hlsym{(}\hlstd{camino\textunderscore aumento}\hlsym{);}\\ +\hlline{101\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{costo\textunderscore camino\ }\hlsym{==\ }\hlstd{No\textunderscore hay\textunderscore camino}\hlsym{)\ }\hlstd{}\hlkwa{return\ }\hlstd{No\textunderscore hay\textunderscore camino}\hlsym{;}\\ +\hlline{102\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlslc{//\ saturar\ el\ camino\ de\ aumento}\\ +\hlline{103\ }\hlstd{}\hlstd{\ \ }\hlstd{int64\ mn\ }\hlsym{=\ }\hlstd{INF}\hlsym{;}\\ +\hlline{104\ }\hlstd{}\hlstd{\ \ }\hlstd{\\ +\hlline{105\ }}\hlstd{\ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{camino\textunderscore aumento}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{()\ {-}\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ \{}\\ +\hlline{106\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwb{const\ }\hlstd{int64\ v\ }\hlsym{=\ }\hlstd{camino\textunderscore aumento}\hlsym{{[}}\hlstd{i\ }\hlsym{+\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]},\ }\hlstd{w\ }\hlsym{=\ }\hlstd{camino\textunderscore aumento}\hlsym{{[}}\hlstd{i}\hlsym{{]};}\\ +\hlline{107\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{flujo}\hlsym{{[}}\hlstd{v}\hlsym{{]}{[}}\hlstd{w}\hlsym{{]}\ $<$\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ \{}\\ +\hlline{108\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{mn\ }\hlsym{=\ }\hlstd{}\hlkwd{min}\hlstd{}\hlsym{(}\hlstd{mn}\hlsym{,\ {-}}\hlstd{flujo}\hlsym{{[}}\hlstd{v}\hlsym{{]}{[}}\hlstd{w}\hlsym{{]});}\\ +\hlline{109\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}\ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{110\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{mn\ }\hlsym{=\ }\hlstd{}\hlkwd{min}\hlstd{}\hlsym{(}\hlstd{mn}\hlsym{,\ }\hlstd{}\hlkwd{capacidad}\hlstd{}\hlsym{(}\hlstd{v}\hlsym{,\ }\hlstd{w}\hlsym{)\ {-}\ }\hlstd{flujo}\hlsym{{[}}\hlstd{v}\hlsym{{]}{[}}\hlstd{w}\hlsym{{]});}\\ +\hlline{111\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{112\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{113\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{camino\textunderscore aumento}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{()\ {-}\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ \{}\\ +\hlline{114\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwb{const\ }\hlstd{int64\ v\ }\hlsym{=\ }\hlstd{camino\textunderscore aumento}\hlsym{{[}}\hlstd{i\ }\hlsym{+\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]},\ }\hlstd{w\ }\hlsym{=\ }\hlstd{camino\textunderscore aumento}\hlsym{{[}}\hlstd{i}\hlsym{{]};}\\ +\hlline{115\ }\hlstd{}\hlstd{\ \ \ }\hlstd{flujo}\hlsym{{[}}\hlstd{v}\hlsym{{]}{[}}\hlstd{w}\hlsym{{]}\ +=\ }\hlstd{mn}\hlsym{;}\\ +\hlline{116\ }\hlstd{}\hlstd{\ \ \ }\hlstd{flujo}\hlsym{{[}}\hlstd{w}\hlsym{{]}{[}}\hlstd{v}\hlsym{{]}\ {-}=\ }\hlstd{mn}\hlsym{;}\\ +\hlline{117\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{118\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{mn\ }\hlsym{==\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ }\hlstd{}\hlkwa{return\ }\hlstd{No\textunderscore hay\textunderscore camino}\hlsym{;}\\ +\hlline{119\ }\hlstd{}\hlstd{\ \ }\hlstd{flujo\textunderscore total\ }\hlsym{+=\ }\hlstd{mn}\hlsym{;}\\ +\hlline{120\ }\hlstd{}\hlstd{\ \ }\hlstd{costo\textunderscore total\ }\hlsym{+=\ }\hlstd{costo\textunderscore camino\ }\hlsym{{*}\ }\hlstd{mn}\hlsym{;}\\ +\hlline{121\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{122\ }\hlstd{\\ +\hlline{123\ }\ }\hlkwa{return\ }\hlstd{costo\textunderscore total}\hlsym{;}\\ +\hlline{124\ }\hlstd{}\hlsym{\}}\\ +\hlline{125\ }\hlstd{}\\ +\hlline{126\ }\hlkwb{int\ }\hlstd{}\hlkwd{main}\hlstd{}\hlsym{()\ \{}\\ +\hlline{127\ }\hlstd{\ int64\ m}\hlsym{;}\\ +\hlline{128\ }\hlstd{\ }\hlkwa{while\ }\hlstd{}\hlsym{(}\hlstd{cin\ }\hlsym{$>$$>$\ }\hlstd{n\ }\hlsym{$>$$>$\ }\hlstd{m}\hlsym{)\ \{}\\ +\hlline{129\ }\hlstd{}\hlstd{\ \ }\hlstd{n}\hlsym{++;}\\ +\hlline{130\ }\hlstd{}\hlstd{\ \ }\hlstd{grafo\ }\hlsym{=\ }\hlstd{}\hlkwd{vvint}\hlstd{}\hlsym{(}\hlstd{n}\hlsym{,\ }\hlstd{}\hlkwd{vint}\hlstd{}\hlsym{());}\\ +\hlline{131\ }\hlstd{}\hlstd{\ \ }\hlstd{costo\ }\hlsym{=\ }\hlstd{}\hlkwd{vvint}\hlstd{}\hlsym{(}\hlstd{n}\hlsym{,\ }\hlstd{}\hlkwd{vint}\hlstd{}\hlsym{(}\hlstd{n}\hlsym{,\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{));}\\ +\hlline{132\ }\hlstd{}\hlstd{\ \ }\hlstd{flujo\ }\hlsym{=\ }\hlstd{}\hlkwd{vvint}\hlstd{}\hlsym{(}\hlstd{n}\hlsym{,\ }\hlstd{}\hlkwd{vint}\hlstd{}\hlsym{(}\hlstd{n}\hlsym{,\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{));}\\ +\hlline{133\ }\hlstd{\\ +\hlline{134\ }}\hlstd{\ \ }\hlstd{}\hlkwd{agregar}\hlstd{}\hlsym{(}\hlstd{}\hlnum{0}\hlstd{}\hlsym{,\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{,\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{);}\\ +\hlline{135\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{m}\hlsym{)\ \{}\\ +\hlline{136\ }\hlstd{}\hlstd{\ \ \ }\hlstd{int64\ v1}\hlsym{,\ }\hlstd{v2}\hlsym{,\ }\hlstd{c}\hlsym{;}\\ +\hlline{137\ }\hlstd{}\hlstd{\ \ \ }\hlstd{cin\ }\hlsym{$>$$>$\ }\hlstd{v1\ }\hlsym{$>$$>$\ }\hlstd{v2\ }\hlsym{$>$$>$\ }\hlstd{c}\hlsym{;}\\ +\hlline{138\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwd{agregar}\hlstd{}\hlsym{(}\hlstd{v1}\hlsym{,\ }\hlstd{v2}\hlsym{,\ }\hlstd{c}\hlsym{);}\\ +\hlline{139\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{140\ }\hlstd{}\hlstd{\ \ }\hlstd{cin\ }\hlsym{$>$$>$\ }\hlstd{capacidad\textunderscore eje0\ }\hlsym{$>$$>$\ }\hlstd{capacidad\textunderscore enlace}\hlsym{;}\\ +\hlline{141\ }\hlstd{}\hlstd{\ \ }\hlstd{int64\ r\ }\hlsym{=\ }\hlstd{}\hlkwd{resolver}\hlstd{}\hlsym{();}\\ +\hlline{142\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{r\ }\hlsym{==\ }\hlstd{No\textunderscore hay\textunderscore camino}\hlsym{)\ \{}\\ +\hlline{143\ }\hlstd{}\hlstd{\ \ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{}\hlstr{"Impossible."}\hlstd{\ }\hlsym{$<$$<$\ }\hlstd{endl}\hlsym{;}\\ +\hlline{144\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}\ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{145\ }\hlstd{}\hlstd{\ \ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{r\ }\hlsym{$<$$<$\ }\hlstd{endl}\hlsym{;}\\ +\hlline{146\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{147\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{148\ }\hlstd{\ }\hlkwa{return\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{149\ }\hlstd{}\hlsym{\}}\\ +\hlline{150\ }\hlstd{}\\ +\mbox{} +\normalfont +\shorthandon{"} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/figuras/grafo.dot b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/figuras/grafo.dot new file mode 100644 index 0000000..b88888e --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/figuras/grafo.dot @@ -0,0 +1,56 @@ +digraph g{ +rankdir="LR"; + +"Windsor\n 8:00" +"London\n 9:55"[rotate="90"] +"Kitchener\n 11:30" +"Guelph\n 12:25" +"Toronto\n 13:30"[color="#DDDDFF",style=filled]"Montreal\n 18:20" +"Kitchener\n 8:45" +"Waterloo\n 9:00"[color="#DDFFDD",style=filled] +"Waterloo\n 8:00"[color="#DDFFDD",style=filled] +"Waterloo\n 7:00"[color="#DDFFDD",style=filled] +"Waterloo\n 23:00"[color="#DDFFDD",style=filled] +"Hamilton\n 10:45" +"Niagara\n 11:50" +"Niagara\n 12:00" +"Toronto\n 14:00"[color="#DDDDFF",style=filled] +"Toronto\n 8:45"[color="#DDDDFF",style=filled] +"Guleph\n 23:55" +"Guleph\n 6:00" +"Toronto\n 7:05"[color="#DDDDFF",style=filled] +"FINAL"[color="#FFDDDD",style=filled] + +"Windsor\n 8:00"->"London\n 9:55" [label="115"] +"London\n 9:55"->"Kitchener\n 11:30" [label="95"] +"Kitchener\n 11:30"->"Guelph\n 12:25"[label="55"] +"Guelph\n 12:25"->"Toronto\n 13:30"[label="65"] +"Toronto\n 13:30"->"Montreal\n 18:20"[label="290"] +"Waterloo\n 8:00"->"Kitchener\n 8:45"[label="45"] +"Kitchener\n 11:30"->"Kitchener\n 8:45"[label="1275"] +"Kitchener\n 8:45"->"Kitchener\n 11:30"[label="165"] +"Waterloo\n 9:00"->"Hamilton\n 10:45"[label="105"] +"Hamilton\n 10:45"->"Niagara\n 11:50"[label="65"] +"Niagara\n 12:00"->"Toronto\n 14:00"[label="120"] +"Niagara\n 11:50"->"Niagara\n 12:00"[label="10"] +"Niagara\n 12:00"->"Niagara\n 11:50"[label="1430"] +"Waterloo\n 7:00"->"Toronto\n 8:45"[label="105"] +"Waterloo\n 23:00"->"Guleph\n 23:55"[label="55"] +"Guleph\n 6:00"->"Toronto\n 7:05"[label="65"] +"Guelph\n 12:25"->"Guleph\n 23:55"[label="690"] +"Guleph\n 23:55"->"Guleph\n 6:00"[label="365"] +"Guleph\n 6:00"->"Guelph\n 12:25"[label="385"] +"Toronto\n 13:30"->"FINAL" +"Toronto\n 14:00"->"FINAL" +"Toronto\n 8:45"->"FINAL" +"Toronto\n 7:05"->"FINAL" +"Toronto\n 13:30"->"Toronto\n 14:00"[label="30"] +"Toronto\n 14:00"->"Toronto\n 7:05"[label="1025"] +"Toronto\n 8:45"->"Toronto\n 13:30"[label="285"] +"Toronto\n 7:05"->"Toronto\n 8:45"[label="100"] +"Waterloo\n 7:00"->"Waterloo\n 8:00"[label="60"] +"Waterloo\n 8:00"->"Waterloo\n 9:00"[label="60"] +"Waterloo\n 9:00"->"Waterloo\n 23:00"[label="840"] +"Waterloo\n 23:00"->"Waterloo\n 7:00"[label="480"] + +} diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/figuras/grafo.pdf b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/figuras/grafo.pdf new file mode 100644 index 0000000000000000000000000000000000000000..35320b6b4540569796b4ec81caec07cc16e5b9fc GIT binary patch literal 39121 zcwPWHK*hf$P((&8F)lO;CCBWKq6#%2Fd%PYY6?6&FHB`_XLM*FHXtw{QZGhnY;ve|J>k8NJxWzBu zE=fJ-wa&+Nh2js|)_sro{mZxODMFGD85j8S62JIZ{`{@^EnfBcYL_IQtQl^!uP1M{ z?ALs}THR~BTD>H7ZXeZlUEunC-T0EklU-Mc2hUqvZ+1OH9+1zNWAo)L^lrWG{TlW0 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}\hlstd{std}\hlsym{;}\\ +\hlline{\ 7\ }\hlstd{}\\ +\hlline{\ 8\ }\hldir{\#define\ forsn(i,\ s,\ n)\ for\ (int\ i\ =\ (s);\ i\ $<$\ (n);\ i++)}\\ +\hlline{\ 9\ }\hlstd{}\hldir{\#define\ forn(i,\ n)\ forsn\ (i,\ 0,\ n)}\\ +\hlline{10\ }\hlstd{}\\ +\hlline{11\ }\hlkwc{typedef\ }\hlstd{vector}\hlsym{$<$}\hlstd{}\hlkwb{bool}\hlstd{}\hlsym{$>$\ }\hlstd{vbool}\hlsym{;}\\ +\hlline{12\ }\hlstd{}\hlkwc{typedef\ }\hlstd{vector}\hlsym{$<$}\hlstd{vbool}\hlsym{$>$\ }\hlstd{vvbool}\hlsym{;}\\ +\hlline{13\ }\hlstd{}\\ +\hlline{14\ }\hlkwc{typedef\ }\hlstd{}\hlkwb{int\ }\hlstd{Node}\hlsym{;}\\ +\hlline{15\ }\hlstd{}\hlkwb{int\ }\hlstd{rows}\hlsym{;}\\ +\hlline{16\ }\hlstd{}\hlkwb{int\ }\hlstd{cols}\hlsym{;}\\ +\hlline{17\ }\hlstd{vvbool\ mapa}\hlsym{;}\\ +\hlline{18\ }\hlstd{}\\ +\hlline{19\ }\hldir{\#define\ node(r,\ c)}\hlstd{\ \ }\hldir{((r)\ $<$$<$\ 12\ \textbar \ (c))}\\ +\hlline{20\ }\hlstd{}\hldir{\#define\ node\textunderscore row(v)}\hlstd{\ \ }\hldir{((v)\ $>$$>$\ 12)}\\ +\hlline{21\ }\hlstd{}\hldir{\#define\ node\textunderscore col(v)}\hlstd{\ \ }\hldir{((v)\ \&\ 0xfff)}\\ +\hlline{22\ }\hlstd{}\\ +\hlline{23\ }\hldir{\#define\ NONE}\hlstd{\ \ \ }\hldir{0xffffffff}\\ +\hlline{24\ }\hlstd{\\ +\hlline{25\ }Node\ }\hlkwd{vecino}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{bool\ }\hlstd{ns}\hlsym{,\ }\hlstd{Node\ v}\hlsym{)\ \{}\\ +\hlline{26\ }\hlstd{}\hldir{\#define\ sig(x)\ ((x)\ ?\ 1\ :\ {-}1)}\\ +\hlline{27\ }\hlstd{\ }\hlkwb{const\ int\ }\hlstd{r\ }\hlsym{=\ }\hlstd{}\hlkwd{node\textunderscore row}\hlstd{}\hlsym{(}\hlstd{v}\hlsym{)\ {-}\ }\hlstd{ns}\hlsym{,\ }\hlstd{c\ }\hlsym{=\ }\hlstd{}\hlkwd{node\textunderscore col}\hlstd{}\hlsym{(}\hlstd{v}\hlsym{);}\\ +\hlline{28\ }\hlstd{\ }\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{r\ }\hlsym{$<$\ }\hlstd{}\hlnum{0\ }\hlstd{}\hlsym{\textbar \textbar \ }\hlstd{r\ }\hlsym{$>$=\ }\hlstd{rows}\hlsym{)\ }\hlstd{}\hlkwa{return\ }\hlstd{NONE}\hlsym{;}\\ +\hlline{29\ }\hlstd{\ }\hlkwb{const\ int\ }\hlstd{cc\ }\hlsym{=\ }\hlstd{c\ }\hlsym{+\ }\hlstd{}\hlkwd{sig}\hlstd{}\hlsym{(}\hlstd{ns\ \textasciicircum \ mapa}\hlsym{{[}}\hlstd{r}\hlsym{{]}{[}}\hlstd{c}\hlsym{{]});}\\ +\hlline{30\ }\hlstd{\ }\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{cc\ }\hlsym{$<$\ }\hlstd{}\hlnum{0\ }\hlstd{}\hlsym{\textbar \textbar \ }\hlstd{cc\ }\hlsym{$>$=\ }\hlstd{cols}\hlsym{)\ }\hlstd{}\hlkwa{return\ }\hlstd{NONE}\hlsym{;}\\ +\hlline{31\ }\hlstd{\ }\hlkwb{const\ int\ }\hlstd{rr\ }\hlsym{=\ }\hlstd{}\hlkwd{node\textunderscore row}\hlstd{}\hlsym{(}\hlstd{v}\hlsym{)\ +\ }\hlstd{}\hlkwd{sig}\hlstd{}\hlsym{(}\hlstd{ns}\hlsym{)\ {*}\ {-}!(}\hlstd{mapa}\hlsym{{[}}\hlstd{r}\hlsym{{]}{[}}\hlstd{c}\hlsym{{]}\ }\hlstd{\textasciicircum \ mapa}\hlsym{{[}}\hlstd{r}\hlsym{{]}{[}}\hlstd{cc}\hlsym{{]});}\\ +\hlline{32\ }\hlstd{\ }\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{rr\ }\hlsym{$<$\ }\hlstd{}\hlnum{0\ }\hlstd{}\hlsym{\textbar \textbar \ }\hlstd{rr\ }\hlsym{$>$\ }\hlstd{rows}\hlsym{)\ }\hlstd{}\hlkwa{return\ }\hlstd{NONE}\hlsym{;}\\ +\hlline{33\ }\hlstd{\ }\hlkwa{return\ }\hlstd{}\hlkwd{node}\hlstd{}\hlsym{(}\hlstd{rr}\hlsym{,\ }\hlstd{cc}\hlsym{);}\\ +\hlline{34\ }\hlstd{}\hlsym{\}}\\ +\hlline{35\ }\hlstd{}\\ +\hlline{36\ }\hlkwb{int\ }\hlstd{}\hlkwd{resolver}\hlstd{}\hlsym{()\ \{}\\ +\hlline{37\ }\hlstd{}\hldir{\#define\ marcado(v)\ (\textunderscore marcas{[}node\textunderscore row(v){]}{[}node\textunderscore col(v){]})}\\ +\hlline{38\ }\hlstd{}\hldir{\#define\ marcar(v)\ (\textunderscore marcas{[}node\textunderscore row(v){]}{[}node\textunderscore col(v){]}\ =\ true)}\\ +\hlline{39\ }\hlstd{\ }\hlkwb{int\ }\hlstd{cant\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{40\ }\hlstd{\ vvbool\ }\hlkwd{\textunderscore marcas}\hlstd{}\hlsym{(}\hlstd{rows\ }\hlsym{+\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{,\ }\hlstd{}\hlkwd{vbool}\hlstd{}\hlsym{(}\hlstd{cols}\hlsym{,\ }\hlstd{}\hlkwa{false}\hlstd{}\hlsym{));}\\ +\hlline{41\ }\hlstd{\ }\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{c}\hlsym{,\ }\hlstd{cols}\hlsym{)\ \{}\\ +\hlline{42\ }\hlstd{}\hlstd{\ \ }\hlstd{Node\ v\ }\hlsym{=\ }\hlstd{}\hlkwd{node}\hlstd{}\hlsym{(}\hlstd{}\hlnum{0}\hlstd{}\hlsym{,\ }\hlstd{c}\hlsym{);}\\ +\hlline{43\ }\hlstd{\\ +\hlline{44\ }}\hlstd{\ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwd{marcado}\hlstd{}\hlsym{(}\hlstd{v}\hlsym{))\ }\hlstd{}\hlkwa{continue}\hlstd{}\hlsym{;}\\ +\hlline{45\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{marcar}\hlstd{}\hlsym{(}\hlstd{v}\hlsym{);}\\ +\hlline{46\ }\hlstd{\\ +\hlline{47\ }}\hlstd{\ \ }\hlstd{}\hlkwa{for\ }\hlstd{}\hlsym{(;;)\ \{}\\ +\hlline{48\ }\hlstd{}\hlstd{\ \ \ }\hlstd{Node\ w\ }\hlsym{=\ }\hlstd{NONE}\hlsym{;}\\ +\hlline{49\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{direction}\hlsym{,\ }\hlstd{}\hlnum{2}\hlstd{}\hlsym{)\ \{}\\ +\hlline{50\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{Node\ vv\ }\hlsym{=\ }\hlstd{}\hlkwd{vecino}\hlstd{}\hlsym{(}\hlstd{direction}\hlsym{,\ }\hlstd{v}\hlsym{);}\\ +\hlline{51\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{vv\ }\hlsym{==\ }\hlstd{NONE\ }\hlsym{\textbar \textbar \ }\hlstd{}\hlkwd{marcado}\hlstd{}\hlsym{(}\hlstd{vv}\hlsym{))\ }\hlstd{}\hlkwa{continue}\hlstd{}\hlsym{;}\\ +\hlline{52\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{assert}\hlstd{}\hlsym{(}\hlstd{w\ }\hlsym{==\ }\hlstd{NONE}\hlsym{);}\\ +\hlline{53\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{w\ }\hlsym{=\ }\hlstd{vv}\hlsym{;}\\ +\hlline{54\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{55\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{w\ }\hlsym{==\ }\hlstd{NONE}\hlsym{)\ }\hlstd{}\hlkwa{break}\hlstd{}\hlsym{;}\\ +\hlline{56\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwd{node\textunderscore row}\hlstd{}\hlsym{(}\hlstd{w}\hlsym{)\ ==\ }\hlstd{rows}\hlsym{)\ \{}\\ +\hlline{57\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{cant}\hlsym{++;}\\ +\hlline{58\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{break}\hlstd{}\hlsym{;}\\ +\hlline{59\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{60\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwd{marcar}\hlstd{}\hlsym{(}\hlstd{w}\hlsym{);}\\ +\hlline{61\ }\hlstd{}\hlstd{\ \ \ }\hlstd{v\ }\hlsym{=\ }\hlstd{w}\hlsym{;}\\ +\hlline{62\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{63\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{64\ }\hlstd{\ }\hlkwa{return\ }\hlstd{cant}\hlsym{;}\\ +\hlline{65\ }\hlstd{}\hlsym{\}}\\ +\hlline{66\ }\hlstd{}\\ +\hlline{67\ }\hlkwb{int\ }\hlstd{}\hlkwd{main}\hlstd{}\hlsym{()\ \{}\\ +\hlline{68\ }\hlstd{\ }\hlkwb{int\ }\hlstd{ncases}\hlsym{;}\\ +\hlline{69\ }\hlstd{\ cin\ }\hlsym{$>$$>$\ }\hlstd{ncases}\hlsym{;}\\ +\hlline{70\ }\hlstd{\ \\ +\hlline{71\ }\ }\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{ncases}\hlsym{)\ \{}\\ +\hlline{72\ }\hlstd{}\hlstd{\ \ }\hlstd{cin\ }\hlsym{$>$$>$\ }\hlstd{cols\ }\hlsym{$>$$>$\ }\hlstd{rows}\hlsym{;}\\ +\hlline{73\ }\hlstd{}\hlstd{\ \ }\hlstd{mapa\ }\hlsym{=\ }\hlstd{}\hlkwd{vvbool}\hlstd{}\hlsym{(}\hlstd{rows}\hlsym{,\ }\hlstd{}\hlkwd{vbool}\hlstd{}\hlsym{(}\hlstd{cols}\hlsym{));}\\ +\hlline{74\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{r}\hlsym{,\ }\hlstd{rows}\hlsym{)\ \{}\\ +\hlline{75\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{c}\hlsym{,\ }\hlstd{cols}\hlsym{)\ \{}\\ +\hlline{76\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{char\ }\hlstd{mapa\textunderscore rc}\hlsym{;}\\ +\hlline{77\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{cin\ }\hlsym{$>$$>$\ }\hlstd{mapa\textunderscore rc}\hlsym{;}\\ +\hlline{78\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{mapa}\hlsym{{[}}\hlstd{r}\hlsym{{]}{[}}\hlstd{c}\hlsym{{]}\ =\ (}\hlstd{mapa\textunderscore rc\ }\hlsym{==\ }\hlstd{}\hlstr{`}\hlesc{$\backslash$$\backslash$}\hlstr{`}\hlstd{}\hlsym{);}\\ +\hlline{79\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{80\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{81\ }\hlstd{\\ +\hlline{82\ }}\hlstd{\ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{}\hlkwd{resolver}\hlstd{}\hlsym{()\ $<$$<$\ }\hlstd{endl}\hlsym{;}\\ +\hlline{83\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{84\ }\hlstd{\\ +\hlline{85\ }\ }\hlkwa{return\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{86\ }\hlstd{}\hlsym{\}}\hlstd{}\\ +\mbox{} +\normalfont +\shorthandon{"} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/trains.tex b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/trains.tex new file mode 100644 index 0000000..a8543a5 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/trains.tex @@ -0,0 +1,454 @@ +\section{10362 - Trains} +\textbf{Problema:} Dado un conjunto de rutas de tren, determinar las conexiones +``\'optimas'' entre dos estaciones dadas. Una conexi\'on $c$ es \'optima +si se cumple lo siguiente: + +\begin{enumerate} +\item[(A)] No hay una conexi\'on $c'$ que salga m\'as tarde y llegue m\'as temprano o a la misma hora que $c$. +\item[(B)] No hay una conexi\'on $c'$ que salga a la misma hora y llegue m\'as temprano que $c$. +\end{enumerate} + +\subsection{Resolución} + +La idea del algoritmo propuesto es primero encontrar los caminos m\'as +cortos (en minutos) entre la estaci\'on de origen y la estaci\'on de +destino. Estos cumplen con la condici\'on (B). Una vez hecho esto, +determinar cu\'ales de ellos cumplen con la condici\'on (A). + +El problema de encontrar los caminos m\'as cortos se modela como un +problema de camino m\'inimo. + +\subsubsection{Descripci\'on del grafo asociado al problema} +En primer lugar, construimos un grafo orientado con pesos en los ejes +$G = (V,E)$, cuyos nodos +representan una estaci\'on y una hora del d\'ia, y cuyos ejes representan +una manera de llegar de una pareja estaci\'on/hora a otra. El grafo +contiene los siguientes nodos: + +$(n,h)\in V \longleftrightarrow$ existe un tren que pasa por la estaci\'on +$n$ a las $h$ horas $(h \in [\text{0:00}..\text{23:59}])$ + +%%$FINAL \in V$ + +Adem\'as, hay un eje desde $(n_1,h_1)$ hasta $(n_2,h_2) \longleftrightarrow$ se cumple alguno de los dos casos siguientes: +\begin{enumerate} +\item Existe un tren que pasa por $n_1$ a las $h_1$ y cuya siguiente parada es en $n_2$ a las $h_2$ (sin pasar por estaciones intermedias). +\item $n_1 = n_2$ (es la misma estaci\'on) y $h_2$ es el horario que sigue a $h_1$ en orden cronol\'ogico, sin pasar por horas intermedias. +\end{enumerate} +%\begin{enumerate} +%\item existe una ruta que permite tomar un tren en $n_1$ a las $h_1$ y llegar a $n_2$ a las $h_2$. +%\item $n_1=n_2 \wedge h_1 h_2 \wedge \nexists h_3 / (n_1,h_3) \in V \wedge ( h_1 < h_3 \vee h_3 < h_2)$ +%\end{enumerate} + +Los ejes que resultan de la primera condici\'on tienen como peso asociado el tiempo de viaje. +Si bien se conoce la hora del d\'ia asociada a cada nodo, es necesario conocer el peso +expl\'icitamente, porque el tiempo de viaje entre dos estaciones {\em puede} ser mayor a un d\'ia. + +Los ejes que resultan de la segunda condici\'on representan la posibilidad de quedarse +en una estaci\'on y esperar el próximo tren. En este caso, el peso del eje es la diferencia +entre $h_2$ y $h_1$. Cuando decimos que $h_2$ es el horario que sigue a $h_1$ +``en orden cronol\'ogico'', tambi\'en hay que considerar que $h_1$ puede ser +el \'ultimo tren del d\'ia y $h_2$ el primer tren del d\'ia siguiente. En ese caso +el peso del eje es la diferencia m\'odulo 24 horas. + +%TODO: esto hay que explicarlo mas y/o mejor? +El grafo descripto modela el problema porque una conexión permite +llegar de una estaci\'on/hora a otra si y s\'olo si existe +un camino entre los dos nodos correspondientes del grafo, de manera tal que el tiempo que +tarda la conexi\'on es el peso del camino. Esto es porque o bien el +camino es una ruta directa sin cambiar de tren (en cuyo caso, por +los ejes del caso $1$, hay un camino en el grafo con el peso apropiado), +o bien la conexión usa fragmentos de varias rutas. Para hacer esto, +es necesario esperar cierto tiempo en una estaci\'on para cambiar de tren. +El tiempo de espera debe ser contabilizado +también, lo que se logra con los ejes del caso $2$. Si es posible hacer +una combinación sin esperar, es porque se llega a una estaci\'on a la misma +hora en que sale el siguiente tren. Esto no representa un problema +porque el enunciado indica que el tiempo necesario para realizar la conexión +está incorporado en los horarios de los trenes. Por el caso $1$, ese nodo +tiene ambos ejes, y el camino es realizable. De manera similar +se ve lo inverso, es decir que cualquier camino en el grafo representa +una conexi\'on v\'alida. + +Notar que, en el primer caso, se agrega un eje s\'olo cuando la ruta no pasa por estaciones +intermedias. De manera similar, en el segundo caso, se agrega un eje de $(n,h_1)$ a $(n,h_2)$ +s\'olo cuando no existe un horario $h_3$ entre $h_1$ y $h_2$. +Es decir, el grafo se construye {\em sin} hacer la clausura transitiva +de los ejes. No es necesario agregar los ejes restantes, porque lo que +importa es la duraci\'on en minutos de los caminos, y todos +los caminos posibles est\'an dados precisamente la clausura transitiva +de los ejes. +La ventaja es que de esta manera la cantidad de ejes del grafo +es lineal en el tama\~no de la entrada. + +\subsubsection{B\'usqueda de los caminos m\'inimos} + +Una vez que se tiene el grafo descripto en la secci\'on anterior, +el objetivo es determinar las duraciones de las conexiones \'optimas. +Las conexiones \'optimas deben ser caminos mínimos entre nodos de la estaci\'on de origen +($src$) y la estaci\'on de destino ($dst$). Si no se tratara de caminos mínimos, sería posible +encontrar un camino que sale a la misma hora y llega antes (de menor duraci\'on, y por +lo tanto de menor peso), y la conexión no sería \'optima por no cumplir con +la condici\'on (B). + +El primer objetivo es determinar, para cada nodo $(src,h)$ el peso del +camino m\'inimo hasta alg\'un nodo $(dst,h')$. +Los pesos de los ejes son todos positivos, por lo cual es relativamente +sencillo convertir este problema en un problema de camino m\'inimo +{\em single-source}, para as\'i poder aplicar el algoritmo de Dijkstra. + +Para convertir el problema, se agrega un nodo $\textsc{final}$ y, para +cada nodo de la forma $(dst,h)$, un eje de peso 0 hacia el nodo $\textsc{final}$. +Por \'ultimo, se considera el grafo $G'$ que resulta de invertir +todos los ejes en $G$ y se calculan los caminos m\'inimos en $G'$ desde +$\textsc{final}$ hasta todos los dem\'as nodos, usando el algoritmo +de Dijkstra. + +Cada uno de los caminos m\'inimos encontrados en $G'$ que terminan en nodos +de la forma $(src,h)$, corresponden a alg\'un camino en $G$ que empieza en $(src,h)$, +llega hasta alg\'un nodo $(dst,h')$, y por \'ultimo llega a $\textsc{final}$ +mediante un eje de peso 0. El peso del camino correspondiente en $G$ es m\'inimo +y es el mismo que el encontrado en $G'$. + +%Por otro lado, todas los nodos cuya estaci\'on es la de destino, tienen un eje de costo $0$ con el nodo $FINAL$. + +Como observaci\'on adicional, dado que lo que se busca son caminos +m\'inimos, si una estaci\'on $n$ tiene un \'unico horario $h$ en el que salen o +llegan trenes, durante la construcci\'on del grafo $G$ no se agrega el autoeje +$(n,h)$, porque este eje tiene peso de 24 horas y obviamente nunca es conveniente +(existe un camino desde $v$ hasta $w$ que pasa por dicho eje si y s\'olo si existe +un camino de $v$ a $w$ de menor peso que no lo utiliza). + +\begin{figure}[H] +\centering +\includegraphics[scale=0.3]{./figuras/grafo.pdf} +\caption{Grafo resultante para la entrada de ejemplo (antes de invertir los ejes)} +\end{figure} + +\subsubsection{Determinaci\'on de las conexiones \'optimas} + +Una vez obtenidas las duraciones m\'inimas de los caminos que parten de cada +uno de los nodos $(src,h)$, resta s\'olo filtrar de esos caminos aquellos que +cumplen con la condici\'on (A). + +Notar que la condici\'on (A) usa la expresi\'on ``llegar m\'as temprano'' en +el sentido que uno le atribuye intuitivamente, y no a la hora absoluta del día. +Por ejemplo, salir a las 21:00 y llegar a las 22:00 es llegar m\'as temprano +que salir a las 20:00 y llegar a la 1:00, pese a que $\text{1:00} < \text{22:00}$. +Esto es obvio, pero indica que la implementaci\'on debe comparar las duraciones +totales de los viajes m\'as que las horas de llegada. +Algo similar aplica para la expresi\'on ``salir m\'as tarde''. +%En la resolución del problema consideramos el tiempo como cantidad de minutos. + +El siguiente es el algoritmo para elegir las rutas, asumiendo que +las distancias desde cada nodo $v$ hasta el nodo $\textsc{final}$ +ya fueron calculadas: + +\begin{algorithm}[H] +\begin{algorithmic} +\caption{Determina las conexiones \'optimas} +\PARAMS{$distancia_v$ = duraci\'on mínima de la conexi\'on desde un nodo $v$ hasta el nodo $\textsc{final}$} +\STATE mínima hora de llegada $:= \infty$ +\FOR{cada nodo $v$ de la forma $(src,h)$} +\STATE hora de llegada $:= h + distancia_{v} + $ 24 hs +\STATE\COMMENT{tiempo del nodo es la cantidad de tiempo hasta que sale el tren (i.e: si el tren sale a las 8, es la cantidad de minutos hasta las 8)} +\STATE mínima hora de llegada $:= \min($hora de llegada, mínima hora de llegada$)$ +\ENDFOR +\FOR{cada nodo $v$ de la forma $(src,h)$ (se recorren por hora decreciente)} +%\STATE hora de salida $:= h$ +\STATE hora de llegada $:= h + distancia_{v}$ +\IF{hora de llegada $<$ mínima hora de llegada} +\STATE mínima hora de llegada $:=$ hora de llegada +\STATE reportar la conexi\'on que sale a la hora $h$ y tarda $distancia_{v}$ en llegar +\ENDIF +\ENDFOR +\end{algorithmic} +\end{algorithm} + +El primer {\bf for} inicializa el valor de la variable ``m\'inima hora de llegada''. +Para esto se busca, entre todos los nodos $(src,h)$, el que minimiza $h + distancia_{(src,h)} + \text{24 hs}$. +Este valor $H$ representa la hora m\'as temprana a la que se puede llegar a destino partiendo al +d\'ia siguiente, y se usa como cota superior para descartar algunas de las conexiones +que no son \'optimas. +Es decir, si $distancia_{(src,h)} \geq H$, la conexi\'on m\'as corta que empieza +en la estaci\'on de origen tomando el tren de la hora $h$ llega a lo sumo tan temprano +como alguna otra conexi\'on posterior, y por lo tanto no es \'optima. + +Notar que alcanza con usar como cota superior la hora de llegada de +la conexi\'on m\'as corta que empieza en el {\em segundo} d\'ia +(y no es necesario mirar m\'as d\'ias hacia adelante) porque +la conexi\'on m\'as corta que empieza en el cualquier d\'ia +posterior al segundo llega despu\'es de $H$. + +En el segundo {\bf for}, se tiene como invariante que la variable ``m\'inima hora de llegada'' +es la m\'inima hora a la que se puede llegar con una conexi\'on que sale en +una hora posterior a $h$. Inicialmente esto es cierto porque, como ya se justific\'o, +``m\'inima hora de llegada'' se inicializa en $H$. El invariante se mantiene porque +los nodos se recorren por hora decreciente. En cada paso, si la hora a la que se +llega con una conexi\'on que empieza desde el nodo $v$ es menor que la m\'inima +hora a la que se puede llegar saliendo despu\'es de la hora $h$, esto quiere +decir que dicha conexi\'on cumple con la condici\'on (A). Adem\'as, es \'optima +porque tambi\'en cumpl\'ia con la condici\'on (B). + +\subsubsection{Detalles de implementaci\'on y complejidad} + +Todas las horas se representan en minutos. El grafo se representa con listas +de adyacencia. Cada nodo se identifica mediante un par $\langle id, hora \rangle$, +donde $id$ es un entero que representa una estaci\'on. Las listas de adyacencia se guardan +en un diccionario de nodo a lista de vecinos, cada uno con el peso del eje +correspondiente. + +Llamamos $N$ a la cantidad de estaciones y $M$ a la cantidad de ejes +del grafo asociado al problema. Notar que $N \in O(M)$ porque no puede +haber nodos aislados, ya que si una estaci\'on +ocurre en la entrada, debe figurar en al menos una ruta. Adem\'as, +$M$ es lineal en el tama\~no de la entrada, porque +los ejes que representan el camino de un tren deben estar +expl\'icitos en la entrada, mientras la cantidad de ejes que +conectan nodos de la misma estaci\'on es (por la manera en la +que se construye el grafo) a lo sumo igual a la cantidad total +de nodos de la estaci\'on. +% Para construir el grafo, la informaci\'on de las estaciones +%se guarda en un diccionario que dado el nombre de la estaci\'on devuelve su +%id y el conjunto de horas a las que un tren pasa por dicha estaci\'on. + +La implementaci\'on del algoritmo de Dijkstra usa una cola de prioridad +representada mediante un conjunto de tuplas $\langle distancia, nodo \rangle$, +por lo que la complejidad del algoritmo es $O(M \log N)$. El costo del +algoritmo que determina las conexiones \'optimas es $O(N \log N)$. +Previo a resolver el problema, el costo de procesar la entrada es el siguiente: +\begin{itemize} +\item Primero se asigna un id a cada estaci\'on, y se construye un +diccionario que permite ver, dada una estaci\'on (\texttt{string}), qu\'e +id tiene y a qué horas hay trenes que llegan o salen. El costo de +esto es $O(N \log N)$ asumiendo, de acuerdo con el enunciado del +problema, que los nombres de las estaciones tienen un largo m\'aximo fijo +(y razonablemente chico). +\item Despu\'es se construyen las listas de adyacencia. +Esto toma $O(M \log N + N \log N)$. El segundo término proviene del costo de agregar +los ejes entre nodos de la misma estación. Esto se puede hacer en $O(N \log N)$ iterando las +claves del diccionario que guarda los ids y las horas de cada estaci\'on. +\end{itemize} + +Finalmente la complejidad es $O(N \log N + M \log N) \subseteq O(M \log N)$. + +\subsection{Implementación} +\noindent +\ttfamily +\shorthandoff{"}\\ +\hlstd{}\hlline{\ 1\ }\hldir{\#include\ $<$iostream$>$}\\ +\hlline{\ 2\ }\hlstd{}\hldir{\#include\ $<$string$>$}\\ +\hlline{\ 3\ }\hlstd{}\hldir{\#include\ $<$map$>$}\\ +\hlline{\ 4\ }\hlstd{}\hldir{\#include\ $<$set$>$}\\ +\hlline{\ 5\ }\hlstd{}\hldir{\#include\ $<$vector$>$}\\ +\hlline{\ 6\ }\hlstd{}\hldir{\#include\ $<$list$>$}\\ +\hlline{\ 7\ }\hlstd{}\hldir{\#include\ $<$cassert$>$}\\ +\hlline{\ 8\ }\hlstd{}\hldir{\#include\ $<$cstdlib$>$}\\ +\hlline{\ 9\ }\hlstd{}\\ +\hlline{10\ }\hlkwa{using\ namespace\ }\hlstd{std}\hlsym{;}\\ +\hlline{11\ }\hlstd{}\\ +\hlline{12\ }\hldir{\#define\ forsn(i,\ s,\ n)\ for\ (int\ i\ =\ (s);\ i\ $<$\ (n);\ i++)}\\ +\hlline{13\ }\hlstd{}\hldir{\#define\ forn(i,\ n)}\hlstd{\ \ }\hldir{forsn\ (i,\ 0,\ n)}\\ +\hlline{14\ }\hlstd{}\hldir{\#define\ forall(x,\ s)\ for\ (typeof((s).begin())\ x\ =\ (s).begin();\ x\ !=\ (s).end();\ x++)}\\ +\hlline{15\ }\hlstd{}\hldir{\#define\ dforall(x,\ s)\ for\ (typeof((s).rbegin())\ x\ =\ (s).rbegin();\ x\ !=\ (s).rend();\ x++)}\\ +\hlline{16\ }\hlstd{}\\ +\hlline{17\ }\hlkwc{typedef\ }\hlstd{}\hlkwb{int\ }\hlstd{Id}\hlsym{;\ }\hlstd{}\hlslc{//\ station\ id}\\ +\hlline{18\ }\hlstd{}\hlkwc{typedef\ }\hlstd{}\hlkwb{int\ }\hlstd{Time}\hlsym{;}\\ +\hlline{19\ }\hlstd{}\hlkwc{typedef\ }\hlstd{pair}\hlsym{$<$}\hlstd{Id}\hlsym{,\ }\hlstd{Time}\hlsym{$>$\ }\hlstd{Nodo}\hlsym{;}\\ +\hlline{20\ }\hlstd{}\\ +\hlline{21\ }\hlkwb{struct\ }\hlstd{Edge\ }\hlsym{\{}\\ +\hlline{22\ }\hlstd{\ Nodo\ dest}\hlsym{;}\\ +\hlline{23\ }\hlstd{\ Time\ cost}\hlsym{;}\\ +\hlline{24\ }\hlstd{}\hlsym{\};}\\ +\hlline{25\ }\hlstd{}\hlkwc{typedef\ }\hlstd{vector}\hlsym{$<$}\hlstd{Edge}\hlsym{$>$\ }\hlstd{Ady}\hlsym{;}\\ +\hlline{26\ }\hlstd{}\hlkwc{typedef\ }\hlstd{map}\hlsym{$<$}\hlstd{Nodo}\hlsym{,\ }\hlstd{Ady}\hlsym{$>$\ }\hlstd{Grafo}\hlsym{;}\\ +\hlline{27\ }\hlstd{}\\ +\hlline{28\ }\hlkwc{typedef\ }\hlstd{map}\hlsym{$<$}\hlstd{string}\hlsym{,\ }\hlstd{pair}\hlsym{$<$}\hlstd{Id}\hlsym{,\ }\hlstd{set}\hlsym{$<$}\hlstd{Time}\hlsym{$>$\ $>$\ $>$\ }\hlstd{Stations}\hlsym{;}\\ +\hlline{29\ }\hlstd{}\\ +\hlline{30\ }\hlslc{//\ map$<$Nodo,\ Ady$>$::iterator}\\ +\hlline{31\ }\hlstd{}\hldir{\#define\ \textunderscore nodo}\hlstd{\ \ }\hldir{first}\\ +\hlline{32\ }\hlstd{}\hldir{\#define\ \textunderscore ady}\hlstd{\ \ }\hldir{second}\\ +\hlline{33\ }\hlstd{}\\ +\hlline{34\ }\hlslc{//\ Stations::iterator}\\ +\hlline{35\ }\hlstd{}\hldir{\#define\ \textunderscore info}\hlstd{\ \ }\hldir{second}\\ +\hlline{36\ }\hlstd{}\\ +\hlline{37\ }\hlslc{//\ pair$<$Id,\ set$<$Time$>$\ $>$}\\ +\hlline{38\ }\hlstd{}\hldir{\#define\ \textunderscore id}\hlstd{\ \ }\hldir{first}\\ +\hlline{39\ }\hlstd{}\hldir{\#define\ \textunderscore timeset\ second}\\ +\hlline{40\ }\hlstd{}\\ +\hlline{41\ }\hlslc{//\ Nodo}\\ +\hlline{42\ }\hlstd{}\hldir{\#define\ \textunderscore time}\hlstd{\ \ }\hldir{second}\\ +\hlline{43\ }\hlstd{}\\ +\hlline{44\ }\hldir{\#define\ HOUR\ 60}\\ +\hlline{45\ }\hlstd{}\hldir{\#define\ DAY\ (24\ {*}\ HOUR)}\\ +\hlline{46\ }\hlstd{\\ +\hlline{47\ }Id\ }\hlkwc{inline\ }\hlstd{}\hlkwd{register\textunderscore station}\hlstd{}\hlsym{(}\hlstd{Stations}\hlsym{\&\ }\hlstd{stations}\hlsym{,\ }\hlstd{}\hlkwb{const\ }\hlstd{string}\hlsym{\&\ }\hlstd{station\textunderscore name}\hlsym{,\ }\hlstd{Time\ time}\hlsym{)\ \{}\\ +\hlline{48\ }\hlstd{\ Stations}\hlsym{::}\hlstd{iterator\ }\hlkwd{it}\hlstd{}\hlsym{(}\hlstd{stations}\hlsym{.}\hlstd{}\hlkwd{find}\hlstd{}\hlsym{(}\hlstd{station\textunderscore name}\hlsym{));}\\ +\hlline{49\ }\hlstd{\ }\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{it\ }\hlsym{==\ }\hlstd{stations}\hlsym{.}\hlstd{}\hlkwd{end}\hlstd{}\hlsym{())\ \{}\\ +\hlline{50\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlslc{//\ create}\\ +\hlline{51\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwb{const\ }\hlstd{Id\ a\ }\hlsym{=\ }\hlstd{stations}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{();}\\ +\hlline{52\ }\hlstd{}\hlstd{\ \ }\hlstd{set}\hlsym{$<$}\hlstd{Time}\hlsym{$>$\ }\hlstd{s}\hlsym{;}\\ +\hlline{53\ }\hlstd{}\hlstd{\ \ }\hlstd{s}\hlsym{.}\hlstd{}\hlkwd{insert}\hlstd{}\hlsym{(}\hlstd{time}\hlsym{);}\\ +\hlline{54\ }\hlstd{}\hlstd{\ \ }\hlstd{stations}\hlsym{{[}}\hlstd{station\textunderscore name}\hlsym{{]}\ =\ }\hlstd{pair}\hlsym{$<$}\hlstd{Id}\hlsym{,\ }\hlstd{set}\hlsym{$<$}\hlstd{Time}\hlsym{$>$\ $>$(}\hlstd{a}\hlsym{,\ }\hlstd{s}\hlsym{);}\\ +\hlline{55\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{return\ }\hlstd{a}\hlsym{;}\\ +\hlline{56\ }\hlstd{\ }\hlsym{\}\ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{57\ }\hlstd{}\hlstd{\ \ }\hlstd{pair}\hlsym{$<$}\hlstd{Id}\hlsym{,}\hlstd{set}\hlsym{$<$}\hlstd{Time}\hlsym{$>$\ $>$\&\ }\hlstd{t\ }\hlsym{=\ }\hlstd{stations}\hlsym{{[}}\hlstd{station\textunderscore name}\hlsym{{]};}\\ +\hlline{58\ }\hlstd{}\hlstd{\ \ }\hlstd{t}\hlsym{.}\hlstd{\textunderscore timeset}\hlsym{.}\hlstd{}\hlkwd{insert}\hlstd{}\hlsym{(}\hlstd{time}\hlsym{);}\\ +\hlline{59\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{return\ }\hlstd{t}\hlsym{.}\hlstd{\textunderscore id}\hlsym{;}\\ +\hlline{60\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{61\ }\hlstd{}\hlsym{\}}\\ +\hlline{62\ }\hlstd{}\\ +\hlline{63\ }\hlkwc{inline\ }\hlstd{}\hlkwb{int\ }\hlstd{}\hlkwd{time\textunderscore in\textunderscore minutes}\hlstd{}\hlsym{(}\hlstd{string}\hlsym{\&\ }\hlstd{s}\hlsym{)\ \{}\\ +\hlline{64\ }\hlstd{\ }\hlslc{//\ h:mm\ hh:mm\ hhh:mm\ ...}\\ +\hlline{65\ }\hlstd{\ }\hlkwb{const\ int\ }\hlstd{l\ }\hlsym{=\ }\hlstd{s}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{();}\\ +\hlline{66\ }\hlstd{\ }\hlkwd{assert}\hlstd{}\hlsym{(}\hlstd{s}\hlsym{{[}}\hlstd{l\ }\hlsym{{-}\ }\hlstd{}\hlnum{3}\hlstd{}\hlsym{{]}\ ==\ }\hlstd{}\hlstr{`:`}\hlstd{}\hlsym{);}\\ +\hlline{67\ }\hlstd{\ }\hlkwa{return\ }\hlstd{}\hlkwd{atoi}\hlstd{}\hlsym{(}\hlstd{s}\hlsym{.}\hlstd{}\hlkwd{substr}\hlstd{}\hlsym{(}\hlstd{}\hlnum{0}\hlstd{}\hlsym{,\ }\hlstd{l\ }\hlsym{{-}\ }\hlstd{}\hlnum{3}\hlstd{}\hlsym{).}\hlstd{}\hlkwd{c\textunderscore str}\hlstd{}\hlsym{())\ {*}\ }\hlstd{HOUR\ }\hlsym{+\ }\hlstd{}\hlkwd{atoi}\hlstd{}\hlsym{(}\hlstd{s}\hlsym{.}\hlstd{}\hlkwd{substr}\hlstd{}\hlsym{(}\hlstd{l\ }\hlsym{{-}\ }\hlstd{}\hlnum{2}\hlstd{}\hlsym{,\ }\hlstd{}\hlnum{2}\hlstd{}\hlsym{).}\hlstd{}\hlkwd{c\textunderscore str}\hlstd{}\hlsym{());}\\ +\hlline{68\ }\hlstd{}\hlsym{\}}\\ +\hlline{69\ }\hlstd{}\\ +\hlline{70\ }\hlkwb{void\ }\hlstd{}\hlkwd{print\textunderscore graph}\hlstd{}\hlsym{(}\hlstd{Grafo}\hlsym{\&\ }\hlstd{g}\hlsym{)\ \{}\\ +\hlline{71\ }\hlstd{\ }\hlkwd{forall\ }\hlstd{}\hlsym{(}\hlstd{x}\hlsym{,\ }\hlstd{g}\hlsym{)\ \{}\\ +\hlline{72\ }\hlstd{}\hlstd{\ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{}\hlstr{"Hasta:\ "}\hlstd{\ }\hlsym{$<$$<$\ }\hlstd{x}\hlsym{{-}$>$}\hlstd{\textunderscore nodo}\hlsym{.}\hlstd{\textunderscore id\ }\hlsym{$<$$<$\ }\hlstd{}\hlstr{"\ a\ las\ "}\hlstd{\ }\hlsym{$<$$<$\ (}\hlstd{x}\hlsym{{-}$>$}\hlstd{\textunderscore nodo}\hlsym{.}\hlstd{\textunderscore time\ }\hlsym{/\ }\hlstd{}\hlnum{60}\hlstd{}\hlsym{)\ $<$$<$\ }\hlstd{}\hlstr{":"}\hlstd{\ }\hlsym{$<$$<$\ (}\hlstd{x}\hlsym{{-}$>$}\hlstd{\textunderscore nodo}\hlsym{.}\hlstd{\textunderscore time\ \Righttorque\\ +\hlline{73\ }}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\%\ }\hlstd{}\hlnum{60}\hlstd{}\hlsym{)\ $<$$<$\ }\hlstd{endl}\hlsym{;}\\ +\hlline{74\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{forall\ }\hlstd{}\hlsym{(}\hlstd{y}\hlsym{,\ }\hlstd{x}\hlsym{{-}$>$}\hlstd{\textunderscore ady}\hlsym{)\ \{}\\ +\hlline{75\ }\hlstd{}\hlstd{\ \ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{}\hlstr{"}\hlstd{\ \ \ \ }\hlstr{desde\ "}\hlstd{\ }\hlsym{$<$$<$\ }\hlstd{y}\hlsym{{-}$>$}\hlstd{dest}\hlsym{.}\hlstd{\textunderscore id\\ +\hlline{76\ }}\hlstd{\ \ \ \ }\hlstd{}\hlsym{$<$$<$\ }\hlstd{}\hlstr{"\ a\ las\ "}\hlstd{\ }\hlsym{$<$$<$\ (}\hlstd{y}\hlsym{{-}$>$}\hlstd{dest}\hlsym{.}\hlstd{\textunderscore time\ }\hlsym{/\ }\hlstd{}\hlnum{60}\hlstd{}\hlsym{)\ $<$$<$\ }\hlstd{}\hlstr{":"}\hlstd{\ }\hlsym{$<$$<$\ (}\hlstd{y}\hlsym{{-}$>$}\hlstd{dest}\hlsym{.}\hlstd{\textunderscore time\ }\hlsym{\%\ }\hlstd{}\hlnum{60}\hlstd{}\hlsym{)}\\ +\hlline{77\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{$<$$<$\ }\hlstd{}\hlstr{"\ costo:\ "}\hlstd{\ }\hlsym{$<$$<$\ (}\hlstd{y}\hlsym{{-}$>$}\hlstd{cost\ }\hlsym{/\ }\hlstd{}\hlnum{60}\hlstd{}\hlsym{)\ $<$$<$\ }\hlstd{}\hlstr{":"}\hlstd{\ }\hlsym{$<$$<$\ (}\hlstd{y}\hlsym{{-}$>$}\hlstd{cost\ }\hlsym{\%\ }\hlstd{}\hlnum{60}\hlstd{}\hlsym{)\ $<$$<$\ }\hlstd{endl}\hlsym{;}\\ +\hlline{78\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{79\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{80\ }\hlstd{}\hlsym{\}}\\ +\hlline{81\ }\hlstd{}\\ +\hlline{82\ }\hldir{\#define\ INF\ 0x7fffffff}\\ +\hlline{83\ }\hlstd{}\\ +\hlline{84\ }\hlkwc{inline\ }\hlstd{}\hlkwb{void\ }\hlstd{}\hlkwd{dijkstra}\hlstd{}\hlsym{(}\hlstd{Stations}\hlsym{\&\ }\hlstd{stations}\hlsym{,\ }\hlstd{Grafo}\hlsym{\&\ }\hlstd{graph}\hlsym{,\ }\hlstd{}\hlkwb{const\ }\hlstd{string}\hlsym{\&\ }\hlstd{origen}\hlsym{,\ }\hlstd{}\hlkwb{const\ }\hlstd{string}\hlsym{\&\ }\hlstd{destino}\hlsym{)\ \{}\\ +\hlline{85\ }\hlstd{\ }\hlkwb{const\ }\hlstd{Id\ id\textunderscore origen\ }\hlsym{=\ }\hlstd{stations}\hlsym{{[}}\hlstd{origen}\hlsym{{]}.}\hlstd{\textunderscore id}\hlsym{;}\\ +\hlline{86\ }\hlstd{\ }\hlkwb{const\ }\hlstd{Id\ id\textunderscore destino\ }\hlsym{=\ }\hlstd{stations}\hlsym{{[}}\hlstd{destino}\hlsym{{]}.}\hlstd{\textunderscore id}\hlsym{;}\\ +\hlline{87\ }\hlstd{\\ +\hlline{88\ }\ set}\hlsym{$<$}\hlstd{pair}\hlsym{$<$}\hlstd{Time}\hlsym{,\ }\hlstd{Nodo}\hlsym{$>$\ $>$\ }\hlstd{cola}\hlsym{;}\\ +\hlline{89\ }\hlstd{\ map}\hlsym{$<$}\hlstd{Nodo}\hlsym{,\ }\hlstd{Time}\hlsym{$>$\ }\hlstd{distancia}\hlsym{;}\\ +\hlline{90\ }\hlstd{\\ +\hlline{91\ }\ }\hlslc{//\ inicializar\ distancias}\\ +\hlline{92\ }\hlstd{\ }\hlkwd{forall\ }\hlstd{}\hlsym{(}\hlstd{st}\hlsym{,\ }\hlstd{stations}\hlsym{)\ \{}\\ +\hlline{93\ }\hlstd{}\hlstd{\ \ }\hlstd{Id\ station\textunderscore id\ }\hlsym{=\ }\hlstd{st}\hlsym{{-}$>$}\hlstd{\textunderscore info}\hlsym{.}\hlstd{\textunderscore id}\hlsym{;}\\ +\hlline{94\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{forall\ }\hlstd{}\hlsym{(}\hlstd{t}\hlsym{,\ }\hlstd{st}\hlsym{{-}$>$}\hlstd{\textunderscore info}\hlsym{.}\hlstd{\textunderscore timeset}\hlsym{)\ \{}\\ +\hlline{95\ }\hlstd{}\hlstd{\ \ \ }\hlstd{Nodo\ }\hlkwd{v}\hlstd{}\hlsym{(}\hlstd{station\textunderscore id}\hlsym{,\ {*}}\hlstd{t}\hlsym{);}\\ +\hlline{96\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{station\textunderscore id\ }\hlsym{==\ }\hlstd{id\textunderscore destino}\hlsym{)\ \{}\\ +\hlline{97\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{cola}\hlsym{.}\hlstd{}\hlkwd{insert}\hlstd{}\hlsym{(}\hlstd{pair}\hlsym{$<$}\hlstd{Time}\hlsym{,}\hlstd{Nodo}\hlsym{$>$(}\hlstd{}\hlnum{0}\hlstd{}\hlsym{,\ }\hlstd{v}\hlsym{));}\\ +\hlline{98\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{distancia}\hlsym{{[}}\hlstd{v}\hlsym{{]}\ =\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{99\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}\ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{100\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{distancia}\hlsym{{[}}\hlstd{v}\hlsym{{]}\ =\ }\hlstd{INF}\hlsym{;}\\ +\hlline{101\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{102\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{103\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{104\ }\hlstd{\ }\hlkwa{while\ }\hlstd{}\hlsym{(!}\hlstd{cola}\hlsym{.}\hlstd{}\hlkwd{empty}\hlstd{}\hlsym{())\ \{}\\ +\hlline{105\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlslc{//\ buscar\ el\ minimo}\\ +\hlline{106\ }\hlstd{}\hlstd{\ \ }\hlstd{Time\ min\textunderscore dist\ }\hlsym{=\ }\hlstd{cola}\hlsym{.}\hlstd{}\hlkwd{begin}\hlstd{}\hlsym{(){-}$>$}\hlstd{first}\hlsym{;}\\ +\hlline{107\ }\hlstd{\\ +\hlline{108\ }}\hlstd{\ \ }\hlstd{}\hlslc{//\ borrarlo\ de\ la\ cola}\\ +\hlline{109\ }\hlstd{}\hlstd{\ \ }\hlstd{Nodo\ min\textunderscore node\ }\hlsym{=\ }\hlstd{cola}\hlsym{.}\hlstd{}\hlkwd{begin}\hlstd{}\hlsym{(){-}$>$}\hlstd{second}\hlsym{;}\\ +\hlline{110\ }\hlstd{}\hlstd{\ \ }\hlstd{cola}\hlsym{.}\hlstd{}\hlkwd{erase}\hlstd{}\hlsym{(}\hlstd{cola}\hlsym{.}\hlstd{}\hlkwd{begin}\hlstd{}\hlsym{());}\\ +\hlline{111\ }\hlstd{\\ +\hlline{112\ }}\hlstd{\ \ }\hlstd{}\hlslc{//\ procesar\ min\textunderscore node}\\ +\hlline{113\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{forall\ }\hlstd{}\hlsym{(}\hlstd{eje}\hlsym{,\ }\hlstd{graph}\hlsym{{[}}\hlstd{min\textunderscore node}\hlsym{{]})\ \{}\\ +\hlline{114\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwb{const\ }\hlstd{Time\ dist\textunderscore nueva\ }\hlsym{=\ }\hlstd{min\textunderscore dist\ }\hlsym{+\ }\hlstd{eje}\hlsym{{-}$>$}\hlstd{cost}\hlsym{;}\\ +\hlline{115\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{const\ }\hlstd{Time\ dist\textunderscore actual\ }\hlsym{=\ }\hlstd{distancia}\hlsym{{[}}\hlstd{eje}\hlsym{{-}$>$}\hlstd{dest}\hlsym{{]};}\\ +\hlline{116\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{dist\textunderscore nueva\ }\hlsym{$<$\ }\hlstd{dist\textunderscore actual}\hlsym{)\ \{}\\ +\hlline{117\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{dist\textunderscore actual\ }\hlsym{!=\ }\hlstd{INF}\hlsym{)\ \{}\\ +\hlline{118\ }\hlstd{}\hlstd{\ \ \ \ \ }\hlstd{cola}\hlsym{.}\hlstd{}\hlkwd{erase}\hlstd{}\hlsym{(}\hlstd{cola}\hlsym{.}\hlstd{}\hlkwd{find}\hlstd{}\hlsym{(}\hlstd{pair}\hlsym{$<$}\hlstd{Time}\hlsym{,}\hlstd{Nodo}\hlsym{$>$(}\hlstd{dist\textunderscore actual}\hlsym{,\ }\hlstd{eje}\hlsym{{-}$>$}\hlstd{dest}\hlsym{)));}\\ +\hlline{119\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{120\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{distancia}\hlsym{{[}}\hlstd{eje}\hlsym{{-}$>$}\hlstd{dest}\hlsym{{]}\ =\ }\hlstd{dist\textunderscore nueva}\hlsym{;}\\ +\hlline{121\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{cola}\hlsym{.}\hlstd{}\hlkwd{insert}\hlstd{}\hlsym{(}\hlstd{pair}\hlsym{$<$}\hlstd{Time}\hlsym{,}\hlstd{Nodo}\hlsym{$>$(}\hlstd{dist\textunderscore nueva}\hlsym{,\ }\hlstd{eje}\hlsym{{-}$>$}\hlstd{dest}\hlsym{));}\\ +\hlline{122\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{123\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{124\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{125\ }\hlstd{\\ +\hlline{126\ }\ list}\hlsym{$<$}\hlstd{pair}\hlsym{$<$}\hlstd{Time}\hlsym{,\ }\hlstd{Time}\hlsym{$>$\ $>$\ }\hlstd{salida}\hlsym{;}\\ +\hlline{127\ }\hlstd{\ Time\ min\textunderscore hora\textunderscore llega\ }\hlsym{=\ }\hlstd{INF}\hlsym{;}\\ +\hlline{128\ }\hlstd{\ }\hlkwd{forall\ }\hlstd{}\hlsym{(}\hlstd{t}\hlsym{,\ }\hlstd{stations}\hlsym{{[}}\hlstd{origen}\hlsym{{]}.}\hlstd{\textunderscore timeset}\hlsym{)\ \{}\\ +\hlline{129\ }\hlstd{}\hlstd{\ \ }\hlstd{Nodo\ }\hlkwd{v}\hlstd{}\hlsym{(}\hlstd{id\textunderscore origen}\hlsym{,\ {*}}\hlstd{t}\hlsym{);}\\ +\hlline{130\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwb{const\ }\hlstd{Time\ hora\textunderscore llega\ }\hlsym{=\ {*}}\hlstd{t\ }\hlsym{+\ }\hlstd{distancia}\hlsym{{[}}\hlstd{v}\hlsym{{]}\ +\ }\hlstd{DAY}\hlsym{;}\\ +\hlline{131\ }\hlstd{}\hlstd{\ \ }\hlstd{min\textunderscore hora\textunderscore llega\ }\hlsym{=\ }\hlstd{}\hlkwd{min}\hlstd{}\hlsym{(}\hlstd{min\textunderscore hora\textunderscore llega}\hlsym{,\ }\hlstd{hora\textunderscore llega}\hlsym{);}\\ +\hlline{132\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{133\ }\hlstd{\ }\hlkwd{dforall\ }\hlstd{}\hlsym{(}\hlstd{t}\hlsym{,\ }\hlstd{stations}\hlsym{{[}}\hlstd{origen}\hlsym{{]}.}\hlstd{\textunderscore timeset}\hlsym{)\ \{}\\ +\hlline{134\ }\hlstd{}\hlstd{\ \ }\hlstd{Nodo\ }\hlkwd{v}\hlstd{}\hlsym{(}\hlstd{id\textunderscore origen}\hlsym{,\ {*}}\hlstd{t}\hlsym{);}\\ +\hlline{135\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwb{const\ }\hlstd{Time\ hora\textunderscore sale\ }\hlsym{=\ {*}}\hlstd{t}\hlsym{;}\\ +\hlline{136\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwb{const\ }\hlstd{Time\ hora\textunderscore llega\ }\hlsym{=\ {*}}\hlstd{t\ }\hlsym{+\ }\hlstd{distancia}\hlsym{{[}}\hlstd{v}\hlsym{{]};}\\ +\hlline{137\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{hora\textunderscore llega\ }\hlsym{$>$=\ }\hlstd{min\textunderscore hora\textunderscore llega}\hlsym{)\ }\hlstd{}\hlkwa{continue}\hlstd{}\hlsym{;}\\ +\hlline{138\ }\hlstd{}\hlstd{\ \ }\hlstd{min\textunderscore hora\textunderscore llega\ }\hlsym{=\ }\hlstd{hora\textunderscore llega}\hlsym{;}\\ +\hlline{139\ }\hlstd{}\hlstd{\ \ }\hlstd{salida}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore front}\hlstd{}\hlsym{(}\hlstd{pair}\hlsym{$<$}\hlstd{Time}\hlsym{,\ }\hlstd{Time}\hlsym{$>$(}\hlstd{hora\textunderscore sale}\hlsym{,\ }\hlstd{distancia}\hlsym{{[}}\hlstd{v}\hlsym{{]}));}\\ +\hlline{140\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{141\ }\hlstd{\ }\hlkwd{forall\ }\hlstd{}\hlsym{(}\hlstd{res}\hlsym{,\ }\hlstd{salida}\hlsym{)\ \{}\\ +\hlline{142\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{printf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%.2i:\%.2i\ "}\hlstd{}\hlsym{,\ }\hlstd{res}\hlsym{{-}$>$}\hlstd{first\ }\hlsym{/\ }\hlstd{}\hlnum{60}\hlstd{}\hlsym{,\ }\hlstd{res}\hlsym{{-}$>$}\hlstd{first\ }\hlsym{\%\ }\hlstd{}\hlnum{60}\hlstd{}\hlsym{);}\\ +\hlline{143\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{printf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%i:\%.2i}\hlesc{$\backslash$n}\hlstr{"}\hlstd{}\hlsym{,\ }\hlstd{res}\hlsym{{-}$>$}\hlstd{second\ }\hlsym{/\ }\hlstd{}\hlnum{60}\hlstd{}\hlsym{,\ }\hlstd{res}\hlsym{{-}$>$}\hlstd{second\ }\hlsym{\%\ }\hlstd{}\hlnum{60}\hlstd{}\hlsym{);}\\ +\hlline{144\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{145\ }\hlstd{}\hlsym{\}}\\ +\hlline{146\ }\hlstd{}\\ +\hlline{147\ }\hldir{\#define\ add\textunderscore edge(g,\ v1,\ v2,\ c)\ ((g){[}(v1){]}.push\textunderscore back((Edge)\{dest:\ (v2),\ cost:\ (c)\}))}\\ +\hlline{148\ }\hlstd{}\hlkwb{int\ }\hlstd{}\hlkwd{main}\hlstd{}\hlsym{()\ \{}\\ +\hlline{149\ }\hlstd{\ }\hlkwb{int\ }\hlstd{ncases}\hlsym{;}\\ +\hlline{150\ }\hlstd{\ cin\ }\hlsym{$>$$>$\ }\hlstd{ncases}\hlsym{;}\\ +\hlline{151\ }\hlstd{\\ +\hlline{152\ }\ }\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{c}\hlsym{,\ }\hlstd{ncases}\hlsym{)\ \{}\\ +\hlline{153\ }\hlstd{}\hlstd{\ \ }\hlstd{Stations\ stations}\hlsym{;}\\ +\hlline{154\ }\hlstd{}\hlstd{\ \ }\hlstd{Grafo\ graph}\hlsym{;}\\ +\hlline{155\ }\hlstd{\\ +\hlline{156\ }}\hlstd{\ \ }\hlstd{}\hlkwb{int\ }\hlstd{num\textunderscore trains}\hlsym{;}\\ +\hlline{157\ }\hlstd{}\hlstd{\ \ }\hlstd{cin\ }\hlsym{$>$$>$\ }\hlstd{num\textunderscore trains}\hlsym{;}\\ +\hlline{158\ }\hlstd{\\ +\hlline{159\ }}\hlstd{\ \ }\hlstd{}\hlslc{//\ read\ trains\ and\ stations}\\ +\hlline{160\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{t}\hlsym{,\ }\hlstd{num\textunderscore trains}\hlsym{)\ \{}\\ +\hlline{161\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{num\textunderscore stations}\hlsym{;}\\ +\hlline{162\ }\hlstd{}\hlstd{\ \ \ }\hlstd{cin\ }\hlsym{$>$$>$\ }\hlstd{num\textunderscore stations}\hlsym{;}\\ +\hlline{163\ }\hlstd{\\ +\hlline{164\ }}\hlstd{\ \ \ }\hlstd{Nodo\ prev}\hlsym{;}\\ +\hlline{165\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{time\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{166\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{s}\hlsym{,\ }\hlstd{num\textunderscore stations}\hlsym{)\ \{}\\ +\hlline{167\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{string\ time\textunderscore str}\hlsym{,\ }\hlstd{station\textunderscore name}\hlsym{;}\\ +\hlline{168\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{cin\ }\hlsym{$>$$>$\ }\hlstd{time\textunderscore str\ }\hlsym{$>$$>$\ }\hlstd{station\textunderscore name}\hlsym{;}\\ +\hlline{169\ }\hlstd{\\ +\hlline{170\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ }\hlstd{Time\ cost\ }\hlsym{=\ }\hlstd{}\hlkwd{time\textunderscore in\textunderscore minutes}\hlstd{}\hlsym{(}\hlstd{time\textunderscore str}\hlsym{);}\\ +\hlline{171\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{time\ }\hlsym{=\ (}\hlstd{time\ }\hlsym{+\ }\hlstd{cost}\hlsym{)\ \%\ }\hlstd{DAY}\hlsym{;}\\ +\hlline{172\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ }\hlstd{Id\ station\textunderscore id\ }\hlsym{=\ }\hlstd{}\hlkwd{register\textunderscore station}\hlstd{}\hlsym{(}\hlstd{stations}\hlsym{,\ }\hlstd{station\textunderscore name}\hlsym{,\ }\hlstd{time}\hlsym{);}\\ +\hlline{173\ }\hlstd{\\ +\hlline{174\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ }\hlstd{Nodo\ }\hlkwd{next}\hlstd{}\hlsym{(}\hlstd{station\textunderscore id}\hlsym{,\ }\hlstd{time}\hlsym{);}\\ +\hlline{175\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{s\ }\hlsym{!=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ \{}\\ +\hlline{176\ }\hlstd{}\hlstd{\ \ \ \ \ }\hlstd{}\hlkwd{add\textunderscore edge}\hlstd{}\hlsym{(}\hlstd{graph}\hlsym{,\ }\hlstd{next}\hlsym{,\ }\hlstd{prev}\hlsym{,\ }\hlstd{cost}\hlsym{);}\\ +\hlline{177\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{178\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{prev\ }\hlsym{=\ }\hlstd{next}\hlsym{;}\\ +\hlline{179\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{180\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{181\ }\hlstd{\\ +\hlline{182\ }}\hlstd{\ \ }\hlstd{}\hlslc{//\ complete\ the\ graph\ with\ the\ self\ edges\ for\ each\ station}\\ +\hlline{183\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{forall\ }\hlstd{}\hlsym{(}\hlstd{station}\hlsym{,\ }\hlstd{stations}\hlsym{)\ \{}\\ +\hlline{184\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwb{const\ }\hlstd{Id\ id\ }\hlsym{=\ }\hlstd{station}\hlsym{{-}$>$}\hlstd{\textunderscore info}\hlsym{.}\hlstd{\textunderscore id}\hlsym{;}\\ +\hlline{185\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwb{const\ }\hlstd{set}\hlsym{$<$}\hlstd{Time}\hlsym{$>$\&\ }\hlstd{timeset\ }\hlsym{=\ }\hlstd{station}\hlsym{{-}$>$}\hlstd{\textunderscore info}\hlsym{.}\hlstd{\textunderscore timeset}\hlsym{;}\\ +\hlline{186\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{timeset}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{()\ ==\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ }\hlstd{}\hlkwa{continue}\hlstd{}\hlsym{;}\\ +\hlline{187\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwd{forall\ }\hlstd{}\hlsym{(}\hlstd{t1}\hlsym{,\ }\hlstd{timeset}\hlsym{)\ \{}\\ +\hlline{188\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{set}\hlsym{$<$}\hlstd{Time}\hlsym{$>$::}\hlstd{iterator\ t2\ }\hlsym{=\ }\hlstd{t1}\hlsym{;}\\ +\hlline{189\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{t2}\hlsym{++;}\\ +\hlline{190\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ }\hlstd{Nodo\ }\hlkwd{v1}\hlstd{}\hlsym{(}\hlstd{id}\hlsym{,\ {*}}\hlstd{t1}\hlsym{);}\\ +\hlline{191\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ }\hlstd{Nodo\ }\hlkwd{v2}\hlstd{}\hlsym{(}\hlstd{id}\hlsym{,\ }\hlstd{t2\ }\hlsym{==\ }\hlstd{timeset}\hlsym{.}\hlstd{}\hlkwd{end}\hlstd{}\hlsym{()\ }\hlstd{?\ }\hlsym{{*}}\hlstd{timeset}\hlsym{.}\hlstd{}\hlkwd{begin}\hlstd{}\hlsym{()\ :\ {*}}\hlstd{t2}\hlsym{);}\\ +\hlline{192\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{Time\ cost\ }\hlsym{=\ }\hlstd{v2}\hlsym{.}\hlstd{\textunderscore time\ }\hlsym{{-}\ }\hlstd{v1}\hlsym{.}\hlstd{\textunderscore time}\hlsym{;}\\ +\hlline{193\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{cost\ }\hlsym{$<$\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ }\hlstd{cost\ }\hlsym{+=\ }\hlstd{DAY}\hlsym{;}\\ +\hlline{194\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{add\textunderscore edge}\hlstd{}\hlsym{(}\hlstd{graph}\hlsym{,\ }\hlstd{v2}\hlsym{,\ }\hlstd{v1}\hlsym{,\ }\hlstd{cost}\hlsym{);}\\ +\hlline{195\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{196\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{197\ }\hlstd{\\ +\hlline{198\ }}\hlstd{\ \ }\hlstd{string\ origen}\hlsym{,\ }\hlstd{destino}\hlsym{;}\\ +\hlline{199\ }\hlstd{}\hlstd{\ \ }\hlstd{cin\ }\hlsym{$>$$>$\ }\hlstd{origen\ }\hlsym{$>$$>$\ }\hlstd{destino}\hlsym{;}\\ +\hlline{200\ }\hlstd{\\ +\hlline{201\ }}\hlstd{\ \ }\hlstd{}\hlkwd{dijkstra}\hlstd{}\hlsym{(}\hlstd{stations}\hlsym{,\ }\hlstd{graph}\hlsym{,\ }\hlstd{origen}\hlsym{,\ }\hlstd{destino}\hlsym{);}\\ +\hlline{202\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{c\ }\hlsym{!=\ }\hlstd{ncases\ }\hlsym{{-}\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ \{}\\ +\hlline{203\ }\hlstd{}\hlstd{\ \ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{endl}\hlsym{;}\\ +\hlline{204\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{205\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{206\ }\hlstd{\ }\hlkwa{return\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{207\ }\hlstd{}\hlsym{\}}\\ +\hlline{208\ }\hlstd{}\\ +\mbox{} +\normalfont +\shorthandon{"} + + + + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/trans_algorithmic.tex b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/trans_algorithmic.tex new file mode 100644 index 0000000..9ce8c65 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/doc/trans_algorithmic.tex @@ -0,0 +1,15 @@ +\renewcommand{\algorithmicrequire}{\textcolor{blue}{\textbf{Requiere:}}} +\renewcommand{\algorithmicensure}{\textbf{Devuelve:}} +\renewcommand{\algorithmicend}{\textbf{Fin}} +\renewcommand{\algorithmicif}{\textcolor{blue}{\textbf{Si}}} +\renewcommand{\algorithmicthen}{\textcolor{blue}{}} %%\textbf{entonces}}} +\renewcommand{\algorithmicelse}{\textcolor{red}{\textbf{Si no}}} +\renewcommand{\algorithmicelsif }{\textcolor{blue}{\textbf{Si no y}}} +\renewcommand{\algorithmicendif}{\textcolor{blue}{\textbf{Fin si}}} +\renewcommand{\algorithmicfor}{\textcolor{ForestGreen}{\textbf{Para}}} +\renewcommand{\algorithmicendfor}{\textcolor{ForestGreen}{\textbf{Fin para}}} +\renewcommand{\algorithmicwhile}{\textcolor{ForestGreen}{\textbf{Mientras}}} +\renewcommand{\algorithmicendwhile}{\textcolor{ForestGreen}{\textbf{Fin mientras}}} +\renewcommand{\algorithmicdo}{\textcolor{ForestGreen}{}} %%\textbf{hacer}}} +\renewcommand{\algorithmicreturn}{\textbf{Devolver}} +\floatname{algorithm}{Algoritmo} diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/labyrinth/main.cpp b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/labyrinth/main.cpp new file mode 100644 index 0000000..8d62f97 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/labyrinth/main.cpp @@ -0,0 +1,86 @@ +#include +#include +#include +#include + +using namespace std; + +#define forsn(i, s, n) for (int i = (s); i < (n); i++) +#define forn(i, n) forsn (i, 0, n) + +typedef vector vbool; +typedef vector vvbool; + +typedef int Node; +int rows; +int cols; +vvbool mapa; + +#define node(r, c) ((r) << 12 | (c)) +#define node_row(v) ((v) >> 12) +#define node_col(v) ((v) & 0xfff) + +#define NONE 0xffffffff + +Node vecino(bool ns, Node v) { +#define sig(x) ((x) ? 1 : -1) + const int r = node_row(v) - ns, c = node_col(v); + if (r < 0 || r >= rows) return NONE; + const int cc = c + sig(ns ^ mapa[r][c]); + if (cc < 0 || cc >= cols) return NONE; + const int rr = node_row(v) + sig(ns) * -!(mapa[r][c] ^ mapa[r][cc]); + if (rr < 0 || rr > rows) return NONE; + return node(rr, cc); +} + +int resolver() { +#define marcado(v) (_marcas[node_row(v)][node_col(v)]) +#define marcar(v) (_marcas[node_row(v)][node_col(v)] = true) + int cant = 0; + vvbool _marcas(rows + 1, vbool(cols, false)); + forn (c, cols) { + Node v = node(0, c); + + if (marcado(v)) continue; + marcar(v); + + for (;;) { + Node w = NONE; + forn (direction, 2) { + Node vv = vecino(direction, v); + if (vv == NONE || marcado(vv)) continue; + assert(w == NONE); + w = vv; + } + if (w == NONE) break; + if (node_row(w) == rows) { + cant++; + break; + } + marcar(w); + v = w; + } + } + return cant; +} + +int main() { + int ncases; + cin >> ncases; + + forn (i, ncases) { + cin >> cols >> rows; + mapa = vvbool(rows, vbool(cols)); + forn (r, rows) { + forn (c, cols) { + char mapa_rc; + cin >> mapa_rc; + mapa[r][c] = (mapa_rc == '\\'); + } + } + + cout << resolver() << endl; + } + + return 0; +} diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/trains/main.cpp b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/trains/main.cpp new file mode 100644 index 0000000..a26322c --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpb/trains/main.cpp @@ -0,0 +1,207 @@ +#include +#include +#include +#include +#include +#include +#include +#include + +using namespace std; + +#define forsn(i, s, n) for (int i = (s); i < (n); i++) +#define forn(i, n) forsn (i, 0, n) +#define forall(x, s) for (typeof((s).begin()) x = (s).begin(); x != (s).end(); x++) +#define dforall(x, s) for (typeof((s).rbegin()) x = (s).rbegin(); x != (s).rend(); x++) + +typedef int Id; // station id +typedef int Time; +typedef pair Nodo; + +struct Edge { + Nodo dest; + Time cost; +}; +typedef vector Ady; +typedef map Grafo; + +typedef map > > Stations; + +// map::iterator +#define _nodo first +#define _ady second + +// Stations::iterator +#define _info second + +// pair > +#define _id first +#define _timeset second + +// Nodo +#define _time second + +#define HOUR 60 +#define DAY (24 * HOUR) + +Id inline register_station(Stations& stations, const string& station_name, Time time) { + Stations::iterator it(stations.find(station_name)); + if (it == stations.end()) { + // create + const Id a = stations.size(); + set

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+\hlline{\ 6\ }\hlstd{}\\ +\hlline{\ 7\ }\hlkwa{using\ namespace\ }\hlstd{std}\hlsym{;}\\ +\hlline{\ 8\ }\hlstd{}\\ +\hlline{\ 9\ }\hlkwc{typedef\ }\hlstd{}\hlkwb{unsigned\ long\ long\ int\ }\hlstd{lluint}\hlsym{;}\\ +\hlline{10\ }\hlstd{}\hlkwc{typedef\ }\hlstd{vector}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$\ }\hlstd{vint}\hlsym{;}\\ +\hlline{11\ }\hlstd{}\\ +\hlline{12\ }\hldir{\#define\ forsn(i,\ s,\ n)\ for\ (int\ i\ =\ (s);\ i\ $<$\ (n);\ i++)}\\ +\hlline{13\ }\hlstd{}\hldir{\#define\ forn(i,\ n)\ forsn\ (i,\ 0,\ n)}\\ +\hlline{14\ }\hlstd{}\\ +\hlline{15\ }\hlslc{//\ Pre\ KMP}\\ +\hlline{16\ }\hlstd{}\\ +\hlline{17\ }\hlkwb{void\ }\hlstd{}\hlkwd{pkmp}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ }\hlstd{string}\hlsym{\&\ }\hlstd{s}\hlsym{,\ }\hlstd{vint}\hlsym{\&\ }\hlstd{f}\hlsym{)\ \{}\\ +\hlline{18\ }\hlstd{\ }\hlkwb{int\ }\hlstd{z\ }\hlsym{=\ }\hlstd{f}\hlsym{{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}\ =\ {-}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{19\ }\hlstd{\ }\hlkwd{forsn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{,\ }\hlstd{s}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{()\ +\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ \{}\\ +\hlline{20\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{while\ }\hlstd{}\hlsym{(}\hlstd{z\ }\hlsym{!=\ {-}}\hlstd{}\hlnum{1\ }\hlstd{}\hlsym{\&\&\ }\hlstd{s}\hlsym{{[}}\hlstd{i\ }\hlsym{{-}\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]}\ !=\ }\hlstd{s}\hlsym{{[}}\hlstd{z}\hlsym{{]})\ }\hlstd{z\ }\hlsym{=\ }\hlstd{f}\hlsym{{[}}\hlstd{z}\hlsym{{]};}\\ +\hlline{21\ }\hlstd{}\hlstd{\ \ }\hlstd{f}\hlsym{{[}}\hlstd{i}\hlsym{{]}\ =\ ++}\hlstd{z}\hlsym{;\ }\hlstd{}\hlslc{//\ z\ might\ be\ {-}1}\\ +\hlline{22\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{23\ }\hlstd{}\hlsym{\}}\\ +\hlline{24\ }\hlstd{}\\ +\hlline{25\ }\hlslc{//\ Buffer}\\ +\hlline{26\ }\hlstd{}\\ +\hlline{27\ }\hldir{\#define\ TAMBUF\ 65536}\\ +\hlline{28\ }\hlstd{lluint\ pos}\hlsym{;}\\ +\hlline{29\ }\hlstd{}\hlkwb{char\ }\hlstd{buf}\hlsym{{[}}\hlstd{TAMBUF}\hlsym{{]};}\\ +\hlline{30\ }\hlstd{}\hlkwb{int\ }\hlstd{buf\textunderscore size}\hlsym{;}\\ +\hlline{31\ }\hlstd{}\\ +\hlline{32\ }\hldir{\#define\ buf\textunderscore sync()\ \{\ $\backslash$}\\ +\hlline{33\ }\hldir{\ cin.getline(buf,\ TAMBUF\ +\ 1);\ $\backslash$}\\ +\hlline{34\ }\hldir{\ pos\ +=\ buf\textunderscore size;\ $\backslash$}\\ +\hlline{35\ }\hldir{\ buf\textunderscore size\ =\ cin.gcount();\ $\backslash$}\\ +\hlline{36\ }\hldir{\ cin.clear();\ $\backslash$}\\ +\hlline{37\ }\hldir{\}}\\ +\hlline{38\ }\hlstd{}\\ +\hlline{39\ }\hldir{\#define\ buf\textunderscore start()\ \{\ $\backslash$}\\ +\hlline{40\ }\hldir{\ buf\textunderscore sync();\ $\backslash$}\\ +\hlline{41\ }\hldir{\ pos\ =\ 0;\ $\backslash$}\\ +\hlline{42\ }\hldir{\}}\\ +\hlline{43\ }\hlstd{}\\ +\hlline{44\ }\hlslc{//\ KMP}\\ +\hlline{45\ }\hlstd{}\\ +\hlline{46\ }\hlkwb{void\ }\hlstd{}\hlkwd{kmp}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ }\hlstd{string}\hlsym{\&\ }\hlstd{s}\hlsym{,\ }\hlstd{vint}\hlsym{\&\ }\hlstd{f}\hlsym{)\ \{}\\ +\hlline{47\ }\hlstd{\ }\hlkwd{buf\textunderscore start}\hlstd{}\hlsym{();}\\ +\hlline{48\ }\hlstd{\ }\hlkwb{const\ int\ }\hlstd{final\ }\hlsym{=\ }\hlstd{s}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{();}\\ +\hlline{49\ }\hlstd{\ }\hlkwb{int\ }\hlstd{state\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{50\ }\hlstd{\ }\hlkwa{while\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwa{true}\hlstd{}\hlsym{)\ \{}\\ +\hlline{51\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{buf\textunderscore size}\hlsym{)\ \{}\\ +\hlline{52\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{state\ }\hlsym{==\ }\hlstd{final}\hlsym{)\ \{}\\ +\hlline{53\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{cout\ }\hlsym{$<$$<$\ (}\hlstd{pos\ }\hlsym{+\ }\hlstd{i\ }\hlsym{{-}\ }\hlstd{final}\hlsym{)\ $<$$<$\ }\hlstd{}\hlstr{"\ "}\hlstd{}\hlsym{;}\\ +\hlline{54\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{55\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlkwa{while\ }\hlstd{}\hlsym{(}\hlstd{s}\hlsym{{[}}\hlstd{state}\hlsym{{]}\ !=\ }\hlstd{buf}\hlsym{{[}}\hlstd{i}\hlsym{{]})\ \{}\\ +\hlline{56\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{state\ }\hlsym{=\ }\hlstd{f}\hlsym{{[}}\hlstd{state}\hlsym{{]};}\\ +\hlline{57\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{state\ }\hlsym{==\ {-}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ }\hlstd{}\hlkwa{break}\hlstd{}\hlsym{;}\\ +\hlline{58\ }\hlstd{}\hlstd{\ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{59\ }\hlstd{}\hlstd{\ \ \ }\hlstd{state}\hlsym{++;}\\ +\hlline{60\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{\}}\\ +\hlline{61\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{buf\textunderscore size\ }\hlsym{$<$\ }\hlstd{TAMBUF}\hlsym{)\ }\hlstd{}\hlkwa{break}\hlstd{}\hlsym{;}\\ +\hlline{62\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{buf\textunderscore sync}\hlstd{}\hlsym{();}\\ +\hlline{63\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{64\ }\hlstd{}\hlsym{\}}\\ +\hlline{65\ }\hlstd{}\\ +\hlline{66\ }\hlkwb{int\ }\hlstd{}\hlkwd{main}\hlstd{}\hlsym{()\ \{}\\ +\hlline{67\ }\hlstd{\ }\hlkwa{for\ }\hlstd{}\hlsym{(;;)\ \{}\\ +\hlline{68\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwb{int\ }\hlstd{needle\textunderscore size}\hlsym{;}\\ +\hlline{69\ }\hlstd{}\hlstd{\ \ }\hlstd{string\ needle}\hlsym{;}\\ +\hlline{70\ }\hlstd{}\hlstd{\ \ }\hlstd{cin\ }\hlsym{$>$$>$\ }\hlstd{needle\textunderscore size}\hlsym{;}\\ +\hlline{71\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{cin}\hlsym{.}\hlstd{}\hlkwd{eof}\hlstd{}\hlsym{())\ }\hlstd{}\hlkwa{break}\hlstd{}\hlsym{;}\\ +\hlline{72\ }\hlstd{}\hlstd{\ \ }\hlstd{cin\ }\hlsym{$>$$>$\ }\hlstd{needle}\hlsym{;}\\ +\hlline{73\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{assert}\hlstd{}\hlsym{(}\hlstd{needle\textunderscore size\ }\hlsym{==\ }\hlstd{needle}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{());}\\ +\hlline{74\ }\hlstd{}\hlstd{\ \ }\hlstd{cin}\hlsym{.}\hlstd{}\hlkwd{ignore}\hlstd{}\hlsym{(}\hlstd{}\hlnum{1}\hlstd{}\hlsym{);}\\ +\hlline{75\ }\hlstd{\\ +\hlline{76\ }}\hlstd{\ \ }\hlstd{vint\ }\hlkwd{f}\hlstd{}\hlsym{(}\hlstd{needle}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{()\ +\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{);}\\ +\hlline{77\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{pkmp}\hlstd{}\hlsym{(}\hlstd{needle}\hlsym{,\ }\hlstd{f}\hlsym{);}\\ +\hlline{78\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{kmp}\hlstd{}\hlsym{(}\hlstd{needle}\hlsym{,\ }\hlstd{f}\hlsym{);}\\ +\hlline{79\ }\hlstd{}\hlstd{\ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{endl}\hlsym{;}\\ +\hlline{80\ }\hlstd{\ }\hlsym{\}}\\ +\hlline{81\ }\hlstd{\ }\hlkwa{return\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{82\ }\hlstd{}\hlsym{\}}\\ +\hlline{83\ }\hlstd{}\\ +\mbox{} +\normalfont +\shorthandon{"} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/doc/newdistinct.tex b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/doc/newdistinct.tex new file mode 100644 index 0000000..2f50bf6 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/doc/newdistinct.tex @@ -0,0 +1,240 @@ +\section{705 - SUBST1} +Dado un string $s$, encontrar el número total de substrings distintas. + +\subsection{Resolución} +Para resolver este problema, primero notamos que todo \textit{substring} de la cadena $s$ +es prefijo de algún sufijo de $s$ (la vuelta también es cierta: todo prefijo de algún +sufijo es \textit{substring} de $s$). A partir de esto, vemos que para contar la cantidad +de \textit{substrings} distintos se puede contar la cantidad de prefijos distintos que +tienen todos los sufijos. + +Las subcadenas que estén repetidas deben ser necesariamente prefijos de más de un sufijo. +Esto se debe a que si cada subcadena está definida por un par de índices válidos $i$, $j$ +dentro de la cadena (con $i < j$), una aparición repetida de la misma subcadena involucra +que dicha subcadena ocurra en 2 lugares distintos dentro de la cadena, lo que por lo tanto define +una posición de inicio $i$ distinta. Para cada uno de estos $i$ existe un sufijo correspondiente +tomando $j=longitud(cadena)$. + +Por lo tanto, para contabilizar rapidamente las subcadenas distintas, resulta muy útil +tener los sufijos ordenados lexicográficamente. Si una subcadena aparece más de una vez +en la cadena, cada aparición es prefijo de un sufijo de la cadena. Como todos estos +sufijos comienzan por la misma cadena, se encontrarán agrupados en el \textit{suffix +array} ordenado de la misma. + +Si consideramos los dos sufijos en las posiciones $i$ y $i+1$ del \textit{suffix array}, +vemos que todas las cadenas repetidas que introduce este último son tantas como el largo +del máximo prefijo común entre estos dos sufijos. Esto resulta del hecho de que toda cadena +repetida es un prefijo, y de que hay tantos subprefijos idénticos posibles como la longitud del +prefijo repetido máximo. Además, no es necesario mirar ningún prefijo anterior al $i$, ya que +si el sufijo $i+1$ tuviera un prefijo compartido más largo con algún otro sufijo que con el $i$, +este tercer sufijo se encontraría posicionado en la posición $i$ (ya que sería lexicográficamente +más próximo al sufijo $i+1$). + + +En base a esto, para resolver el ejercicio construimos el \textit{suffix array}, y a continuación +la tabla asociada del {\sc{lcp}}\footnote{No hace falta computar la tabla del {\sc{lcp}}, puesto +que es suficiente con ir haciendo la suma agregada de los valores, ahorrándose así espacio en memoria} que +se utiliza para contar las subcadenas. + +La idea es la siguiente: si consideramos el sufijo $j$, de largo $|s|-(j-1)$, vemos que en +principio introduce $|s|-(j-1)$ prefijos, pero como vimos antes, hay que descontar los prefijos +ya contados anteriormente, lo cual corresponde a $lcp[j]$. + +El algoritmo es entonces: + +\begin{algorithm}[H] +\begin{algorithmic} +\caption{Calcula la cantidad de subcadenas diferentes en una cadena} +\PARAMS{string $s$} +\STATE sa, rank = Suffix Array y su permutación inversa +\STATE lcp = tabular el LCP usando sa y rank +\STATE substrings = 0 +\FOR{i en [0,...N)} +\STATE $substrings += |sa[i]| - lcp[i]$ +\ENDFOR +\RETURN substrings +\end{algorithmic} +\end{algorithm} + + +La construcción del \textit{suffix array} se hace con un algoritmo simplificado respecto +del visto en clase. Se hacen varias pasadas duplicando cada vez el valor de una variable $K$. +El algoritmo ordena cada vez el \textit{suffix array} garantizando el orden definitivo si +solo se cuentan los primeros $K$ caracteres de cada sufijo. Así, se hacen a lo sumo $\log_2(n)$ +pasadas. El costo de cada una es el de realizar el ordenamiento con comparaciones en $O(1)$, +siguiendo la idea detallada en el paper de Karp, Miller y Rosenberg. Utilizando un +algoritmo de ordenamiento apropiado se obtiene así un costo total de $O(n \log^2(n))$ para +la construcción del \textit{sorted suffix array}. + +Para construir el {\sc{lcp}} utilizamos el algoritmo de Kasai visto en clase, por lo que la complejidad +es $O(n)$ siendo $n$ la cantidad de caracteres del string $s$. La suma de la cantidad de \textit{substrings} +nuevas de cada sufijo es también $O(n)$. + +Finalmente dado que el cálculo de la cantidad de \textit{substrings} se realiza con una sola +pasada sobre el {\sc{lcp}}, cuyo tamaño es lineal, concluimos que la complejidad del algoritmo es +$O(n \log^2 n)$, pero podría mejorarse a $O(n)$ usando un algoritmo más sofisticado para la +construcción del \textit{suffix array}. + + +En base a esto, la complejidad final es $O(n \log^2 n)$. + +\subsection{Implementación} + +\noindent +\ttfamily +\shorthandoff{"} +\hlstd{}\hlline{\ 1\ }\hldir{\#include\ $<$string.h$>$}\\ +\hlline{\ 2\ }\hlstd{}\hldir{\#include\ $<$cstdio$>$}\\ +\hlline{\ 3\ }\hlstd{}\hldir{\#include\ $<$algorithm$>$}\\ +\hlline{\ 4\ }\hlstd{}\\ +\hlline{\ 5\ }\hlkwa{using\ }\hlstd{std}\hlsym{::}\hlstd{sort}\hlsym{;}\\ +\hlline{\ 6\ }\hlstd{}\hlkwa{using\ }\hlstd{std}\hlsym{::}\hlstd{swap}\hlsym{;}\\ +\hlline{\ 7\ }\hlstd{}\\ +\hlline{\ 8\ }\hlkwb{static\ char\ }\hlstd{text}\hlsym{{[}}\hlstd{}\hlnum{50001}\hlstd{}\hlsym{{]};}\\ +\hlline{\ 9\ }\hlstd{}\hlkwb{static\ unsigned\ int\ }\hlstd{sa}\hlsym{{[}}\hlstd{}\hlnum{50000}\hlstd{}\hlsym{{]};}\\ +\hlline{10\ }\hlstd{}\hlkwb{static\ unsigned\ int\ }\hlstd{rank1}\hlsym{{[}}\hlstd{}\hlnum{50000}\hlstd{}\hlsym{{]}=\{}\hlstd{}\hlnum{0}\hlstd{}\hlsym{\};}\\ +\hlline{11\ }\hlstd{}\hlkwb{static\ unsigned\ int\ }\hlstd{rank2}\hlsym{{[}}\hlstd{}\hlnum{50000}\hlstd{}\hlsym{{]}=\{}\hlstd{}\hlnum{0}\hlstd{}\hlsym{\};}\\ +\hlline{12\ }\hlstd{}\\ +\hlline{13\ }\hlkwb{static\ int\ }\hlstd{N}\hlsym{;}\\ +\hlline{14\ }\hlstd{}\hlkwb{static\ long\ long\ }\hlstd{total}\hlsym{;}\\ +\hlline{15\ }\hlstd{}\hlkwb{static\ unsigned\ }\hlstd{cuantos}\hlsym{;}\\ +\hlline{16\ }\hlstd{}\\ +\hlline{17\ }\hlkwb{bool\ }\hlstd{parar}\hlsym{;}\\ +\hlline{18\ }\hlstd{}\hlkwb{int\ }\hlstd{bucket}\hlsym{,\ }\hlstd{aux}\hlsym{,\ }\hlstd{desde}\hlsym{,\ }\hlstd{actual}\hlsym{;}\\ +\hlline{19\ }\hlstd{}\hlkwb{unsigned\ int}\hlstd{}\hlsym{{*}\ }\hlstd{ahora}\hlsym{;}\\ +\hlline{20\ }\hlstd{}\hlkwb{unsigned\ int}\hlstd{}\hlsym{{*}\ }\hlstd{proximo}\hlsym{;}\\ +\hlline{21\ }\hlstd{}\\ +\hlline{22\ }\\ +\hlline{23\ }\hlslc{//\ Comparador}\\ +\hlline{24\ }\hlstd{}\hlkwb{struct\ }\hlstd{Comparador\ }\hlsym{\{}\\ +\hlline{25\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ int\ }\hlstd{K}\hlsym{;}\\ +\hlline{26\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ unsigned\ int}\hlstd{}\hlsym{{*}\ }\hlstd{rank}\hlsym{;}\\ +\hlline{27\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{Comparador}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ int\ }\hlstd{j}\hlsym{,}\hlstd{}\hlkwb{const\ unsigned\ int}\hlstd{}\hlsym{{*}\ }\hlstd{vrank}\hlsym{):\ }\hlstd{}\hlkwd{K}\hlstd{}\hlsym{(}\hlstd{j}\hlsym{),\ }\hlstd{}\hlkwd{rank}\hlstd{}\hlsym{(}\hlstd{vrank}\hlsym{)\ \{\};}\\ +\hlline{28\ }\hlstd{\\ +\hlline{29\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{bool\ }\hlstd{}\hlkwc{inline\ operator}\hlstd{}\hlsym{()(}\hlstd{}\hlkwb{const\ int\ }\hlstd{i}\hlsym{,\ }\hlstd{}\hlkwb{const\ int\ }\hlstd{j}\hlsym{)\ }\hlstd{}\hlkwb{const\ }\hlstd{}\hlsym{\{}\\ +\hlline{30\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{}\hlkwd{clave}\hlstd{}\hlsym{(}\hlstd{i}\hlsym{)\ $<$\ }\hlstd{}\hlkwd{clave}\hlstd{}\hlsym{(}\hlstd{j}\hlsym{);}\\ +\hlline{31\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{32\ }\hlstd{\\ +\hlline{33\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{}\hlkwc{inline\ }\hlstd{}\hlkwd{clave}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ int\ }\hlstd{i}\hlsym{)\ }\hlstd{}\hlkwb{const\ }\hlstd{}\hlsym{\{}\\ +\hlline{34\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{+}\hlstd{K\ }\hlsym{$<$\ }\hlstd{N\ ?\ rank}\hlsym{{[}}\hlstd{i}\hlsym{+}\hlstd{K}\hlsym{{]}+}\hlstd{}\hlnum{1\ }\hlstd{}\hlsym{:\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{);}\\ +\hlline{35\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{36\ }\hlstd{}\hlsym{\};}\\ +\hlline{37\ }\hlstd{}\\ +\hlline{38\ }\\ +\hlline{39\ }\hlkwb{int\ }\hlstd{}\hlkwd{main}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{int\ }\hlstd{argc}\hlsym{,\ }\hlstd{}\hlkwb{const\ char\ }\hlstd{}\hlsym{{*}}\hlstd{argv}\hlsym{{[}{]})\ \{}\\ +\hlline{40\ }\hlstd{\\ +\hlline{41\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{scanf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%d"}\hlstd{}\hlsym{,\ \&}\hlstd{cuantos}\hlsym{);}\\ +\hlline{42\ }\hlstd{\\ +\hlline{43\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{for\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwb{int\ }\hlstd{c\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;\ }\hlstd{c\ }\hlsym{$<$\ }\hlstd{cuantos}\hlsym{;\ }\hlstd{c}\hlsym{++)\ \{}\\ +\hlline{44\ }\hlstd{\\ +\hlline{45\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{scanf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%s"}\hlstd{}\hlsym{,\ }\hlstd{text}\hlsym{);}\\ +\hlline{46\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{N\ }\hlsym{=\ }\hlstd{}\hlkwd{strlen}\hlstd{}\hlsym{(}\hlstd{text}\hlsym{);}\\ +\hlline{47\ }\hlstd{\\ +\hlline{48\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlslc{//\ Suffix\ Array}\\ +\hlline{49\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{for\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwb{int\ }\hlstd{i\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;\ }\hlstd{i\ }\hlsym{$<$\ }\hlstd{N}\hlsym{;\ }\hlstd{i}\hlsym{++)\ \{}\\ +\hlline{50\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{sa}\hlsym{{[}}\hlstd{i}\hlsym{{]}\ =\ }\hlstd{i}\hlsym{;}\\ +\hlline{51\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{rank1}\hlsym{{[}}\hlstd{i}\hlsym{{]}\ =\ }\hlstd{text}\hlsym{{[}}\hlstd{i}\hlsym{{]};}\\ +\hlline{52\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{53\ }\hlstd{\\ +\hlline{54\ }\\ +\hlline{55\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{sort}\hlstd{}\hlsym{(}\hlstd{sa}\hlsym{,\ }\hlstd{sa}\hlsym{+}\hlstd{N}\hlsym{,\ }\hlstd{}\hlkwd{Comparador}\hlstd{}\hlsym{(}\hlstd{}\hlnum{0}\hlstd{}\hlsym{,\ }\hlstd{rank1}\hlsym{));}\\ +\hlline{56\ }\hlstd{\\ +\hlline{57\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{bucket\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{58\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{rank1}\hlsym{{[}}\hlstd{sa}\hlsym{{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}{]}\ =\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{59\ }\hlstd{\\ +\hlline{60\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{for\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwb{int\ }\hlstd{t\ }\hlsym{=\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;\ }\hlstd{t\ }\hlsym{$<$\ }\hlstd{N}\hlsym{;\ }\hlstd{t}\hlsym{++)\ \{}\\ +\hlline{61\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{text}\hlsym{{[}}\hlstd{sa}\hlsym{{[}}\hlstd{t}\hlsym{{-}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]}{]}\ ==\ }\hlstd{text}\hlsym{{[}}\hlstd{sa}\hlsym{{[}}\hlstd{t}\hlsym{{]}{]})\ \{}\\ +\hlline{62\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{rank1}\hlsym{{[}}\hlstd{sa}\hlsym{{[}}\hlstd{t}\hlsym{{]}{]}\ =\ }\hlstd{bucket}\hlsym{;}\\ +\hlline{63\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}\ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{64\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{bucket\ }\hlsym{=\ }\hlstd{t}\hlsym{;}\\ +\hlline{65\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{rank1}\hlsym{{[}}\hlstd{sa}\hlsym{{[}}\hlstd{t}\hlsym{{]}{]}\ =\ }\hlstd{bucket}\hlsym{;}\\ +\hlline{66\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{67\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{68\ }\hlstd{\\ +\hlline{69\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{parar\ }\hlsym{=\ }\hlstd{}\hlkwa{true}\hlstd{}\hlsym{;}\\ +\hlline{70\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{ahora\ }\hlsym{=\ }\hlstd{rank1}\hlsym{;}\\ +\hlline{71\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{proximo\ }\hlsym{=\ }\hlstd{rank2}\hlsym{;}\\ +\hlline{72\ }\hlstd{\\ +\hlline{73\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{for\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwb{int\ }\hlstd{K\ }\hlsym{=\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;\ }\hlstd{K\ }\hlsym{$<$\ }\hlstd{N}\hlsym{;\ }\hlstd{K\ }\hlsym{{*}=\ }\hlstd{}\hlnum{2}\hlstd{}\hlsym{)\ \{}\\ +\hlline{74\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{desde\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{75\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{actual\ }\hlsym{=\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{76\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{Comparador\ }\hlkwd{comparador}\hlstd{}\hlsym{(}\hlstd{K}\hlsym{,}\hlstd{ahora}\hlsym{);}\\ +\hlline{77\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{while\ }\hlstd{}\hlsym{(}\hlstd{actual\ }\hlsym{$<$\ }\hlstd{N}\hlsym{)\ \{}\\ +\hlline{78\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{while\ }\hlstd{}\hlsym{(}\hlstd{actual}\hlsym{$<$\ }\hlstd{N\ }\hlsym{\&\&\ }\hlstd{ahora}\hlsym{{[}}\hlstd{sa}\hlsym{{[}}\hlstd{actual}\hlsym{{]}{]}\ ==\ }\hlstd{ahora}\hlsym{{[}}\hlstd{sa}\hlsym{{[}}\hlstd{actual}\hlsym{{-}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]}{]})\ \{}\\ +\hlline{79\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{actual}\hlsym{++;}\\ +\hlline{80\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{81\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{actual\ }\hlsym{$>$\ }\hlstd{desde}\hlsym{+}\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ \{}\\ +\hlline{82\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{sort}\hlstd{}\hlsym{(}\hlstd{sa}\hlsym{+}\hlstd{desde}\hlsym{,\ }\hlstd{sa}\hlsym{+}\hlstd{actual}\hlsym{,\ }\hlstd{comparador}\hlsym{);}\\ +\hlline{83\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{84\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{desde\ }\hlsym{=\ }\hlstd{actual}\hlsym{;}\\ +\hlline{85\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{actual}\hlsym{++;}\\ +\hlline{86\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{87\ }\hlstd{\\ +\hlline{88\ }}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{bucket\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{89\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{proximo}\hlsym{{[}}\hlstd{sa}\hlsym{{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}{]}\ =\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{90\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{aux\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{91\ }\hlstd{\\ +\hlline{92\ }}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{for\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwb{int\ }\hlstd{t\ }\hlsym{=\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;\ }\hlstd{t\ }\hlsym{$<$\ }\hlstd{N}\hlsym{;\ }\hlstd{t}\hlsym{++)\ \{}\\ +\hlline{93\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{ahora}\hlsym{{[}}\hlstd{sa}\hlsym{{[}}\hlstd{t}\hlsym{{]}{]}\ ==\ }\hlstd{aux\ }\hlsym{\&\&\ }\hlstd{comparador}\hlsym{.}\hlstd{}\hlkwd{clave}\hlstd{}\hlsym{(}\hlstd{sa}\hlsym{{[}}\hlstd{t}\hlsym{{-}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]})\ ==\ }\hlstd{comparador}\hlsym{.}\hlstd{}\hlkwd{clave}\hlstd{}\hlsym{(}\hlstd{sa}\hlsym{{[}}\hlstd{t}\hlsym{{]}))\ \{}\\ +\hlline{94\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{proximo}\hlsym{{[}}\hlstd{sa}\hlsym{{[}}\hlstd{t}\hlsym{{]}{]}\ =\ }\hlstd{bucket}\hlsym{;}\\ +\hlline{95\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{parar\ }\hlsym{=\ }\hlstd{}\hlkwa{false}\hlstd{}\hlsym{;}\\ +\hlline{96\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}\ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{97\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{aux\ }\hlsym{=\ }\hlstd{ahora}\hlsym{{[}}\hlstd{sa}\hlsym{{[}}\hlstd{t}\hlsym{{]}{]};}\\ +\hlline{98\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{bucket\ }\hlsym{=\ }\hlstd{t}\hlsym{;}\\ +\hlline{99\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{proximo}\hlsym{{[}}\hlstd{sa}\hlsym{{[}}\hlstd{t}\hlsym{{]}{]}\ =\ }\hlstd{bucket}\hlsym{;}\\ +\hlline{100\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{101\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{102\ }\hlstd{\\ +\hlline{103\ }}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{swap}\hlstd{}\hlsym{(}\hlstd{ahora}\hlsym{,\ }\hlstd{proximo}\hlsym{);}\\ +\hlline{104\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{parar}\hlsym{)\ }\hlstd{}\hlkwa{break}\hlstd{}\hlsym{;}\\ +\hlline{105\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{parar\ }\hlsym{=\ }\hlstd{}\hlkwa{true}\hlstd{}\hlsym{;}\\ +\hlline{106\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{107\ }\hlstd{\\ +\hlline{108\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlslc{//\ LCP\ (Kasai)}\\ +\hlline{109\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{total\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{110\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{k\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{111\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{for\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwb{int\ }\hlstd{i\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;\ }\hlstd{i\ }\hlsym{$<$\ }\hlstd{N}\hlsym{;\ }\hlstd{i}\hlsym{++)\ \{}\\ +\hlline{112\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{k\ }\hlsym{$>$\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ \{}\\ +\hlline{113\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{k}\hlsym{{-}{-};}\\ +\hlline{114\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{115\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{ahora}\hlsym{{[}}\hlstd{i}\hlsym{{]}\ ==\ }\hlstd{N}\hlsym{{-}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ \{}\\ +\hlline{116\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{total\ }\hlsym{+=\ }\hlstd{N\ }\hlsym{+\ }\hlstd{}\hlnum{1\ }\hlstd{}\hlsym{{-}\ }\hlstd{sa}\hlsym{{[}}\hlstd{N}\hlsym{{-}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]};}\\ +\hlline{117\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{k\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{118\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{continue}\hlstd{}\hlsym{;}\\ +\hlline{119\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{120\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{j\ }\hlsym{=\ }\hlstd{sa}\hlsym{{[}}\hlstd{ahora}\hlsym{{[}}\hlstd{i}\hlsym{{]}+}\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]};}\\ +\hlline{121\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{while\ }\hlstd{}\hlsym{(}\hlstd{text}\hlsym{{[}}\hlstd{i}\hlsym{+}\hlstd{k}\hlsym{{]}\ ==\ }\hlstd{text}\hlsym{{[}}\hlstd{j}\hlsym{+}\hlstd{k}\hlsym{{]})\ }\hlstd{k}\hlsym{++;}\\ +\hlline{122\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{total\ }\hlsym{+=\ }\hlstd{N\ }\hlsym{{-}\ }\hlstd{k\ }\hlsym{{-}\ }\hlstd{sa}\hlsym{{[}}\hlstd{ahora}\hlsym{{[}}\hlstd{i}\hlsym{{]}{]};}\\ +\hlline{123\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{124\ }\hlstd{\\ +\hlline{125\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlslc{//\ El\ codigo\ de\ arriba\ pone\ un\ {-}1\ en\ la}\\ +\hlline{126\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlslc{//\ fila\ final\ del\ LCP\ en\ lugar\ de\ un\ 0\ en\ la\ primera,}\\ +\hlline{127\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlslc{//\ asi\ que\ hay\ que\ restarlo\ ahora.}\\ +\hlline{128\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{total\ }\hlsym{=\ }\hlstd{total\ }\hlsym{{-}\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{129\ }\hlstd{\\ +\hlline{130\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{printf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%lld}\hlesc{$\backslash$n}\hlstr{"}\hlstd{}\hlsym{,\ }\hlstd{total}\hlsym{);}\\ +\hlline{131\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{132\ }\hlstd{}\hlsym{\}}\hlstd{}\\ +\mbox{} +\normalfont +\shorthandon{"} + + +La implementación es bastante directa a partir de lo expresado anteriormente. Se +reservan arreglos estáticos de memoria para mejorar la eficiencia del algoritmo, y se +utiliza la función de ordenamiento provista por la STL cuyo rendimiento es excelente. + +Se utilizan dos arreglos para los \textit{buckets}, que se van intercambiando en $O(1)$ +mediante un \textit{swap} de punteros para ir modificando los valores en cada +pasada. El objeto comparador \textit{Comparador} se utiliza para realizar las comparaciones +entre los prefijos, utilizando como clave su número de \textit{bucket}. En la primera +pasada, se inicializan los números de \textit{bucket} con los valores de los caracteres en la cadena, +pero enseguida se sobreescriben esos valores con enteros entre $0$ y $n-1$. Esto evita +especializar el método de comparación para la primera pasada del programa. + +Como era de esperarse, el invariante del ciclo principal es que al comenzar +el cuerpo del ciclo, están ordenados los sufijos si solo se tienen en cuenta +sus primeros $K$ caracteres. + +El algoritmo de Kasai sigue la implementación convencional, y la suma +de los valores es la esperada. diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/doc/rmq.tex b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/doc/rmq.tex new file mode 100644 index 0000000..6236eaa --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/doc/rmq.tex @@ -0,0 +1,285 @@ +\section{11235 - Frequent values} +\textbf{Problema:} Dado un arreglo de números ordenados de forma no decreciente, y un par de indices $i$, $j$; encontrar la mayor frecuencia (repeticiones de un numero) en el rango $[i,j]$ del arreglo. + +\subsection{Resolución} +Dado que el arreglo esta ordenado, las apariciones de un número están todas juntas. En otras palabras, si $k$ está en el arreglo, vale que: + +$\exists i,j / k \notin a[0..i-1] \wedge \forall t \in a[i..j], a[t] = k \wedge k \notin a[j+1..n]$ + +Esto es útil porque significa que todas las apariciones de un elemento están juntas, +es decir que en el arreglo los elementos iguales están en subarreglos. Podemos +considerar entonces el arreglo que se obtiene de considerar las longitudes de esos +subarreglos (consideramos subarreglos máximos - los que abarcan todas las apariciones +de un elemento). Por ejemplo, si el arreglo original es: +$$a = -1, -1, 1, 1, 1, 1, 3, 10, 10, 10$$ +el arreglo de las cantidades es: +$$c = 2, 4, 1, 3$$ + +Definimos además: + +$s(i) = k \longleftrightarrow c[k]$ representa al subarreglo que contiene a los elementos que son iguales a $a[i]$ + +$d(i) = 0 \longleftrightarrow \forall 0 \leq t \leq i, a[t] = a[i] $ + +$d(i) = k > 0 \longleftrightarrow a[k] = a[i] \wedge a[k-1] < a[i]$ + + +$h(i) = n - 1 \longleftrightarrow \forall i \leq t < n, a[t] = a[i] $ + +$h(i) = k < n -1 \longleftrightarrow a[k] = a[i] \wedge a[k+1] > a[i]$ + +Intuitivamente, $d(i)$ y $h(i)$ son los extremos del intervalo en a, tal que $\forall d(i) \leq t \leq h(i), a[t] == a[i]$. Notemos entonces que vale que: + +$\forall i,j / s(i) = s(j) \Rightarrow d(i)=d(j) \wedge h(i)=h(j)$ + +Esto es así ya que si $s(i) = s(j)$, se desprende que $a[i] = a[j]$ + +El arreglo $c$ es útil para resolver el problema. Si tenemos que dar la máxima frecuencia +en $[i,j]$, puede pasar que: +\begin{itemize} +\item $a[i] = a[j]$, con lo cual la máxima frecuencia es el largo de $[i,j]$ +\item $a[i] \neq a[j]$, en este caso podemos usar el arreglo $c$ para hacer una consulta +por el máximo en el intervalo $[s(i)..s(j)]$. Esto sólo es cierto si $i$ es el extremo +izquierdo de un subarreglo de $a$, y $j$ es el extremo derecho de otro. + +Si esto no se cumple, hay que considerar que del subarreglo que corresponde +a $i$ o a $j$ sólo importa una parte. + +Entonces, la máxima frecuencia se puede obtener como: +$$max(\Vert [i..h(i)] \Vert, \Vert [d(j)..j] \Vert, max(c[s(i)+1...s(j)-1]))$$ + +Esto corresponde al máximo entre la cantidad de valores iguales a $a[i]$ que caen en el +intervalo pedido, la cantidad de valores iguales a $a[j]$ y la máxima frecuencia entre ellos. +\end{itemize} + +Al cargar el arreglo se pueden computar $s$, $d$, $h$ y $c$, de la siguiente manera: + +\begin{algorithm}[H] +\begin{algorithmic} +\caption{Calculo de $s$, $d$, $h$ y $c$ a partir del arreglo ordenado} +\PARAMS{arreglo $a$, ordenado de forma no decreciente} +\STATE $i = 0$ +\STATE $actual = a[i]$ +\STATE $intervalo = 0$ +\STATE $desde = 0$ +\STATE $hasta = 0$ +\STATE $s(i) = intervalo$ +\STATE $c[intervalo] = 1$ +\STATE $i = 1$ +\WHILE{$i < \Vert a \Vert - 1 $} + \IF{$actual = a[i-1]$} + \STATE $hasta++$ + \STATE $c[intervalo]++$ + \ELSE + \STATE $h(intervalo) = hasta$ + \STATE $d(intervalo) = desde$ + \STATE $intervalo++$ + \STATE $hasta++$ + \STATE $desde = hasta$ + \STATE $actual = a[i]$ + \STATE $c[intervalo] = 1$ + \ENDIF + \STATE $s(i) = intervalo$ + \STATE $i++$ +\ENDWHILE +\STATE $h(intervalo) = hasta$ +\STATE $d(intervalo) = desde$ +\end{algorithmic} +\end{algorithm} + +Para guardar $s,d$ y $h$ se pueden usar arreglos, e indexar $h y d$ siempre por $s(i)$. + +Una vez que tenemos esto, queda computar eficientemente el máximo en $c[s(i)+1...s(j)-1]$. +Para ello usamos la estructura \textit{\textbf{Sparse Table} }\footnote{http://www.topcoder.com/tc?module=Static\&d1=tutorials\&d2=lowestCommonAncestor}. + +Una vez construida esta estructura podemos comenzar a responder las consultas. El siguiente es el algoritmo para responderlas: + +\begin{algorithm}[H] +\begin{algorithmic} +\caption{Resolución de queries} +\PARAMS{$i,j$ indices del arreglo $a$} +\IF{s(i) == s(j)} + \RETURN $j-i+1$ \COMMENT{$\Vert[i..j]\Vert$} +\ELSE + \STATE res = $max( h(s(i)) - i +1, j - d(s(j)) + 1)$ \COMMENT{$max(\Vert [i..h(i)] \Vert, \Vert [d(j)..j] \Vert)$} + \STATE res = $max(res, rmq(c, h(s(i))+1, d(s(j))-1))$ \COMMENT{usar la sparse table para obtener el maximo en el rango de c} + \RETURN res +\ENDIF +\end{algorithmic} +\end{algorithm} + +Con respecto a la complejidad, primero computamos $s,d,h$ y $c$, lo que podemos hacer en $O(n)$ mientras +cargamos los números. Luego armamos la \textit{sparse table} para el arreglo $c$, que tiene $O(n)$ elementos +(pueden ser $n$, si todos los elementos de $a$ son distintos). Por lo tanto, la construcción de la tabla es +$O(n \log n)$. Usando el algoritmo antes mostrado, podemos responder a las consultas en $O(1)$, ya que la +consulta a la tabla cuesta $O(1)$. Por lo tanto, si hay $q$ queries que responder, el orden total del algoritmo +es $O(n \log n + q)$. Ajustando un poco el calculo, vemos que la tabla no tiene siempre $O(n*\log n)$ posiciones, +sino que tiene $O(d*\log d)$ posiciones, donde $d$ es la cantidad de elementos distintos. Si bien $O(d*\log d) +\subseteq O(n*\log n)$, potencialmente $d$ es más chico que $n$. Considerando que igualmente deben cargarse +todos los valores del arreglo original, el orden es $O(n + d*\log d + q)$. + +\subsection{Implementación} +\noindent +\ttfamily +\shorthandoff{"}\\ +\hlstd{}\hlline{\ 1\ }\hldir{\#include\ $<$iostream$>$}\\ +\hlline{\ 2\ }\hlstd{}\hldir{\#include\ $<$vector$>$}\\ +\hlline{\ 3\ }\hlstd{}\hldir{\#include\ $<$list$>$}\\ +\hlline{\ 4\ }\hlstd{}\hldir{\#include\ $<$stdlib.h$>$}\\ +\hlline{\ 5\ }\hlstd{}\hldir{\#include\ $<$utility$>$}\\ +\hlline{\ 6\ }\hlstd{}\hldir{\#include\ $<$cassert$>$}\\ +\hlline{\ 7\ }\hlstd{}\hldir{\#include\ $<$sys/types.h$>$}\\ +\hlline{\ 8\ }\hlstd{}\hldir{\#include\ $<$sys/stat.h$>$}\\ +\hlline{\ 9\ }\hlstd{}\hldir{\#include\ $<$fcntl.h$>$}\\ +\hlline{10\ }\hlstd{}\hldir{\#include\ $<$stdio.h$>$}\\ +\hlline{11\ }\hlstd{}\hlkwa{using\ namespace\ }\hlstd{std}\hlsym{;}\\ +\hlline{12\ }\hlstd{}\hldir{\#define\ forit(it,l)\ for(it=(l).begin();it\ !=\ (l).end();\ it++)}\\ +\hlline{13\ }\hlstd{}\hldir{\#define\ forn(i,n)\ for(unsigned}\hlstd{\ \ }\hldir{i=\ 0;\ i\ $<$\ ((unsigned)(n));\ i++)}\\ +\hlline{14\ }\hlstd{}\hldir{\#define\ foreachin(it,s)\ for(typeof((s).begin())\ it\ =\ ((s).begin());\ it\ !=\ ((s).end());\ it++)}\\ +\hlline{15\ }\hlstd{}\hldir{\#define\ forsn(i,s,n)\ for(int\ i\ =\ (s);\ i\ $<$\ (n);\ i++)}\\ +\hlline{16\ }\hlstd{}\hlkwb{void\ }\hlstd{}\hlkwc{inline\ }\hlstd{}\hlkwd{llenar\textunderscore tabla}\hlstd{}\hlsym{(}\hlstd{vector}\hlsym{$<$}\hlstd{vector}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$\ $>$\&\ }\hlstd{tabla}\hlsym{,\ }\hlstd{}\hlkwb{const\ }\hlstd{vector}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$\&\ }\hlstd{frec}\hlsym{)\ \{}\\ +\hlline{17\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{n\ }\hlsym{=\ }\hlstd{tabla}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{();}\\ +\hlline{18\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{i}\hlsym{,\ }\hlstd{j}\hlsym{;}\\ +\hlline{19\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlslc{//init\ de\ los\ intervalos\ de\ largo\ 1}\\ +\hlline{20\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{forn}\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,}\hlstd{n}\hlsym{)}\\ +\hlline{21\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{tabla}\hlsym{{[}}\hlstd{i}\hlsym{{]}{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}\ =\ }\hlstd{i}\hlsym{;}\\ +\hlline{22\ }\hlstd{\\ +\hlline{23\ }}\hlstd{\ \ \ \ }\hlstd{}\hlslc{//llenado\ de\ la\ tabla\ desde\ los\ mas\ chicos\ a\ los\ mas\ grandes}\\ +\hlline{24\ }\hlstd{\ }\hlkwb{unsigned\ }\hlstd{t}\hlsym{=}\hlstd{}\hlnum{2}\hlstd{}\hlsym{;}\\ +\hlline{25\ }\hlstd{\ }\hlkwb{unsigned\ }\hlstd{t\textunderscore ant}\hlsym{=}\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{26\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{for\ }\hlstd{}\hlsym{(}\hlstd{j\ }\hlsym{=\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;\ }\hlstd{t\ }\hlsym{$<$=\ }\hlstd{n}\hlsym{;\ }\hlstd{j}\hlsym{++)\ \{}\\ +\hlline{27\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{for\ }\hlstd{}\hlsym{(}\hlstd{i\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;\ }\hlstd{i\ }\hlsym{+\ (}\hlstd{t}\hlsym{)\ {-}\ }\hlstd{}\hlnum{1\ }\hlstd{}\hlsym{$<$\ }\hlstd{n}\hlsym{;\ }\hlstd{i}\hlsym{++)\ \{}\\ +\hlline{28\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{k\ }\hlsym{=\ }\hlstd{j\ }\hlsym{{-}\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{29\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{frec}\hlsym{{[}}\hlstd{tabla}\hlsym{{[}}\hlstd{i}\hlsym{{]}{[}}\hlstd{k}\hlsym{{]}{]}\ $>$\ }\hlstd{frec}\hlsym{{[}}\hlstd{tabla}\hlsym{{[}}\hlstd{i\ }\hlsym{+\ (}\hlstd{t\textunderscore ant}\hlsym{){]}{[}}\hlstd{k}\hlsym{{]}{]})}\\ +\hlline{30\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{tabla}\hlsym{{[}}\hlstd{i}\hlsym{{]}{[}}\hlstd{j}\hlsym{{]}\ =\ }\hlstd{tabla}\hlsym{{[}}\hlstd{i}\hlsym{{]}{[}}\hlstd{k}\hlsym{{]};}\\ +\hlline{31\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{else}\\ +\hlline{32\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{tabla}\hlsym{{[}}\hlstd{i}\hlsym{{]}{[}}\hlstd{j}\hlsym{{]}\ =\ }\hlstd{tabla}\hlsym{{[}}\hlstd{i\ }\hlsym{+\ (}\hlstd{t\textunderscore ant}\hlsym{){]}{[}}\hlstd{k}\hlsym{{]};}\\ +\hlline{33\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{34\ }\hlstd{}\hlstd{\ \ }\hlstd{t\textunderscore ant}\hlsym{=}\hlstd{t}\hlsym{;}\\ +\hlline{35\ }\hlstd{}\hlstd{\ \ }\hlstd{t}\hlsym{=}\hlstd{t}\hlsym{$<$$<$}\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{36\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{37\ }\hlstd{}\hlsym{\}}\\ +\hlline{38\ }\hlstd{}\\ +\hlline{39\ }\\ +\hlline{40\ }\hlkwb{static\ }\hlstd{}\hlkwc{inline\ }\hlstd{}\hlkwb{uint32\textunderscore t\ }\hlstd{}\hlkwd{log\textunderscore 2}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ uint32\textunderscore t\ }\hlstd{x}\hlsym{)\ \{}\\ +\hlline{41\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwb{uint32\textunderscore t\ }\hlstd{y}\hlsym{;}\\ +\hlline{42\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{asm\ }\hlstd{}\hlsym{(\ }\hlstd{}\hlstr{"}\hlesc{$\backslash$t}\hlstr{bsr\ \%1,\ \%0}\hlesc{$\backslash$n}\hlstr{"}\hlstd{\\ +\hlline{43\ }}\hlstd{\ \ \ \ \ \ }\hlstd{}\hlsym{:\ }\hlstd{}\hlstr{"=r"}\hlstd{}\hlsym{(}\hlstd{y}\hlsym{)}\\ +\hlline{44\ }\hlstd{}\hlstd{\ \ \ \ \ \ }\hlstd{}\hlsym{:\ }\hlstd{}\hlstr{"r"}\hlstd{\ }\hlsym{(}\hlstd{x}\hlsym{)}\\ +\hlline{45\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlsym{);}\\ +\hlline{46\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwa{return\ }\hlstd{y}\hlsym{;}\\ +\hlline{47\ }\hlstd{}\hlsym{\}}\\ +\hlline{48\ }\hlstd{\\ +\hlline{49\ }\\ +\hlline{50\ }\ }\hlkwb{void\ }\hlstd{}\hlkwc{inline\ }\hlstd{}\hlkwd{cargar\textunderscore numeros}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{int\ }\hlstd{cant\textunderscore numeros}\hlsym{,}\hlstd{vector}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$\&\ }\hlstd{frec}\hlsym{,}\hlstd{vector}\hlsym{$<$}\hlstd{pair}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{,}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$\ $>$\&\ }\Righttorque\\ +\hlline{51\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{intervalostupla}\hlsym{,}\hlstd{vector}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$\&\ }\hlstd{intervaloindice}\hlsym{,}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{\&\ }\hlstd{intervalo}\hlsym{)\ \{}\\ +\hlline{52\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{i\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{53\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{numero}\hlsym{;}\\ +\hlline{54\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{desde}\hlsym{,}\hlstd{hasta}\hlsym{;\ }\hlstd{}\hlslc{//intervalo\ donde\ todos\ los\ elementos\ son\ iguales\ {[}\ {]}}\\ +\hlline{55\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{actual}\hlsym{;\ }\hlstd{}\hlslc{//elemento\ cuya\ frecuencia\ estoy\ construyendo}\\ +\hlline{56\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{while\ }\hlstd{}\hlsym{(}\hlstd{i\ }\hlsym{$<$\ }\hlstd{cant\textunderscore numeros}\hlsym{)\ \{}\\ +\hlline{57\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{scanf\ }\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%d"}\hlstd{}\hlsym{,\&}\hlstd{numero}\hlsym{);}\\ +\hlline{58\ }\hlstd{\\ +\hlline{59\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{i\ }\hlsym{==\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ \{}\\ +\hlline{60\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{actual}\hlsym{=}\hlstd{numero}\hlsym{;}\\ +\hlline{61\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{desde}\hlsym{=}\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{62\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{hasta}\hlsym{=}\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{63\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}\ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{64\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{actual}\hlsym{==}\hlstd{numero}\hlsym{)\ \{\ }\hlstd{}\hlslc{//si\ son\ iguales,\ incremento\ el\ hasta\ y\ su\ frecuencia}\\ +\hlline{65\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{hasta}\hlsym{++;}\\ +\hlline{66\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{frec}\hlsym{{[}}\hlstd{intervalo}\hlsym{{]}++;}\\ +\hlline{67\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{68\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlslc{//\ si\ son\ distintos,\ se\ cerró\ un\ intervalo,\ hay\ que\ empezar\ a\ armar\ otro}\\ +\hlline{69\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{70\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{intervalostupla}\hlsym{{[}}\hlstd{intervalo}\hlsym{{]}\ =\ }\hlstd{pair}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{,}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$(}\hlstd{desde}\hlsym{,}\hlstd{hasta}\hlsym{);}\\ +\hlline{71\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{intervalo}\hlsym{++;}\\ +\hlline{72\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{hasta}\hlsym{++;}\\ +\hlline{73\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{desde}\hlsym{=}\hlstd{hasta}\hlsym{;}\\ +\hlline{74\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{actual\ }\hlsym{=\ }\hlstd{numero}\hlsym{;}\\ +\hlline{75\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{76\ }\hlstd{\\ +\hlline{77\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{78\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{intervaloindice}\hlsym{{[}}\hlstd{i}\hlsym{{]}=}\hlstd{intervalo}\hlsym{;}\\ +\hlline{79\ }\hlstd{\\ +\hlline{80\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{i}\hlsym{++;}\\ +\hlline{81\ }\hlstd{\\ +\hlline{82\ }}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{83\ }\hlstd{\\ +\hlline{84\ }}\hlstd{\ \ \ \ }\hlstd{}\hlslc{//hack:\ el\ ultimo\ siempre\ quedaba\ sin\ agregar}\\ +\hlline{85\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{intervalostupla}\hlsym{{[}}\hlstd{intervalo}\hlsym{{]}\ =\ }\hlstd{pair}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{,}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$(}\hlstd{desde}\hlsym{,}\hlstd{hasta}\hlsym{);}\\ +\hlline{86\ }\hlstd{}\hlsym{\}}\\ +\hlline{87\ }\hlstd{}\\ +\hlline{88\ }\hlkwb{void\ }\hlstd{}\hlkwc{inline\ }\hlstd{}\hlkwd{procesar\textunderscore queries}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ int\ }\hlstd{queries}\hlsym{,}\hlstd{}\hlkwb{const\ }\hlstd{vector}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$\&\ }\hlstd{frec}\hlsym{,}\hlstd{}\hlkwb{const\ }\hlstd{vector}\hlsym{$<$}\hlstd{pair}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{,}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$\ $>$\&\ }\Righttorque\\ +\hlline{89\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{intervalostupla}\hlsym{,}\hlstd{}\hlkwb{const\ }\hlstd{vector}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$\&\ }\hlstd{intervaloindice}\hlsym{,}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{\&\ }\hlstd{intervalo}\hlsym{)\ \{}\\ +\hlline{90\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{vector}\hlsym{$<$}\hlstd{vector}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$\ $>$\ }\hlstd{}\hlkwd{tabla}\hlstd{}\hlsym{(}\hlstd{intervalo}\hlsym{+}\hlstd{}\hlnum{1}\hlstd{}\hlsym{,\ }\hlstd{vector}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$(}\hlstd{}\hlkwd{log\textunderscore 2}\hlstd{}\hlsym{(}\hlstd{intervalo}\hlsym{+}\hlstd{}\hlnum{1}\hlstd{}\hlsym{)+}\hlstd{}\hlnum{1}\hlstd{}\hlsym{));}\\ +\hlline{91\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{llenar\textunderscore tabla}\hlstd{}\hlsym{(}\hlstd{tabla}\hlsym{,}\hlstd{frec}\hlsym{);}\\ +\hlline{92\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{unsigned\ }\hlstd{x}\hlsym{,}\hlstd{y}\hlsym{;}\\ +\hlline{93\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{i}\hlsym{=}\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{94\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{while\ }\hlstd{}\hlsym{(}\hlstd{i\ }\hlsym{$<$\ }\hlstd{queries}\hlsym{)\ \{}\\ +\hlline{95\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{scanf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%u\ \%u"}\hlstd{}\hlsym{,\&}\hlstd{x}\hlsym{,\&}\hlstd{y}\hlsym{);}\\ +\hlline{96\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{desde}\hlsym{,\ }\hlstd{hasta}\hlsym{;}\\ +\hlline{97\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlslc{//desde\ y\ hasta\ son\ los\ intervalos\ extremos\ que\ hay\ que\ mirar.}\\ +\hlline{98\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlslc{//No\ necesariamente\ estan\ completos}\\ +\hlline{99\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{desde\ }\hlsym{=\ }\hlstd{intervaloindice}\hlsym{{[}}\hlstd{x}\hlsym{{-}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]};}\\ +\hlline{100\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{hasta\ }\hlsym{=\ }\hlstd{intervaloindice}\hlsym{{[}}\hlstd{y}\hlsym{{-}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]};}\\ +\hlline{101\ }\hlstd{\\ +\hlline{102\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{res}\hlsym{;}\\ +\hlline{103\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlslc{//\ Si\ esos\ indices\ son\ parte\ del\ mismo\ intervalo,\ la\ frecuencia\ es\ la\ distancia\ entre\ ellos.}\\ +\hlline{104\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{desde}\hlsym{==}\hlstd{hasta}\hlsym{)\ \{}\\ +\hlline{105\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{res\ }\hlsym{=\ }\hlstd{y}\hlsym{{-}}\hlstd{x}\hlsym{+}\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{106\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}\ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{107\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlslc{//calculo\ por\ separado\ los\ intervalos\ que\ pueden\ ser\ truncos}\\ +\hlline{108\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{frec\textunderscore i\ }\hlsym{=\ }\hlstd{intervalostupla}\hlsym{{[}}\hlstd{desde}\hlsym{{]}.}\hlstd{second\ }\hlsym{{-}\ }\hlstd{x\ }\hlsym{+\ }\hlstd{}\hlnum{2}\hlstd{}\hlsym{;}\\ +\hlline{109\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{frec\textunderscore j\ }\hlsym{=\ }\hlstd{y\ }\hlsym{{-}\ }\hlstd{intervalostupla}\hlsym{{[}}\hlstd{hasta}\hlsym{{]}.}\hlstd{first\ }\hlsym{;}\\ +\hlline{110\ }\hlstd{\\ +\hlline{111\ }}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlslc{//el\ siguiente\ del\ desde\ y\ el\ anterior\ del\ hasta\ si\ estan\ completos}\\ +\hlline{112\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{unsigned\ int\ }\hlstd{intervalo\textunderscore completo\textunderscore i\ }\hlsym{=\ }\hlstd{desde}\hlsym{+}\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{113\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{unsigned\ int\ }\hlstd{intervalo\textunderscore completo\textunderscore j\ }\hlsym{=\ }\hlstd{hasta}\hlsym{{-}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{114\ }\hlstd{\\ +\hlline{115\ }}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{res\ }\hlsym{=\ }\hlstd{}\hlkwd{max}\hlstd{}\hlsym{(}\hlstd{frec\textunderscore i}\hlsym{,}\hlstd{frec\textunderscore j}\hlsym{);}\\ +\hlline{116\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if}\hlstd{}\hlsym{(}\hlstd{intervalo\textunderscore completo\textunderscore i\ }\hlsym{$<$=\ }\hlstd{intervalo\textunderscore completo\textunderscore j}\hlsym{)\{}\\ +\hlline{117\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{unsigned\ int\ }\hlstd{k\ }\hlsym{=\ }\hlstd{}\hlkwd{log\textunderscore 2}\hlstd{}\hlsym{(}\hlstd{intervalo\textunderscore completo\textunderscore j\ }\hlsym{{-}\ }\hlstd{intervalo\textunderscore completo\textunderscore i\ }\hlsym{+\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{);}\\ +\hlline{118\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{aux\ }\hlsym{=\ }\hlstd{frec}\hlsym{{[}}\hlstd{tabla}\hlsym{{[}}\hlstd{intervalo\textunderscore completo\textunderscore j}\hlsym{{-}(}\hlstd{}\hlnum{1}\hlstd{}\hlsym{$<$$<$}\hlstd{k}\hlsym{)+}\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]}{[}}\hlstd{k}\hlsym{{]}{]};}\\ +\hlline{119\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{frec}\hlsym{{[}}\hlstd{tabla}\hlsym{{[}}\hlstd{intervalo\textunderscore completo\textunderscore i}\hlsym{{]}{[}}\hlstd{k}\hlsym{{]}{]}\ $>$=\ }\hlstd{aux\ }\hlsym{)}\\ +\hlline{120\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{res\ }\hlsym{=\ }\hlstd{}\hlkwd{max}\hlstd{}\hlsym{(}\hlstd{res}\hlsym{,}\hlstd{frec}\hlsym{{[}}\hlstd{tabla}\hlsym{{[}}\hlstd{intervalo\textunderscore completo\textunderscore i}\hlsym{{]}{[}}\hlstd{k}\hlsym{{]}{]});}\\ +\hlline{121\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{else}\\ +\hlline{122\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{res\ }\hlsym{=\ }\hlstd{}\hlkwd{max}\hlstd{}\hlsym{(}\hlstd{res}\hlsym{,}\hlstd{aux}\hlsym{);}\\ +\hlline{123\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{124\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{125\ }\hlstd{\\ +\hlline{126\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{printf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%d}\hlesc{$\backslash$n}\hlstr{"}\hlstd{}\hlsym{,}\hlstd{res}\hlsym{);}\\ +\hlline{127\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{i}\hlsym{++;}\\ +\hlline{128\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{129\ }\hlstd{}\hlsym{\}}\\ +\hlline{130\ }\hlstd{}\\ +\hlline{131\ }\hlkwb{int\ }\hlstd{}\hlkwd{main}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{int\ }\hlstd{argc}\hlsym{,\ }\hlstd{}\hlkwb{char}\hlstd{}\hlsym{{*}{*}\ }\hlstd{argv}\hlsym{)\ \{}\hlstd{\ \ }\hlsym{}\\ +\hlline{132\ }\hlstd{\\ +\hlline{133\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{cant\textunderscore numeros}\hlsym{,}\hlstd{queries}\hlsym{;}\\ +\hlline{134\ }\hlstd{\ }\hlkwd{scanf\ }\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%d"}\hlstd{}\hlsym{,\&}\hlstd{cant\textunderscore numeros}\hlsym{);}\\ +\hlline{135\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{\\ +\hlline{136\ }\\ +\hlline{137\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{while\ }\hlstd{}\hlsym{(}\hlstd{cant\textunderscore numeros\ }\hlsym{$>$\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ \{}\\ +\hlline{138\ }\hlstd{}\hlstd{\ \ }\hlstd{}\hlkwd{scanf\ }\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%d"}\hlstd{}\hlsym{,\&}\hlstd{queries}\hlsym{);}\\ +\hlline{139\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{vector}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$\ }\hlstd{}\hlkwd{frec}\hlstd{}\hlsym{(}\hlstd{cant\textunderscore numeros}\hlsym{,}\hlstd{}\hlnum{1}\hlstd{}\hlsym{);}\hlstd{}\hlslc{//vector\ de\ frecuencias}\\ +\hlline{140\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{intervalo\ }\hlsym{=}\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\hlstd{}\hlslc{//cantidad\ de\ intervalos}\\ +\hlline{141\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{vector}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$\ }\hlstd{}\hlkwd{intervaloindice}\hlstd{}\hlsym{(}\hlstd{cant\textunderscore numeros}\hlsym{);\ }\hlstd{}\hlslc{//dado\ un\ indice\ del\ arreglo,\ devuelve\ el\ numero\ }\Righttorque\\ +\hlline{142\ }\hlslc{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlslc{de\ intervalo\ en\ el\ que\ esta}\\ +\hlline{143\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{vector}\hlsym{$<$}\hlstd{pair}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{,}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$\ $>$\ }\hlstd{}\hlkwd{intervalostupla}\hlstd{}\hlsym{(}\hlstd{cant\textunderscore numeros}\hlsym{);\ }\hlstd{}\hlslc{//dado\ un\ numero\ de\ intervalo,\ da\ su\ }\Righttorque\\ +\hlline{144\ }\hlslc{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlslc{desde\ y\ hasta}\\ +\hlline{145\ }\hlstd{\\ +\hlline{146\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{cargar\textunderscore numeros}\hlstd{}\hlsym{(}\hlstd{cant\textunderscore numeros}\hlsym{,}\hlstd{frec}\hlsym{,}\hlstd{intervalostupla}\hlsym{,\ }\hlstd{intervaloindice}\hlsym{,\ }\hlstd{intervalo}\hlsym{);}\\ +\hlline{147\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{procesar\textunderscore queries}\hlstd{}\hlsym{(}\hlstd{queries}\hlsym{,\ }\hlstd{frec}\hlsym{,}\hlstd{intervalostupla}\hlsym{,\ }\hlstd{intervaloindice}\hlsym{,\ }\hlstd{intervalo}\hlsym{);}\\ +\hlline{148\ }\hlstd{\\ +\hlline{149\ }\\ +\hlline{150\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{scanf\ }\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%d"}\hlstd{}\hlsym{,\&}\hlstd{cant\textunderscore numeros}\hlsym{);}\\ +\hlline{151\ }\hlstd{\\ +\hlline{152\ }}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{153\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{}\hlsym{(}\hlstd{EXIT\textunderscore SUCCESS}\hlsym{);}\\ +\hlline{154\ }\hlstd{}\hlsym{\}}\\ +\hlline{155\ }\hlstd{}\\ +\hlline{156\ }\\ +\mbox{} +\normalfont +\shorthandon{"} + + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/doc/trans_algorithmic.tex b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/doc/trans_algorithmic.tex new file mode 100644 index 0000000..9ce8c65 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/doc/trans_algorithmic.tex @@ -0,0 +1,15 @@ +\renewcommand{\algorithmicrequire}{\textcolor{blue}{\textbf{Requiere:}}} +\renewcommand{\algorithmicensure}{\textbf{Devuelve:}} +\renewcommand{\algorithmicend}{\textbf{Fin}} +\renewcommand{\algorithmicif}{\textcolor{blue}{\textbf{Si}}} +\renewcommand{\algorithmicthen}{\textcolor{blue}{}} %%\textbf{entonces}}} +\renewcommand{\algorithmicelse}{\textcolor{red}{\textbf{Si no}}} +\renewcommand{\algorithmicelsif }{\textcolor{blue}{\textbf{Si no y}}} +\renewcommand{\algorithmicendif}{\textcolor{blue}{\textbf{Fin si}}} +\renewcommand{\algorithmicfor}{\textcolor{ForestGreen}{\textbf{Para}}} +\renewcommand{\algorithmicendfor}{\textcolor{ForestGreen}{\textbf{Fin para}}} +\renewcommand{\algorithmicwhile}{\textcolor{ForestGreen}{\textbf{Mientras}}} +\renewcommand{\algorithmicendwhile}{\textcolor{ForestGreen}{\textbf{Fin mientras}}} +\renewcommand{\algorithmicdo}{\textcolor{ForestGreen}{}} %%\textbf{hacer}}} +\renewcommand{\algorithmicreturn}{\textbf{Devolver}} +\floatname{algorithm}{Algoritmo} diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/needle-haystack/main.cpp b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/needle-haystack/main.cpp new file mode 100644 index 0000000..b9be84a --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/needle-haystack/main.cpp @@ -0,0 +1,83 @@ +#include +#include +#include +#include +#include + +using namespace std; + +typedef unsigned long long int lluint; +typedef vector vint; + +#define forsn(i, s, n) for (int i = (s); i < (n); i++) +#define forn(i, n) forsn (i, 0, n) + +// Pre KMP + +void pkmp(const string& s, vint& f) { + int z = f[0] = -1; + forsn (i, 1, s.size() + 1) { + while (z != -1 && s[i - 1] != s[z]) z = f[z]; + f[i] = ++z; // z might be -1 + } +} + +// Buffer + +#define TAMBUF 65536 +lluint pos; +char buf[TAMBUF]; +int buf_size; + +#define buf_sync() { \ + cin.getline(buf, TAMBUF + 1); \ + pos += buf_size; \ + buf_size = cin.gcount(); \ + cin.clear(); \ +} + +#define buf_start() { \ + buf_sync(); \ + pos = 0; \ +} + +// KMP + +void kmp(const string& s, vint& f) { + buf_start(); + const int final = s.size(); + int state = 0; + while (true) { + forn (i, buf_size) { + if (state == final) { + cout << (pos + i - final) << " "; + } + while (s[state] != buf[i]) { + state = f[state]; + if (state == -1) break; + } + state++; + } + if (buf_size < TAMBUF) break; + buf_sync(); + } +} + +int main() { + for (;;) { + int needle_size; + string needle; + cin >> needle_size; + if (cin.eof()) break; + cin >> needle; + assert(needle_size == needle.size()); + cin.ignore(1); + + vint f(needle.size() + 1); + pkmp(needle, f); + kmp(needle, f); + cout << endl; + } + return 0; +} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/needle-haystack/main_alternativo.cpp b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/needle-haystack/main_alternativo.cpp new file mode 100644 index 0000000..e1998c0 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/needle-haystack/main_alternativo.cpp @@ -0,0 +1,93 @@ +#include +#include +#include +#include +#include + +using namespace std; + +typedef unsigned long long int lluint; +typedef vector vint; +typedef vector vvint; + +#define forsn(i, s, n) for (int i = (s); i < (n); i++) +#define forn(i, n) forsn (i, 0, n) + +void pkmp(const string& s, vint& f) { + int z = f[0] = -1; + forsn (i, 1, s.size() + 1) { + while (z != -1 && s[i - 1] != s[z]) z = f[z]; + f[i] = ++z; // z might be -1 + } +} + +vvint tran; + +#define ALPHA_SIZE 128 +void build_transitions(const string& s) { + uint n = s.size() + 1; + vint f(n); + tran = vvint(n, vint(ALPHA_SIZE, 0)); + pkmp(s, f); + forn (state, n) { + forn (a, ALPHA_SIZE) { + int z = state; + while (z != -1 && s[z] != (char)a) z = f[z]; + tran[state][a] = z + 1; + } + } +} + +// Buffer + +#define TAMBUF 65536 +lluint pos; +char buf[TAMBUF]; +int buf_size; + +#define buf_sync() { \ + cin.getline(buf, TAMBUF + 1); \ + pos += buf_size; \ + buf_size = cin.gcount(); \ + cin.clear(); \ +} + +#define buf_start() { \ + buf_sync(); \ + pos = 0; \ +} + +void search() { + buf_start(); + const int final = tran.size() - 1; + int state = 0; + while (true) { + forn (i, buf_size) { + if (state == final) { + cout << (pos + i - final) << " "; + } + state = tran[state][buf[i]]; + } + if (buf_size < TAMBUF) break; + buf_sync(); + } +} + +int main() { + for (;;) { + int needle_size; + string needle; + cin >> needle_size; + if (cin.eof()) break; + cin >> needle; + assert(needle_size == needle.size()); + cin.ignore(1); + + build_transitions(needle); + search(); + + cout << endl; + } + return 0; +} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/new-distinct-substrings/main.cpp b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/new-distinct-substrings/main.cpp new file mode 100644 index 0000000..32f34b8 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/new-distinct-substrings/main.cpp @@ -0,0 +1,132 @@ +#include +#include +#include + +using std::sort; +using std::swap; + +static char text[50001]; +static unsigned int sa[50000]; +static unsigned int rank1[50000]={0}; +static unsigned int rank2[50000]={0}; + +static int N; +static long long total; +static unsigned cuantos; + +bool parar; +int bucket, aux, desde, actual; +unsigned int* ahora; +unsigned int* proximo; + + +// Comparador +struct Comparador { + const int K; + const unsigned int* rank; + Comparador(const int j,const unsigned int* vrank): K(j), rank(vrank) {}; + + bool inline operator()(const int i, const int j) const { + return clave(i) < clave(j); + } + + int inline clave(const int i) const { + return (i+K < N ? rank[i+K]+1 : 0); + } +}; + + +int main(int argc, const char *argv[]) { + + scanf("%d", &cuantos); + + for (int c = 0; c < cuantos; c++) { + + scanf("%s", text); + N = strlen(text); + + // Suffix Array + for (int i = 0; i < N; i++) { + sa[i] = i; + rank1[i] = text[i]; + } + + + sort(sa, sa+N, Comparador(0, rank1)); + + bucket = 0; + rank1[sa[0]] = 0; + + for (int t = 1; t < N; t++) { + if (text[sa[t-1]] == text[sa[t]]) { + rank1[sa[t]] = bucket; + } else { + bucket = t; + rank1[sa[t]] = bucket; + } + } + + parar = true; + ahora = rank1; + proximo = rank2; + + for (int K = 1; K < N; K *= 2) { + desde = 0; + actual = 1; + Comparador comparador(K,ahora); + while (actual < N) { + while (actual< N && ahora[sa[actual]] == ahora[sa[actual-1]]) { + actual++; + } + if (actual > desde+1) { + sort(sa+desde, sa+actual, comparador); + } + desde = actual; + actual++; + } + + bucket = 0; + proximo[sa[0]] = 0; + aux = 0; + + for (int t = 1; t < N; t++) { + if (ahora[sa[t]] == aux && comparador.clave(sa[t-1]) == comparador.clave(sa[t])) { + proximo[sa[t]] = bucket; + parar = false; + } else { + aux = ahora[sa[t]]; + bucket = t; + proximo[sa[t]] = bucket; + } + } + + swap(ahora, proximo); + if (parar) break; + parar = true; + } + + // LCP (Kasai) + total = 0; + int k = 0; + for (int i = 0; i < N; i++) { + if (k > 0) { + k--; + } + if (ahora[i] == N-1) { + total += N + 1 - sa[N-1]; + k = 0; + continue; + } + int j = sa[ahora[i]+1]; + while (text[i+k] == text[j+k]) k++; + total += N - k - sa[ahora[i]]; + } + + // El codigo de arriba pone un -1 en la + // fila final del LCP en lugar de un 0 en la primera, + // asi que hay que restarlo ahora. + total = total - 1; + + printf("%lld\n", total); + } +} diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/new-distinct-substrings/test.txt b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/new-distinct-substrings/test.txt new file mode 100644 index 0000000..48c5039 --- /dev/null +++ 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tabla.size(); + int i, j; + //init de los intervalos de largo 1 + forn(i,n) + tabla[i][0] = i; + + //llenado de la tabla desde los mas chicos a los mas grandes + unsigned t=2; + unsigned t_ant=1; + for (j = 1; t <= n; j++) { + for (i = 0; i + (t) - 1 < n; i++) { + int k = j - 1; + if (frec[tabla[i][k]] > frec[tabla[i + (t_ant)][k]]) + tabla[i][j] = tabla[i][k]; + else + tabla[i][j] = tabla[i + (t_ant)][k]; + } + t_ant=t; + t=t<<1; + } +} + + +static inline uint32_t log_2(const uint32_t x) { + uint32_t y; + asm ( "\tbsr %1, %0\n" + : "=r"(y) + : "r" (x) + ); + return y; +} + + + void inline cargar_numeros(int cant_numeros,vector& frec,vector >& intervalostupla,vector& intervaloindice,int& intervalo) { + int i = 0; + int numero; + int desde,hasta; //intervalo donde todos los elementos son iguales [ ] + int actual; //elemento cuya frecuencia estoy construyendo + while (i < cant_numeros) { + scanf ("%d",&numero); + + if (i == 0) { + actual=numero; + desde=0; + hasta=0; + } else { + if (actual==numero) { //si son iguales, incremento el hasta y su frecuencia + hasta++; + frec[intervalo]++; + } + // si son distintos, se cerró un intervalo, hay que empezar a armar otro + else { + intervalostupla[intervalo] = pair(desde,hasta); + intervalo++; + hasta++; + desde=hasta; + actual = numero; + } + + } + intervaloindice[i]=intervalo; + + i++; + + } + + //hack: el ultimo siempre quedaba sin agregar + intervalostupla[intervalo] = pair(desde,hasta); +} + +void inline procesar_queries(const int queries,const vector& frec,const vector >& intervalostupla,const vector& intervaloindice,int& intervalo) { + vector > tabla(intervalo+1, vector(log_2(intervalo+1)+1)); + llenar_tabla(tabla,frec); + unsigned x,y; + int i=0; + while (i < queries) { + scanf("%u %u",&x,&y); + int desde, hasta; + //desde y hasta son los intervalos extremos que hay que mirar. + //No necesariamente estan completos + desde = intervaloindice[x-1]; + hasta = intervaloindice[y-1]; + + int res; + // Si esos indices son parte del mismo intervalo, la frecuencia es la distancia entre ellos. + if (desde==hasta) { + res = y-x+1; + } else { + //calculo por separado los intervalos que pueden ser truncos + int frec_i = intervalostupla[desde].second - x + 2; + int frec_j = y - intervalostupla[hasta].first ; + + //el siguiente del desde y el anterior del hasta si estan completos + unsigned int intervalo_completo_i = desde+1; + unsigned int intervalo_completo_j = hasta-1; + + res = max(frec_i,frec_j); + if(intervalo_completo_i <= intervalo_completo_j){ + unsigned int k = log_2(intervalo_completo_j - intervalo_completo_i + 1); + int aux = frec[tabla[intervalo_completo_j-(1<= aux ) + res = max(res,frec[tabla[intervalo_completo_i][k]]); + else + res = max(res,aux); + } + } + + printf("%d\n",res); + i++; + } +} + +int main(int argc, char** argv) { +#ifndef ONLINE_JUDGE + close (0); + open ("test.txt", O_RDONLY); + //close (1); + //open ("myprog.out", O_WRONLY | O_CREAT, 0600); +#endif + + int cant_numeros,queries; + scanf ("%d",&cant_numeros); + + + while (cant_numeros > 0) { + scanf ("%d",&queries); + vector frec(cant_numeros,1);//vector de frecuencias + int intervalo =0;//cantidad de intervalos + vector intervaloindice(cant_numeros); //dado un indice del arreglo, devuelve el numero de intervalo en el que esta + vector > intervalostupla(cant_numeros); //dado un numero de intervalo, da su desde y hasta + + cargar_numeros(cant_numeros,frec,intervalostupla, intervaloindice, intervalo); + procesar_queries(queries, frec,intervalostupla, intervaloindice, intervalo); + + + scanf ("%d",&cant_numeros); + + } + return (EXIT_SUCCESS); +} + + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/rmq/test.txt b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/rmq/test.txt new file mode 100644 index 0000000..b6e7c9f --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpc/rmq/test.txt @@ -0,0 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lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/ballroom/ballroom.cpp new file mode 100644 index 0000000..eb1d617 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/ballroom/ballroom.cpp @@ -0,0 +1,272 @@ +#include +#include +#include +#include +#include +#include +#include +#include + +#define forn(i, n) for (int i = 0; i < (n); i++) +#define TOLERANCIA 1e-8 + +using namespace std; + +struct MaybeDouble { + long double valor; + bool valido; + + MaybeDouble(long double v, bool b): valor(v), valido(b) {}; +}; + +struct Vector { + long double x; + long double y; + + Vector(long double xi, long double yi): x(xi), y(yi) {}; + + long double norma() { + return hypot(x, y); + } + + long double angulo() { + return atan2(y, x); + } + +}; + +struct Columna { + Vector posicion; + long double radio; + + Columna(long double x, long double y, long double r) : posicion(x,y), radio(r) {}; +}; + +typedef Vector Lampara; +typedef pair Intervalo; +typedef pair Segmento; + + +inline long double largo(const Segmento& s) { + return Vector(s.second.x - s.first.x, s.second.y - s.first.y).norma(); +} + +inline long double largo(const Intervalo& i) { + assert(i.first <= i.second); + return i.second - i.first; +} + + +MaybeDouble intersect_segments(const Segmento& s1, const Segmento& s2) { + Vector p1 = s1.first; + Vector p2 = s1.second; + Vector p3 = s2.first; + Vector p4 = s2.second; + + long double den = (p4.y-p3.y)*(p2.x-p1.x) - (p4.x-p3.x)*(p2.y-p1.y); + + long double ua_num = (p4.x-p3.x)*(p1.y-p3.y) - (p4.y-p3.y)*(p1.x-p3.x); + long double ub_num = (p2.x-p1.x)*(p1.y-p3.y) - (p2.y-p1.y)*(p1.x-p3.x); + + if (fabs(den) < TOLERANCIA) { + // Caso en que los segmentos son paralelos + if (fabs(ua_num - ub_num) < TOLERANCIA && fabs(ub_num) < TOLERANCIA) { + // Las rectas son coincidentes, esto no deberia ocurrir + assert(false); + return MaybeDouble((p1.norma() > p2.norma()? 0 : 1), true); + } + return MaybeDouble(0, false); + } + + if (ub_num/den >= 0) { + return MaybeDouble(ua_num/den, true); + } + return MaybeDouble(0, false); +} + + +Intervalo interseccion_intervalos(const Intervalo& i1, const Intervalo& i2) { + + long double d0 = max(i1.first, i2.first); + long double d1 = min(i1.second, i2.second); + + if (d1 < d0) { + return Intervalo(0, 0); + } else { + return Intervalo(d0, d1); + } +} + + +Intervalo rango_oscurecido(const Segmento& pared, const Lampara& lampara, const Columna& columna) { + Vector bisectriz(columna.posicion.x - lampara.x, columna.posicion.y - lampara.y); + long double p = asin(columna.radio/bisectriz.norma()); + long double alpha = bisectriz.angulo(); + + Vector d1(cos(alpha + p), sin(alpha + p)); + Vector d2(cos(alpha - p), sin(alpha - p)); + + MaybeDouble p1 = intersect_segments(pared, Segmento(lampara, Vector(lampara.x + d1.x, lampara.y + d1.y))); + MaybeDouble p2 = intersect_segments(pared, Segmento(lampara, Vector(lampara.x + d2.x, lampara.y + d2.y))); + + long double unidad = largo(pared); + + // Se sabe que los puntos de interseccion estan ordenados correctamente + // porque el angulo de diferencia entre las semirectas es menor a 180, + // entonces no es necesario chequearlo. + Intervalo res; + + if (!p1.valido) { + if (!p2.valido) { + return Intervalo(0, 0); + } else { + res = Intervalo(0, p2.valor); + } + } else { + if (!p2.valido) { + res = Intervalo(p1.valor, 1); + } else { + res = Intervalo(p1.valor, p2.valor); + } + } + + res = interseccion_intervalos(res, Intervalo(0,1)); + return Intervalo(res.first * unidad, res.second * unidad); +} + +void invertir_rango(const list& ints, long double fin, list& out) { + + if (!ints.size()) { + out.push_back(Intervalo(0,fin)); + return; + } + + + list::const_iterator it = ints.begin(); + if (it->first > 0) { + out.push_back(Intervalo(0, it->first)); + } + + it++; + + list::const_iterator itprev = ints.begin(); + while (it != ints.end()) { + out.push_back(Intervalo(itprev->second, it->first)); + it++; + itprev++; + } + + if (itprev->second < fin) { + out.push_back(Intervalo(itprev->second, fin)); + } +} + + +void reduce_union(list& l_o, list& out) { + // elimino repetidos para acelerar el sort + list l; + + for (list::const_iterator itcito = l_o.begin(); itcito != l_o.end(); itcito++) { + if (itcito->first < itcito->second) { + l.push_back(Intervalo(itcito->first, itcito->second)); + } else if (itcito->first > itcito->second) { + assert(false); + } + } + + + if (!l.size()) return; + + l.sort(); + + list::const_iterator it = l.begin(); + Intervalo cand = *it; + Intervalo otro; + + it++; + while (it != l.end()) { + otro = *it; + if (otro.first < otro.second) { + if (otro.first > cand.second) { + out.push_back(cand); + cand = otro; + } else { + if (otro.second > cand.second) { + cand = Intervalo(cand.first, otro.second); + } + } + } + it++; + } + + out.push_back(cand); +} + + +long double resolver(const list& lamparas, const list& columnas, int max_x, int max_y) { + list paredes; + paredes.push_back(Segmento(Vector(0,0), Vector(0, max_y))); + paredes.push_back(Segmento(Vector(0,max_y), Vector(max_x, max_y))); + paredes.push_back(Segmento(Vector(max_x,max_y), Vector(max_x, 0))); + paredes.push_back(Segmento(Vector(max_x,0), Vector(0, 0))); + + long double total = 0; + + for (list::iterator p = paredes.begin(); p != paredes.end(); p++) { + list luces_pared; + for (list::const_iterator l = lamparas.begin(); l != lamparas.end(); l++) { + list zonas_tapadas; + for (list::const_iterator c = columnas.begin(); c != columnas.end(); c++) { + zonas_tapadas.push_back(rango_oscurecido(*p, *l, *c)); + } + + list tapadas_unidas; + list zona_iluminada; + + reduce_union(zonas_tapadas, tapadas_unidas); + invertir_rango(tapadas_unidas, largo(*p), zona_iluminada); + + luces_pared.splice(luces_pared.end(), zona_iluminada); + } + + list luces_pared_unidas; + reduce_union(luces_pared, luces_pared_unidas); + + for (list::iterator it = luces_pared_unidas.begin(); it != luces_pared_unidas.end(); it++) { + total += largo(*it); + } + } + + return total; +} + + +int main() { + + int nl, nc, max_x, max_y; + + for (;;) { + scanf("%d %d %d %d", &nl, &nc, &max_x, &max_y); + + if (!(nl || nc || max_x || max_y)) { + break; + } + + list lamparas; + list columnas; + + int x, y, r; + + forn(i, nl) { + scanf("%d %d", &x, &y); + lamparas.push_back(Lampara(x,y)); + } + + forn(i, nc) { + scanf("%d %d %d", &x, &y, &r); + columnas.push_back(Columna(x, y, r)); + } + + printf("%.4Lf\n", resolver(lamparas, columnas, max_x, max_y)); + } +} diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/ballroom/ballroom.py b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/ballroom/ballroom.py new file mode 100644 index 0000000..24b574b --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/ballroom/ballroom.py @@ -0,0 +1,459 @@ +#!/usr/bin/python +# -*- coding: utf8 -*- + +from __future__ import division + +import psyco +psyco.full() + +import math + + +########### +# Helpers # +########### + +def mod2pi(x): + '''Devuelve un valor de angulo equivalente en [0, 2*pi). + + >>> import math + >>> mod2pi(0.0) + 0.0 + >>> mod2pi(4 * math.pi) + 0.0 + >>> mod2pi(-math.pi) + 3.1415926535897931 + ''' + while x < 0: + x += 2 * math.pi + while x >= 2 * math.pi: + x -= 2 * math.pi + return x + + +def mod360(x): + '''Devuelve un valor de angulo equivalente en [0, 360). + + >>> import math + >>> mod360(0.0) + 0.0 + >>> mod360(360+180) + 180.0 + >>> mod360(-180) + 180.0 + ''' + while x < 0: + x += 360.0 + while x >= 360.0 : + x -= 360.0 + return x + + +########## +# Vector # +########## + +class Vector: + def __init__(self, x, y): + self.x = x + self.y = y + + def __add__(self, otro): + return Vector(self.x + otro.x, self.y + otro.y) + + def __sub__(self, otro): + return Vector(self.x - otro.x, self.y - otro.y) + + def __mul__(self, f): + return Vector(self.x * f, self.y * f) + + def __rmul__(self, f): + return self * f + + def __div__(self, f): + return Vector(self.x / f, self.y / f) + + def __neg__(self): + return Vector(self.x *-1 , self.y * -1) + + def __eq__(self, otro): + return self.x == otro.x and self.y == otro.y + + def __repr__(self): + return '''''' % (self.x, self.y) + + def __iter__(self): + yield self.x + yield self.y + + def __hash__(self): + return hash((self.x,self.y)) + + def dotP(self, otro): + '''Computa el producto escalar de 2 vectores. + + >>> Vector(1,0).dotP(Vector(0,1)) + 0.0 + >>> Vector(1,1).dotP(Vector(1,1)) + 2.0 + ''' + + return self.x * otro.x + self.y * otro.y + + def boundNorm(self, norma): + '''Devuelve un vector idéntico a este pero con la norma + acotada al rango [0, norma] + + >>> Vector(2,0).boundNorm(1) + + >>> Vector(1,1).boundNorm(4) + + >>> Vector(2,2).boundNorm(math.sqrt(2)) + + ''' + + assert norma > 0 + norma_efectiva = min(norma, self.norma()) + factor = norma_efectiva / self.norma() + return self * factor + + def flipY(self): + '''Devuelve un vector idéntico a este con la coordenada + Y invertida (útil para dibujar en la pantalla, que tiene el + sistema de coordenadas con esta particularidad). + ''' + return Vector(self.x, -self.y) + + def norma(self): + '''Computa la norma cartesiana del vector. + + >>> Vector(1,1).norma() + 1.4142135623730951 + >>> Vector(1,0).norma() + 1.0 + >>> Vector(0,1).norma() + 1.0 + ''' + return math.sqrt(self.x**2 + self.y**2) + + def angulo(self): + '''Computa el ángulo polar del vector (en radianes desde la recta y=0). + + >>> Vector(1,0).angulo() + 0.0 + >>> Vector(0,1).angulo() + 1.5707963267948966 + >>> Vector(0,-1).angulo() + -1.5707963267948966 + ''' + if self.x == 0 and self.y == 0: + return 0 + elif self.x >= 0: + return math.asin(self.y/self.norma()) + else: + return -math.asin(self.y/self.norma()) + math.pi + + def grados(self): + '''Computa el ángulo polar del vector (en grados desde la recta y=0). + + >>> Vector(1,0).grados() + 0.0 + >>> Vector(0,1).grados() + 90.0 + >>> Vector(0,-1).grados() + -90.0 + ''' + return math.degrees(self.angulo()) + + def viento(self): + '''Devuelve el viento correspondiente a este vector. + + >>> viento = Vector(10,10).viento() + >>> viento + + >>> Vector(1, 0).viento() + + >>> Vector(-10, 0).viento() + + ''' + return Viento(mod360(270 - self.grados()), self.norma()) + + +########## +# Viento # +########## + +class Viento: + def __init__(self, direccion, intensidad): + '''Construye un viento soplando desde la direccion indicada, + con la intensidad indicada. + + >>> viento = Viento(0, 15) + >>> viento.angulo + 4.7123889803846897 + >>> viento.x + -2.7553642961003488e-15 + >>> viento.y + -15.0 + ''' + + assert 0 <= intensidad + direccion = mod360(direccion) + self.direccion = direccion + self.intensidad = intensidad + + # Precalculo algunas cosas + self.angulo = mod2pi(-math.radians(direccion) - math.pi/2) + self.x = math.cos(self.angulo) * intensidad + self.y = math.sin(self.angulo) * intensidad + + def vector(self): + '''Devuelve el vector asociado a este viento. + + >>> vector = Viento(90,10).vector() + >>> vector.x + -10.0 + >>> vector.y + 1.2246063538223773e-15 + >>> vector.viento() + + ''' + return Vector(self.x, self.y) + + def anguloIncidencia(self, vector_navegacion): + '''Devuelve el ángulo de incidencia del viento sobre un + barco que navega sobre vector_navegacion. + + >>> Viento(0, 10).anguloIncidencia(Vector(-1,1)) + 0.78539816339744828 + >>> Viento(0, 10).anguloIncidencia(Vector(1,1)) + 5.497787143782138 + ''' + return mod2pi(vector_navegacion.angulo() - (-self.vector()).angulo()) + + def __repr__(self): + return "" % (self.direccion, self.intensidad) + + + + + +inf = float('inf') + +def intersect_lines(l1, l2): + + p1 = l1[0] + p2 = l1[1] + p3 = l2[0] + p4 = l2[1] + + den = (p4.y-p3.y)*(p2.x-p1.x) - (p4.x-p3.x)*(p2.y-p1.y) + + ua_num = (p4.x-p3.x)*(p1.y-p3.y) - (p4.y-p3.y)*(p1.x-p3.x) + ub_num = (p2.x-p1.x)*(p1.y-p3.y) - (p2.y-p1.y)*(p1.x-p3.x) + + if abs(den) == 0: + if abs(ua_num - ub_num) == 0 and \ + abs(ub_num) == 0: + return max(p1, p2, key=lambda v: v.norma()) + + return None + + ua = ua_num/den + ub = ub_num/den + + if ub >= 0: + return ua + + return None + + + +def rango_oscurecido(inicio, fin, src, centro, radio): + ''' + Devuelve el rango (en distancia de 0 a ||$inicio-$fin||) + que se encuentra a la sombra de una columna de radio $radio, + ubicada en $centro e iluminada por una fuente de luz puntual en $src. + ''' + + bisectriz = centro - src + p = math.asin(radio/bisectriz.norma()) + alpha = bisectriz.angulo() + + d1 = Vector(math.cos(alpha + p), math.sin(alpha + p)) + d2 = Vector(math.cos(alpha - p), math.sin(alpha - p)) + + p1 = intersect_lines((inicio, fin), (src, src + d1)) + p2 = intersect_lines((inicio, fin), (src, src + d2)) + + unidad = (fin - inicio).norma() + + # Se sabe que los puntos de interseccion estan ordenados correctamente + # porque el angulo de diferencia entre las semirectas es menor a 180, + # entonces no es necesario chequearlo. + if p1 is None: + if p2 is None: + return (0.0, 0.0) + else: + res = (0.0, p2) + else: + if p2 is None: + res = (p1, 1.0) + else: + res = (p1, p2) + + res_bounded = interseccion_intervalos(res, (0.0, 1.0)) + p = (res_bounded[0] * unidad, res_bounded[1] * unidad) + return p + + +def interseccion_intervalos(i1, i2): + '''Devuelve los extremos del intervalo interseccion entre i1 y i2. + + >>> interseccion_intervalos((1,3),(2,8)) + (2, 3) + >>> interseccion_intervalos((1,2), (5,6)) + (5, 5) + >>> interseccion_intervalos((-inf, 8), (6, inf)) + (6, 8) + ''' + + p1, p2 = i1 + p3, p4 = i2 + + d = (max(p1, p3), min(p2, p4)) + if d[1] < d[0]: + return (d[0], d[0]) + else: + return d + + +def reduce_interseccion(l): + cand = (-inf, inf) + for e in l: + cand = interseccion_intervalos(cand, e) + return cand + + +def reduce_union(l): + '''Devuelve la union de la lista de intervalos l + + >>> reduce_union([(1,3), (2,5)]) + [(1, 5)] + >>> reduce_union([(1,3), (4, 6)]) + [(1, 3), (4, 6)] + >>> reduce_union([(1,3), (4, 6), (5, 6)]) + [(1, 3), (4, 6)] + >>> reduce_union([(1,3), (4, 6), (5, 7)]) + [(1, 3), (4, 7)] + ''' + + ordenados = l[:] + ordenados.sort(key=lambda x: x[0]) + + if len(l) == 0: + return [] + + res = [] + cand = ordenados[0] + for i in range(1, len(l)): + otro = ordenados[i] + if otro[0] > cand[1] and otro[0] != otro[1]: + res.append(cand) + cand = otro + else: + if otro[1] > cand[1]: + cand = (cand[0], otro[1]) + + res.append(cand) + return res + + +# Asume que los intervalos estan ordenados por punto de comienzo +def invertir_rango(ints, fin): + ''' + Invierte el conjunto de segmentos (minimo y ordenado) para + tomar su complemento. + + >>> invertir_rango([(3,4)], 8) + [(0, 3), (4, 8)] + >>> invertir_rango([(3,4),(6,8)], 8) + [(0, 3), (4, 6)] + >>> invertir_rango([(0,2), (5,6)], 10) + [(2, 5), (6, 10)] + ''' + + if len(ints) == 0: + return [(0, fin)] + + invertido = [] + if ints[0][0] > 0: + invertido.append((0, ints[0][0])) + + for i in range(1, len(ints)): + invertido.append((ints[i-1][1], ints[i][0])) + + if ints[-1][1] < fin: + invertido.append((ints[-1][1], fin)) + + return invertido + + + + + +def resolver(lamparas, columnas, max_x, max_y): + + paredes = ((Vector(0,0), Vector(0,max_y)), + (Vector(0, max_y), Vector(max_x, max_y)), + (Vector(max_x, max_y), Vector(max_x, 0)), + (Vector(max_x, 0), Vector(0,0))) + + + total = 0 + for p in paredes: + luces_pared = [] + for l in lamparas: + zonas_tapadas = [] + for c in columnas: + r = rango_oscurecido(p[0], p[1], l, c[0], c[1]) + zonas_tapadas.append(r) + zona_iluminada = invertir_rango(reduce_union(zonas_tapadas), (p[1]-p[0]).norma()) + luces_pared += zona_iluminada + luces_pared = reduce_union(luces_pared) + + s = sum(map(lambda x: x[1] - x[0], luces_pared)) + total += s + + print "%.4f" % total + + + +def main(): + import sys + + while True: + nl, nc, max_x, max_y = map(int, sys.stdin.readline().strip().split()) + + if nl == nc == max_x == max_y == 0: + break + + lamparas = [] + for i in range(nl): + lampara = Vector(*(map(float, sys.stdin.readline().strip().split()))) + lamparas.append(lampara) + + columnas = [] + for i in range(nc): + x, y, r = map(float, sys.stdin.readline().strip().split()) + columnas.append((Vector(x,y), r)) + + resolver(lamparas, columnas, max_x, max_y) + + + +if __name__ == '__main__': + #import doctest + #doctest.testmod() + + main() diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/ballroom/test.txt b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/ballroom/test.txt new file mode 100644 index 0000000..3d8d663 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/ballroom/test.txt @@ -0,0 +1,92 @@ +2 1 8 8 +6 6 +2 6 +4 4 2 +1 4 7 7 +3 3 +2 4 1 +4 2 1 +2 2 1 +4 4 1 +2 2 9 7 +1 2 +5 5 +3 3 2 +7 5 1 +1 1 7 4 +2 2 +4 2 1 +2 1 7 4 +2 2 +6 2 +4 2 1 +1 2 8 4 +2 2 +4 2 1 +6 2 1 +2 2 8 4 +2 2 +1 2 +4 2 1 +6 2 1 +3 2 8 4 +2 2 +1 2 +5 1 +4 2 1 +6 2 1 +4 2 8 4 +2 2 +1 2 +5 1 +5 3 +4 2 1 +6 2 1 +4 1 8 4 +2 2 +1 2 +5 1 +5 3 +4 2 1 +1 2 5 6 +2 3 +3 2 1 +3 4 1 +1 1 5 6 +2 3 +3 4 1 +1 1 5 6 +2 3 +3 2 1 +2 1 8 8 +1 1 +3 3 +2 2 1 +4 1 8 8 +1 1 +3 1 +1 3 +3 3 +2 2 1 +1 0 4 4 +1 1 +0 0 4 4 +0 1 4 4 +3 3 2 +1 1 100 50 +50 49 +50 25 10 +1 1 100 50 +50 1 +50 25 10 +1 1 1000000 1000000 +1 1 +99998 2 1 +1 1 1000000 1000000 +1 1 +999998 2 1 +2 1 1000000 1000000 +1 999998 +999998 1 +999998 999998 1 +0 0 0 0 diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/disgruntled/disgruntled.cpp b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/disgruntled/disgruntled.cpp new file mode 100644 index 0000000..bc02152 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/disgruntled/disgruntled.cpp @@ -0,0 +1,256 @@ +#include +#include +#include +#include +#include +#include +#include +#include +using namespace std; +#define forn(i,n) for(int i = 0; i < n; ++i) +#define forsn(i,s,n) for(int i = (s); i < (n); i++) +#define foreachin(it,s) for(__typeof__((s).begin()) it = ((s).begin()); it != ((s).end()); ++it) + +#define inverso_de_73_mod_137 122 +#define inverso_de_137_mod_73 8 +#define coef_137 1096 // 137*8 +#define coef_73 8906 // 73*122 + +static int cuad73[73]; +static int cuad137[137]; + +#define resto(x,y) ((((x) % (y)) + (y)) % (y)) + +// si (a,b) = 1, deja en x el inverso multiplicativo de a ,mod b +// basicamente es la idea del algoritmo de euclides, pero iterativo +// mas info: www.math.hawaii.edu/~lee/discrete/combination.ps +void combinacion(int a, int b, int&x) { + int g0 = a; + int x0 = 1; +// int y0 = 0; + int g1 = b; + int x1 = 0; +// int y1 = 1; + while (g0 % g1 != 0) { +//invariante: a*x_1+b*y_1=g1 + int q = g0 / g1; + int temp = g1; + g1 = g0 - q * g1; + g0 = temp; + temp = x1; + x1 = x0 - q * x1; + x0 = temp; + /* + temp = y1; + y1 = y0 - q * y1; + y0 = temp; + */ + } + x=x1; +} + +/* utiliza la ecuacion: a^2*x +a*b+b \equiv y + * para despejar b, si no es posible, es porque el a no era correcto + * b*(a+1) \equiv y -a^2 + */ +bool obtener_b(int a, int x, int y,int& b) { + if ((a+1) % 73 == 0) { + // para poder encontrar un b, la parte derecha tb tiene que ser congruente a 0 modulo 73 + if (y-resto(a*a,73)*x %73 != 0)return false; + int amas1inv, aux; + combinacion((a+1),137,amas1inv); + amas1inv = resto(amas1inv,137); + + int acuad = a*a %137; + aux = resto((y - acuad*x),137); + b = aux*amas1inv%137; + return true; + } + + if ((a+1)%137 == 0) { + // para poder encontrar un b, la parte derecha tb tiene que ser congruente a 0 modulo 137 + if (y-resto(a*a,137)*x %137 != 0)return false; + int amas1inv, aux; + combinacion((a+1),73,amas1inv); + amas1inv = resto(amas1inv,73); + + int acuad = a*a % 73; + aux = resto((y - acuad*x),73); + b = aux*amas1inv %73; + return true; + } + int amas1inv137, aux; + + combinacion((a+1),137,amas1inv137); + amas1inv137 = resto(amas1inv137,137); + int acuad137 = a*a % 137; + int aux137 = resto((y - acuad137*x),137); + int b137= aux137*amas1inv137 % 137; + int amas1inv73; + combinacion((a+1),73,amas1inv73); + amas1inv73 = resto(amas1inv73,73); + int acuad73 = a*a %73; + int aux73 = resto((y - acuad73*x),73); + int b73= aux73*amas1inv73 %73; + + //usamos teorema chino del resto, para encontrar b + + b = ((b73*coef_137)+(b137*coef_73)) % 10001; + + return true; + +} + +static int numeros[101]; + +bool testear_candidato(int a, int b, int cant,list& res) { + forn(i,cant) { + int f = (a*numeros[i]+b)% 10001; + res.push_back(f); + if (numeros[i+1] < cant && (a*f+b)% 10001 != numeros[i+1]) { + break; + } + } + return res.size() == cant; +} + +void llenar_res(int a,int a1,int x, int y,int cant,list& res,int q) { + int b; + int candidatos[2] = {a,a1}; + int t = 0; + while (true) { + if (obtener_b(candidatos[t],x,y,b)) { + if (testear_candidato(candidatos[t],b,cant,res))break; + } + res.clear(); + t++; + if (t>1) { + candidatos[0]=candidatos[0]+q; + candidatos[1]=candidatos[1]+q; + t=0; + } + } +} + +void resolver(const int cuadk[],int k,int x,int y,int qk, int wk,int cant) { + int qkinv; + + combinacion(qk,k,qkinv); + qkinv = resto(qkinv,k); + int acuad = (wk*qkinv)%k; + int a,a1; + a = cuadk[acuad]; + a1= k -cuadk[acuad]; + list res; + llenar_res(a,a1,x,y,cant,res,k); + foreachin(it,res) { + printf("%d\n",*it); + } +} + + +int main(int argc, char** argv) { + // cuad73[k] = a / a^2 % 73 == k + // notar que alcanza mirar hasta 37 (73/2+1) + // porque j^2 % 73 == (73 - j)^2 + // ademas no hay a1,a2 entre [0,73/2+1) tal que a1^2 % 73 == a2^2 % 73 + forn(each,37) { + cuad73[(each*each)%73] = each; + + } + // simil a lo anterior + forn(each,68) { + cuad137[(each*each)%137]=each; + } + int cant; + scanf("%d",&cant); + while (cant > 0) { + + forn(i,cant) { + scanf("%d",&numeros[i]); + + } + if (cant < 3) { + forn(i, cant) { + printf("%d\n",numeros[cant-1]); + } + } + else { + int x,y,z; + x=numeros[0]; + y=numeros[1]; + z=numeros[2]; + int q,w; + /* Idea: + a*x + b \equiv 0_1 + a*O_1 + b \equiv y + a*y + b \equiv O_2 + a*O_2 +b \equiv z + ----------------- + a^2*x+ab+b \equiv y + a^2*y+ab+b \equiv z + -------------------- + a^2(x-y) \equiv (y-z) + + Resolver esa ecuacion modulo 137 y 73 y obtener candidatos para a. + obtener un b para alguno de los candidatos. usar esa pareja (a,b) + */ + q = (x-y); + w = (y-z); + + int q137 = resto(q,137); + int q73 = resto(q,73); + int w137 = resto(w,137); + int w73 = resto(w,73); + if (q137 == 0) { + if (q73 == 0) { + forn(i,cant) { + printf("%d\n",numeros[cant-1]); + } + } + else { + resolver(cuad73,73,x,y,q73,w73,cant); + } + } + else { + if (q73 == 0) { + resolver(cuad137,137,x,y,q137,w137,cant); + } + else { + int q137inv,q73inv; + + combinacion(q137,137,q137inv); + q137inv = resto(q137inv,137); + int acuad137 = (w137*q137inv)%137; + combinacion(q73,73,q73inv); + q73inv = resto(q73inv,73); + int acuad73 = (w73*q73inv)%73; + int a,b; + int j = cuad73[acuad73]; + int k = cuad137[acuad137]; + list res; + int candidatos[4] = { resto(j*coef_137 + k* coef_73,10001), resto((73-j)*coef_137 + k* coef_73,10001), + resto((73-j)*coef_137 + (137-k)* coef_73,10001), resto(j*coef_137 + (137-k)* coef_73,10001) + }; + forn(i, 4) { + a =candidatos[i] ; + if (obtener_b(a,x,y,b)) { + if (testear_candidato(a,b,cant,res)) { + break; + } + } + res.clear(); + } + foreachin(it,res) { + printf("%d\n",*it); + } + + } + } + + } + if (scanf("%d\n",&cant)!=1)break; + } + return (EXIT_SUCCESS); +} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/algorithm.sty b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/algorithm.sty new file mode 100644 index 0000000..34e1f1f --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/algorithm.sty @@ -0,0 +1,96 @@ +% ALGORITHM STYLE -- Released 8 April 1996 +% for LaTeX-2e +% Copyright -- 1994 Peter Williams +% +% E-mail pwil3058@bigpond.net.au +% +% This style file is free software; you can redistribute it and/or +% modify it under the terms of the GNU Lesser General Public +% License as published by the Free Software Foundation; either +% version 2 of the License, or (at your option) any later version. +% +% This style file is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +% Lesser General Public License for more details. +% +% You should have received a copy of the GNU Lesser General Public +% License along with this style file; if not, write to the +% Free Software Foundation, Inc., 59 Temple Place - Suite 330, +% Boston, MA 02111-1307, USA. +% +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{algorithm} +\typeout{Document Style `algorithm' - floating environment} + +\RequirePackage{float} +\RequirePackage{ifthen} +\newcommand{\ALG@within}{nothing} +\newboolean{ALG@within} +\setboolean{ALG@within}{false} +\newcommand{\ALG@floatstyle}{ruled} +\newcommand{\ALG@name}{Algorithm} +\newcommand{\listalgorithmname}{List of \ALG@name s} + +% Declare Options +% first appearance +\DeclareOption{plain}{ + \renewcommand{\ALG@floatstyle}{plain} +} +\DeclareOption{ruled}{ + \renewcommand{\ALG@floatstyle}{ruled} +} +\DeclareOption{boxed}{ + \renewcommand{\ALG@floatstyle}{boxed} +} +% then numbering convention +\DeclareOption{part}{ + \renewcommand{\ALG@within}{part} + \setboolean{ALG@within}{true} +} +\DeclareOption{chapter}{ + \renewcommand{\ALG@within}{chapter} + \setboolean{ALG@within}{true} +} +\DeclareOption{section}{ + \renewcommand{\ALG@within}{section} + \setboolean{ALG@within}{true} +} +\DeclareOption{subsection}{ + \renewcommand{\ALG@within}{subsection} + \setboolean{ALG@within}{true} +} +\DeclareOption{subsubsection}{ + \renewcommand{\ALG@within}{subsubsection} + \setboolean{ALG@within}{true} +} +\DeclareOption{nothing}{ + \renewcommand{\ALG@within}{nothing} + \setboolean{ALG@within}{true} +} +\DeclareOption*{\edef\ALG@name{\CurrentOption}} + +% ALGORITHM +% +\ProcessOptions +\floatstyle{\ALG@floatstyle} +\ifthenelse{\boolean{ALG@within}}{ + \ifthenelse{\equal{\ALG@within}{part}} + {\newfloat{algorithm}{htbp}{loa}[part]}{} + \ifthenelse{\equal{\ALG@within}{chapter}} + {\newfloat{algorithm}{htbp}{loa}[chapter]}{} + \ifthenelse{\equal{\ALG@within}{section}} + {\newfloat{algorithm}{htbp}{loa}[section]}{} + \ifthenelse{\equal{\ALG@within}{subsection}} + {\newfloat{algorithm}{htbp}{loa}[subsection]}{} + \ifthenelse{\equal{\ALG@within}{subsubsection}} + {\newfloat{algorithm}{htbp}{loa}[subsubsection]}{} + \ifthenelse{\equal{\ALG@within}{nothing}} + {\newfloat{algorithm}{htbp}{loa}}{} +}{ + \newfloat{algorithm}{htbp}{loa} +} +\floatname{algorithm}{\ALG@name} + +\newcommand{\listofalgorithms}{\listof{algorithm}{\listalgorithmname}} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/algorithmic.sty b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/algorithmic.sty new file mode 100644 index 0000000..4dcaa7c --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/algorithmic.sty @@ -0,0 +1,194 @@ +% ALGORITHMIC STYLE for LaTeX version 2e +% +% This style file is free software; you can redistribute it and/or +% modify it under the terms of the GNU Lesser General Public +% License as published by the Free Software Foundation; either +% version 2 of the License, or (at your option) any later version. +% +% This style file is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +% Lesser General Public License for more details. +% +% You should have received a copy of the GNU Lesser General Public +% License along with this style file; if not, write to the +% Free Software Foundation, Inc., 59 Temple Place - Suite 330, +% Boston, MA 02111-1307, USA. +% +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{algorithmic}[2006/06/02] +\typeout{Document Style `algorithmic' - environment} +% +\RequirePackage{ifthen} +\RequirePackage{calc} +\RequirePackage{keyval} +\newboolean{ALC@noend} +\setboolean{ALC@noend}{false} +\newcounter{ALC@line} +\newcounter{ALC@rem} +\newcounter{ALC@depth} +\newlength{\ALC@tlm} +% +\DeclareOption{noend}{\setboolean{ALC@noend}{true}} +% +\ProcessOptions +% +% For keyval-style options +\def\algsetup{\setkeys{ALG}} +% +% For indentation of algorithms +\newlength{\algorithmicindent} +\setlength{\algorithmicindent}{0pt} +\define@key{ALG}{indent}{\setlength{\algorithmicindent}{#1}} +\ifthenelse{\lengthtest{\algorithmicindent=0pt}}% + {\setlength{\algorithmicindent}{1em}}{} +% +% For line numbers' delimiters +\newcommand{\ALC@linenodelimiter}{:} +\define@key{ALG}{linenodelimiter}{\renewcommand{\ALC@linenodelimiter}{#1}} + +% +% For line numbers' size +\newcommand{\ALC@linenosize}{\footnotesize} +\define@key{ALG}{linenosize}{\renewcommand{\ALC@linenosize}{#1}} + +% +% ALGORITHMIC +\newcommand{\algorithmicrequire}{\textbf{Require:}} +\newcommand{\algorithmicensure}{\textbf{Ensure:}} +\newcommand{\algorithmicparams}[1]{\textcolor{RawSienna}{\textbf{Entrada:}} #1} +\newcommand{\algorithmiccomment}[1]{\textcolor{Purple}{\{#1\}}} +\newcommand{\algorithmicend}{\textbf{end}} +\newcommand{\algorithmicif}{\textbf{if}} +\newcommand{\algorithmicthen}{\textbf{then}} +\newcommand{\algorithmicelse}{\textbf{else}} +\newcommand{\algorithmicelsif}{\algorithmicelse\ \algorithmicif} +\newcommand{\algorithmicendif}{\algorithmicend\ \algorithmicif} +\newcommand{\algorithmicfor}{\textbf{for}} +\newcommand{\algorithmicforall}{\textbf{for all}} +\newcommand{\algorithmicdo}{\textbf{do}} +\newcommand{\algorithmicendfor}{\algorithmicend\ \algorithmicfor} +\newcommand{\algorithmicwhile}{\textbf{while}} +\newcommand{\algorithmicendwhile}{\algorithmicend\ \algorithmicwhile} +\newcommand{\algorithmicloop}{\textbf{loop}} +\newcommand{\algorithmicendloop}{\algorithmicend\ \algorithmicloop} +\newcommand{\algorithmicrepeat}{\textbf{repeat}} +\newcommand{\algorithmicuntil}{\textbf{until}} +\newcommand{\algorithmicprint}{\textbf{print}} +\newcommand{\algorithmicreturn}{\textbf{return}} +\newcommand{\algorithmictrue}{\textbf{true}} +\newcommand{\algorithmicfalse}{\textbf{false}} +\def\ALC@setref{% + \def\@currentlabel{\theALC@line}% +} +\def\ALC@item[#1]{% +\if@noparitem \@donoparitem + \else \if@inlabel \indent \par \fi + \ifhmode \unskip\unskip \par \fi + \if@newlist \if@nobreak \@nbitem \else + \addpenalty\@beginparpenalty + \addvspace\@topsep \addvspace{-\parskip}\fi + \else \addpenalty\@itempenalty \addvspace\itemsep + \fi + \global\@inlabeltrue +\fi +\everypar{\global\@minipagefalse\global\@newlistfalse + \if@inlabel\global\@inlabelfalse \hskip -\parindent \box\@labels + \penalty\z@ \fi + \everypar{}}\global\@nobreakfalse +\if@noitemarg \@noitemargfalse \if@nmbrlist \refstepcounter{\@listctr}\fi \fi +\sbox\@tempboxa{\makelabel{#1}}% +\global\setbox\@labels + \hbox{\unhbox\@labels \hskip \itemindent + \hskip -\labelwidth \hskip -\ALC@tlm + \ifdim \wd\@tempboxa >\labelwidth + \box\@tempboxa + \else \hbox to\labelwidth {\unhbox\@tempboxa}\fi + \hskip \ALC@tlm}\ignorespaces} +% +\newenvironment{algorithmic}[1][0]{ +\setcounter{ALC@depth}{\@listdepth}% +\let\@listdepth\c@ALC@depth% +\let\@item\ALC@item% + \newcommand{\ALC@lno}{% +\ifthenelse{\equal{\arabic{ALC@rem}}{0}} +{{\ALC@linenosize \arabic{ALC@line}\ALC@linenodelimiter}}{}% +} +\let\@listii\@listi +\let\@listiii\@listi +\let\@listiv\@listi +\let\@listv\@listi +\let\@listvi\@listi +\let\@listvii\@listi + \newenvironment{ALC@g}{ + \begin{list}{\ALC@lno}{ \itemsep\z@ \itemindent\z@ + \listparindent\z@ \rightmargin\z@ + \topsep\z@ \partopsep\z@ \parskip\z@\parsep\z@ + \leftmargin \algorithmicindent%1em + \addtolength{\ALC@tlm}{\leftmargin} + } + } + {\end{list}} + \newcommand{\ALC@it}{\refstepcounter{ALC@rem}\refstepcounter{ALC@line}\ifthenelse{\equal{\arabic{ALC@rem}}{#1}}{\setcounter{ALC@rem}{0}}{}\item\ALC@setref} + \newcommand{\ALC@com}[1]{\ifthenelse{\equal{##1}{default}}% +{}{\ \algorithmiccomment{##1}}} + \newcommand{\REQUIRE}{\item[\algorithmicrequire]} + \newcommand{\ENSURE}{\item[\algorithmicensure]} + \newcommand{\PRINT}{\ALC@it\algorithmicprint{}\ \ } + \newcommand{\RETURN}{\ALC@it\algorithmicreturn{}\ \ } + \newcommand{\TRUE}{\algorithmictrue{}} + \newcommand{\FALSE}{\algorithmicfalse{}} + \newcommand{\STATE}{\ALC@it} + \newcommand{\STMT}{\ALC@it} + \newcommand{\PARAMS}[1]{\item[\algorithmicparams{##1}]} + \newcommand{\COMMENT}[1]{\algorithmiccomment{##1}} + \newenvironment{ALC@if}{\begin{ALC@g}}{\end{ALC@g}} + \newenvironment{ALC@for}{\begin{ALC@g}}{\end{ALC@g}} + \newenvironment{ALC@whl}{\begin{ALC@g}}{\end{ALC@g}} + \newenvironment{ALC@loop}{\begin{ALC@g}}{\end{ALC@g}} + \newenvironment{ALC@rpt}{\begin{ALC@g}}{\end{ALC@g}} + \renewcommand{\\}{\@centercr} + \newcommand{\IF}[2][default]{\ALC@it\algorithmicif\ ##2\ \algorithmicthen% +\ALC@com{##1}\begin{ALC@if}} + \newcommand{\ELSE}[1][default]{\end{ALC@if}\ALC@it\algorithmicelse% +\ALC@com{##1}\begin{ALC@if}} + \newcommand{\ELSIF}[2][default]% +{\end{ALC@if}\ALC@it\algorithmicelsif\ ##2\ \algorithmicthen% +\ALC@com{##1}\begin{ALC@if}} + \newcommand{\FOR}[2][default]{\ALC@it\algorithmicfor\ ##2\ \algorithmicdo% +\ALC@com{##1}\begin{ALC@for}} + \newcommand{\FORALL}[2][default]{\ALC@it\algorithmicforall\ ##2\ % +\algorithmicdo% +\ALC@com{##1}\begin{ALC@for}} + \newcommand{\WHILE}[2][default]{\ALC@it\algorithmicwhile\ ##2\ % +\algorithmicdo% +\ALC@com{##1}\begin{ALC@whl}} + \newcommand{\LOOP}[1][default]{\ALC@it\algorithmicloop% +\ALC@com{##1}\begin{ALC@loop}} + \newcommand{\REPEAT}[1][default]{\ALC@it\algorithmicrepeat% +\ALC@com{##1}\begin{ALC@rpt}} + \newcommand{\UNTIL}[1]{\end{ALC@rpt}\ALC@it\algorithmicuntil\ ##1} + \ifthenelse{\boolean{ALC@noend}}{ + \newcommand{\ENDIF}{\end{ALC@if}} + \newcommand{\ENDFOR}{\end{ALC@for}} + \newcommand{\ENDWHILE}{\end{ALC@whl}} + \newcommand{\ENDLOOP}{\end{ALC@loop}} + }{ + \newcommand{\ENDIF}{\end{ALC@if}\ALC@it\algorithmicendif} + \newcommand{\ENDFOR}{\end{ALC@for}\ALC@it\algorithmicendfor} + \newcommand{\ENDWHILE}{\end{ALC@whl}\ALC@it\algorithmicendwhile} + \newcommand{\ENDLOOP}{\end{ALC@loop}\ALC@it\algorithmicendloop} + } + \renewcommand{\@toodeep}{} + \begin{list}{\ALC@lno}{\setcounter{ALC@rem}{0}\setcounter{ALC@line}{0}% + \itemsep\z@ \itemindent\z@ \listparindent\z@% + \partopsep\z@ \parskip\z@ \parsep\z@% + \labelsep 0.5em \topsep 0.2em% +\ifthenelse{\equal{#1}{0}} + {\labelwidth 0.5em } + {\labelwidth 1.2em } +\leftmargin\labelwidth \addtolength{\leftmargin}{\labelsep} + \ALC@tlm\labelsep + } +} +{\end{list}} diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/ballroom.tex b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/ballroom.tex new file mode 100644 index 0000000..7e8cb4b --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/ballroom.tex @@ -0,0 +1,376 @@ +\section{3928 - Ballroom Lights} +\textbf{Problema:} +Dada una vista superior de una habitaci'on rectangular en la que hay una serie de +luces (fuentes puntuales de luz) y de columnas (cilindros), determinar la porci'on +del per'imetro de la habitaci'on que se encuentra iluminada por las luces. + +\subsection{Resoluci\'on} + +La soluci'on del problema consiste en calcular los efectos individuales de cada +luz sobre cada columna considerando una 'unica pared, y luego combinarlos de manera +de obtener el resultado total. Para esto, se considera en primer lugar como se +resuelve el caso particular conociendo la ubicaci'on de ambas dentro de la habitaci'on, las +dimensiones de la misma y el radio de la columna. + +\begin{figure}[H] +\centering +\includegraphics[width=12cm]{./figuras/ballroom.png} +\caption{Esquema del caso particular (1 columna, 1 luz, 1 pared)} +\end{figure} + +Esta situaci'on se resuelve con trigonometr'ia simple: conociendo el radio de la +columna ($|I_{1}C|$) y la distancia entre la luz y el centro de la misma ($|LC|$), +podemos calcular el 'angulo $a$: + +$$a = sin^{-1}\frac{|I_{1}C|}{|LC|}$$ + +Con el 'angulo $a$ resulta sencillo construir las intersecciones con la pared posterior. +Es importante tener en cuenta el caso en que dicha intersecci'on no existe (estamos +tratando con una semirecta de origen $L$), o se encuentra fuera del segmento que +corresponde a la pared. + +Finalmente, se calcula el largo del segmento oscurecido por la columna que cae dentro +de la pared. Con este dato, el algoritmo completo es el siguiente: + +\begin{algorithm}[H] +\begin{algorithmic} +\caption{Calcular la longitud del perímetro iluminado} +\FOR{cada pared} + \FOR{cada luz} + \FOR{cada columna} + \STATE obtener la zona oscurecida de esta terna + \ENDFOR + \STATE unir todas las sombras de esta luz + \STATE invertir las sombras para obtener las zonas iluminadas de esta luz + \ENDFOR + \STATE unir todas las zonas iluminadas por cada luz + \STATE calcular la longitud iluminada en esta pared +\ENDFOR +\STATE devolver la suma de las longitudes iluminadas sobre cada pared +\end{algorithmic} +\end{algorithm} + +\subsubsection{Implementaci'on} + +La implementaci'on no tiene mayores particularidades. Nos encontramos con +un problema de error num'erico producto de la utilización valores obtenidos +con las funciones trigonom'etricas. Lo resolvimos utilizando \textbf{long double} +para aumentar la precisi'on de las operaciones. + +Muchos de los datos utilizados en el programa son conjuntos de intervalos +que representan una porci'on (eventualmente discontinua) de los segmentos +que corresponden a las paredes. Estos conjuntos se implementaron sobre secuencias. + + +\subsubsection{Complejidad} + +Llamaremos $C$ a la cantidad de columnas y $L$ a la cantidad de luces. + +Las operaciones utilizadas por el algoritmo son: +\begin{itemize} +\item \textbf{B'usqueda de puntos de intersecci'on}, que se hace en tiempo constante en el modelo uniforme. +\item \textbf{Uni'on de conjuntos de intervalos}, que se hace en $O(n log(n))$ orden'andolos primero. +\item \textbf{Inversi'on de conjuntos de intervalos}, que se hace en $O(n)$ puesto que ya est'an ordenados. +\item \textbf{C'alculo de la longitud cubierta por el conjunto}, que se hace en $O(n)$ puesto que ya est'an ordenados. +\end{itemize} + +Sabemos adem'as que cada columna tiene a lo sumo una sombra sobre cada pared. Por lo tanto, +unir todas las sombras de una luz se hace en $O(C log(C))$. En peor caso, el conjunto +resultante tiene $C$ elementos, lo que corresponde al caso en que todas las sombras +de las columnas son disjuntas. + +La inversi'on se hace entonces en $O(C)$. Para los 'ultimos pasos del ciclo sobre las luces, +se unen las sombras de cada una de ellas. Dado que en peor caso tenemos $L * C$ intervalos +a unir, la uni'on resulta en un costo de $O(LC log(LC))$, seguido del c'alculo de la +longitud en tiempo lineal con un costo de $O(LC)$ dado que tras la uni'on el conjunto +de intervalos se encuentra ordenado. + +Estas operaciones se hacen para cada pared, con un total de 4 que no afecta la complejidad +puesto que es constante. Finalmente, el algoritmo tiene un costo de $O(LC log(LC))$, que es +polinomial en el tama~no de la entrada puesto que la misma tiene tama\~no $O(L+C+t)$ (con +$t=log_2(max(ancho, alto))$). + +\subsection{Implementación} + +\noindent +\ttfamily +\shorthandoff{"}\\ +\hlstd{}\hlline{\ 1\ }\hldir{\#include\ $<$iostream$>$}\\ +\hlline{\ 2\ }\hlstd{}\hldir{\#include\ $<$cmath$>$}\\ +\hlline{\ 3\ }\hlstd{}\hldir{\#include\ $<$cstdio$>$}\\ +\hlline{\ 4\ }\hlstd{}\hldir{\#include\ $<$list$>$}\\ +\hlline{\ 5\ }\hlstd{}\hldir{\#include\ $<$utility$>$}\\ +\hlline{\ 6\ }\hlstd{}\hldir{\#include\ $<$cstdlib$>$}\\ +\hlline{\ 7\ }\hlstd{}\hldir{\#include\ $<$cassert$>$}\\ +\hlline{\ 8\ }\hlstd{}\hldir{\#include\ $<$complex$>$}\\ +\hlline{\ 9\ }\hlstd{}\\ +\hlline{10\ }\hldir{\#define\ forn(i,\ n)\ for\ (int\ i\ =\ 0;\ i\ $<$\ (n);\ i++)}\\ +\hlline{11\ }\hlstd{}\hldir{\#define\ TOLERANCIA\ 1e{-}8}\\ +\hlline{12\ }\hlstd{}\\ +\hlline{13\ }\hlkwa{using\ namespace\ }\hlstd{std}\hlsym{;}\\ +\hlline{14\ }\hlstd{}\\ +\hlline{15\ }\hlkwb{struct\ }\hlstd{MaybeDouble\ }\hlsym{\{}\\ +\hlline{16\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{long\ double\ }\hlstd{valor}\hlsym{;}\\ +\hlline{17\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{bool\ }\hlstd{valido}\hlsym{;}\\ +\hlline{18\ }\hlstd{\\ +\hlline{19\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{MaybeDouble}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{long\ double\ }\hlstd{v}\hlsym{,\ }\hlstd{}\hlkwb{bool\ }\hlstd{b}\hlsym{):\ }\hlstd{}\hlkwd{valor}\hlstd{}\hlsym{(}\hlstd{v}\hlsym{),\ }\hlstd{}\hlkwd{valido}\hlstd{}\hlsym{(}\hlstd{b}\hlsym{)\ \{\};}\\ +\hlline{20\ }\hlstd{}\hlsym{\};}\\ +\hlline{21\ }\hlstd{}\\ +\hlline{22\ }\hlkwb{struct\ }\hlstd{Vector\ }\hlsym{\{}\\ +\hlline{23\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{long\ double\ }\hlstd{x}\hlsym{;}\\ +\hlline{24\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{long\ double\ }\hlstd{y}\hlsym{;}\\ +\hlline{25\ }\hlstd{\\ +\hlline{26\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{Vector}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{long\ double\ }\hlstd{xi}\hlsym{,\ }\hlstd{}\hlkwb{long\ double\ }\hlstd{yi}\hlsym{):\ }\hlstd{}\hlkwd{x}\hlstd{}\hlsym{(}\hlstd{xi}\hlsym{),\ }\hlstd{}\hlkwd{y}\hlstd{}\hlsym{(}\hlstd{yi}\hlsym{)\ \{\};}\\ +\hlline{27\ }\hlstd{\\ +\hlline{28\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{long\ double\ }\hlstd{}\hlkwd{norma}\hlstd{}\hlsym{()}\hlstd{\ \ }\hlsym{\{}\\ +\hlline{29\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{}\hlkwd{hypot}\hlstd{}\hlsym{(}\hlstd{x}\hlsym{,\ }\hlstd{y}\hlsym{);}\\ +\hlline{30\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{31\ }\hlstd{\\ +\hlline{32\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{long\ double\ }\hlstd{}\hlkwd{angulo}\hlstd{}\hlsym{()\ \{}\\ +\hlline{33\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{}\hlkwd{atan2}\hlstd{}\hlsym{(}\hlstd{y}\hlsym{,\ }\hlstd{x}\hlsym{);}\\ +\hlline{34\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{35\ }\hlstd{}\\ +\hlline{36\ }\hlsym{\};}\\ +\hlline{37\ }\hlstd{}\\ +\hlline{38\ }\hlkwb{struct\ }\hlstd{Columna\ }\hlsym{\{}\\ +\hlline{39\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{Vector\ posicion}\hlsym{;}\\ +\hlline{40\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{long\ double\ }\hlstd{radio}\hlsym{;}\\ +\hlline{41\ }\hlstd{\\ +\hlline{42\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{Columna}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{long\ double\ }\hlstd{x}\hlsym{,\ }\hlstd{}\hlkwb{long\ double\ }\hlstd{y}\hlsym{,\ }\hlstd{}\hlkwb{long\ double\ }\hlstd{r}\hlsym{)\ :\ }\hlstd{}\hlkwd{posicion}\hlstd{}\hlsym{(}\hlstd{x}\hlsym{,}\hlstd{y}\hlsym{),\ }\hlstd{}\hlkwd{radio}\hlstd{}\hlsym{(}\hlstd{r}\hlsym{)\ \{\};}\\ +\hlline{43\ }\hlstd{}\hlsym{\};}\\ +\hlline{44\ }\hlstd{}\\ +\hlline{45\ }\hlkwc{typedef\ }\hlstd{Vector\ Lampara}\hlsym{;}\\ +\hlline{46\ }\hlstd{}\hlkwc{typedef\ }\hlstd{pair}\hlsym{$<$}\hlstd{}\hlkwb{long\ double}\hlstd{}\hlsym{,\ }\hlstd{}\hlkwb{long\ double}\hlstd{}\hlsym{$>$\ }\hlstd{Intervalo}\hlsym{;}\\ +\hlline{47\ }\hlstd{}\hlkwc{typedef\ }\hlstd{pair}\hlsym{$<$}\hlstd{Vector}\hlsym{,\ }\hlstd{Vector}\hlsym{$>$\ }\hlstd{Segmento}\hlsym{;}\\ +\hlline{48\ }\hlstd{}\\ +\hlline{49\ }\\ +\hlline{50\ }\hlkwc{inline\ }\hlstd{}\hlkwb{long\ double\ }\hlstd{}\hlkwd{largo}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ }\hlstd{Segmento}\hlsym{\&\ }\hlstd{s}\hlsym{)\ \{}\\ +\hlline{51\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{}\hlkwd{Vector}\hlstd{}\hlsym{(}\hlstd{s}\hlsym{.}\hlstd{second}\hlsym{.}\hlstd{x\ }\hlsym{{-}\ }\hlstd{s}\hlsym{.}\hlstd{first}\hlsym{.}\hlstd{x}\hlsym{,\ }\hlstd{s}\hlsym{.}\hlstd{second}\hlsym{.}\hlstd{y\ }\hlsym{{-}\ }\hlstd{s}\hlsym{.}\hlstd{first}\hlsym{.}\hlstd{y}\hlsym{).}\hlstd{}\hlkwd{norma}\hlstd{}\hlsym{();}\\ +\hlline{52\ }\hlstd{}\hlsym{\}}\\ +\hlline{53\ }\hlstd{}\\ +\hlline{54\ }\hlkwc{inline\ }\hlstd{}\hlkwb{long\ double\ }\hlstd{}\hlkwd{largo}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ }\hlstd{Intervalo}\hlsym{\&\ }\hlstd{i}\hlsym{)\ \{}\\ +\hlline{55\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{assert}\hlstd{}\hlsym{(}\hlstd{i}\hlsym{.}\hlstd{first\ }\hlsym{$<$=\ }\hlstd{i}\hlsym{.}\hlstd{second}\hlsym{);}\\ +\hlline{56\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{i}\hlsym{.}\hlstd{second\ }\hlsym{{-}\ }\hlstd{i}\hlsym{.}\hlstd{first}\hlsym{;}\\ +\hlline{57\ }\hlstd{}\hlsym{\}}\\ +\hlline{58\ }\hlstd{\\ +\hlline{59\ }\\ +\hlline{60\ }MaybeDouble\ }\hlkwd{intersect\textunderscore segments}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ }\hlstd{Segmento}\hlsym{\&\ }\hlstd{s1}\hlsym{,\ }\hlstd{}\hlkwb{const\ }\hlstd{Segmento}\hlsym{\&\ }\hlstd{s2}\hlsym{)\ \{}\\ +\hlline{61\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{Vector\ p1\ }\hlsym{=\ }\hlstd{s1}\hlsym{.}\hlstd{first}\hlsym{;}\\ +\hlline{62\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{Vector\ p2\ }\hlsym{=\ }\hlstd{s1}\hlsym{.}\hlstd{second}\hlsym{;}\\ +\hlline{63\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{Vector\ p3\ }\hlsym{=\ }\hlstd{s2}\hlsym{.}\hlstd{first}\hlsym{;}\\ +\hlline{64\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{Vector\ p4\ }\hlsym{=\ }\hlstd{s2}\hlsym{.}\hlstd{second}\hlsym{;}\\ +\hlline{65\ }\hlstd{\\ +\hlline{66\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{long\ double\ }\hlstd{den\ }\hlsym{=\ (}\hlstd{p4}\hlsym{.}\hlstd{y}\hlsym{{-}}\hlstd{p3}\hlsym{.}\hlstd{y}\hlsym{){*}(}\hlstd{p2}\hlsym{.}\hlstd{x}\hlsym{{-}}\hlstd{p1}\hlsym{.}\hlstd{x}\hlsym{)\ {-}\ (}\hlstd{p4}\hlsym{.}\hlstd{x}\hlsym{{-}}\hlstd{p3}\hlsym{.}\hlstd{x}\hlsym{){*}(}\hlstd{p2}\hlsym{.}\hlstd{y}\hlsym{{-}}\hlstd{p1}\hlsym{.}\hlstd{y}\hlsym{);}\\ +\hlline{67\ }\hlstd{\\ +\hlline{68\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{long\ double\ }\hlstd{ua\textunderscore num\ }\hlsym{=\ (}\hlstd{p4}\hlsym{.}\hlstd{x}\hlsym{{-}}\hlstd{p3}\hlsym{.}\hlstd{x}\hlsym{){*}(}\hlstd{p1}\hlsym{.}\hlstd{y}\hlsym{{-}}\hlstd{p3}\hlsym{.}\hlstd{y}\hlsym{)\ {-}\ (}\hlstd{p4}\hlsym{.}\hlstd{y}\hlsym{{-}}\hlstd{p3}\hlsym{.}\hlstd{y}\hlsym{){*}(}\hlstd{p1}\hlsym{.}\hlstd{x}\hlsym{{-}}\hlstd{p3}\hlsym{.}\hlstd{x}\hlsym{);}\\ +\hlline{69\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{long\ double\ }\hlstd{ub\textunderscore num\ }\hlsym{=\ (}\hlstd{p2}\hlsym{.}\hlstd{x}\hlsym{{-}}\hlstd{p1}\hlsym{.}\hlstd{x}\hlsym{){*}(}\hlstd{p1}\hlsym{.}\hlstd{y}\hlsym{{-}}\hlstd{p3}\hlsym{.}\hlstd{y}\hlsym{)\ {-}\ (}\hlstd{p2}\hlsym{.}\hlstd{y}\hlsym{{-}}\hlstd{p1}\hlsym{.}\hlstd{y}\hlsym{){*}(}\hlstd{p1}\hlsym{.}\hlstd{x}\hlsym{{-}}\hlstd{p3}\hlsym{.}\hlstd{x}\hlsym{);}\\ +\hlline{70\ }\hlstd{\\ +\hlline{71\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwd{fabs}\hlstd{}\hlsym{(}\hlstd{den}\hlsym{)\ $<$\ }\hlstd{TOLERANCIA}\hlsym{)\ \{}\\ +\hlline{72\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlslc{//\ Caso\ en\ que\ los\ segmentos\ son\ paralelos}\\ +\hlline{73\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwd{fabs}\hlstd{}\hlsym{(}\hlstd{ua\textunderscore num\ }\hlsym{{-}\ }\hlstd{ub\textunderscore num}\hlsym{)\ $<$\ }\hlstd{TOLERANCIA\ }\hlsym{\&\&\ }\hlstd{}\hlkwd{fabs}\hlstd{}\hlsym{(}\hlstd{ub\textunderscore num}\hlsym{)\ $<$\ }\hlstd{TOLERANCIA}\hlsym{)\ \{}\\ +\hlline{74\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlslc{//\ Las\ rectas\ son\ coincidentes,\ esto\ no\ deberia\ ocurrir}\\ +\hlline{75\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{assert}\hlstd{}\hlsym{(}\hlstd{}\hlkwa{false}\hlstd{}\hlsym{);}\\ +\hlline{76\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{}\hlkwd{MaybeDouble}\hlstd{}\hlsym{((}\hlstd{p1}\hlsym{.}\hlstd{}\hlkwd{norma}\hlstd{}\hlsym{()\ $>$\ }\hlstd{p2}\hlsym{.}\hlstd{}\hlkwd{norma}\hlstd{}\hlsym{()}\hlstd{?\ }\hlnum{0\ }\hlstd{}\hlsym{:\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{),\ }\hlstd{}\hlkwa{true}\hlstd{}\hlsym{);}\\ +\hlline{77\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{78\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{}\hlkwd{MaybeDouble}\hlstd{}\hlsym{(}\hlstd{}\hlnum{0}\hlstd{}\hlsym{,\ }\hlstd{}\hlkwa{false}\hlstd{}\hlsym{);}\\ +\hlline{79\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{80\ }\hlstd{\\ +\hlline{81\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{ub\textunderscore num}\hlsym{/}\hlstd{den\ }\hlsym{$>$=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ \{}\\ +\hlline{82\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{}\hlkwd{MaybeDouble}\hlstd{}\hlsym{(}\hlstd{ua\textunderscore num}\hlsym{/}\hlstd{den}\hlsym{,\ }\hlstd{}\hlkwa{true}\hlstd{}\hlsym{);}\\ +\hlline{83\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{84\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{}\hlkwd{MaybeDouble}\hlstd{}\hlsym{(}\hlstd{}\hlnum{0}\hlstd{}\hlsym{,\ }\hlstd{}\hlkwa{false}\hlstd{}\hlsym{);}\\ +\hlline{85\ }\hlstd{}\hlsym{\}}\\ +\hlline{86\ }\hlstd{\\ +\hlline{87\ }\\ +\hlline{88\ }Intervalo\ }\hlkwd{interseccion\textunderscore intervalos}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ }\hlstd{Intervalo}\hlsym{\&\ }\hlstd{i1}\hlsym{,\ }\hlstd{}\hlkwb{const\ }\hlstd{Intervalo}\hlsym{\&\ }\hlstd{i2}\hlsym{)\ \{}\\ +\hlline{89\ }\hlstd{\\ +\hlline{90\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{long\ double\ }\hlstd{d0\ }\hlsym{=\ }\hlstd{}\hlkwd{max}\hlstd{}\hlsym{(}\hlstd{i1}\hlsym{.}\hlstd{first}\hlsym{,\ }\hlstd{i2}\hlsym{.}\hlstd{first}\hlsym{);}\\ +\hlline{91\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{long\ double\ }\hlstd{d1\ }\hlsym{=\ }\hlstd{}\hlkwd{min}\hlstd{}\hlsym{(}\hlstd{i1}\hlsym{.}\hlstd{second}\hlsym{,\ }\hlstd{i2}\hlsym{.}\hlstd{second}\hlsym{);}\\ +\hlline{92\ }\hlstd{\\ +\hlline{93\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{d1\ }\hlsym{$<$\ }\hlstd{d0}\hlsym{)\ \{}\\ +\hlline{94\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{}\hlkwd{Intervalo}\hlstd{}\hlsym{(}\hlstd{}\hlnum{0}\hlstd{}\hlsym{,\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{);}\\ +\hlline{95\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}\ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{96\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{}\hlkwd{Intervalo}\hlstd{}\hlsym{(}\hlstd{d0}\hlsym{,\ }\hlstd{d1}\hlsym{);}\\ +\hlline{97\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{98\ }\hlstd{}\hlsym{\}}\\ +\hlline{99\ }\hlstd{\\ +\hlline{100\ }\\ +\hlline{101\ }Intervalo\ }\hlkwd{rango\textunderscore oscurecido}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ }\hlstd{Segmento}\hlsym{\&\ }\hlstd{pared}\hlsym{,\ }\hlstd{}\hlkwb{const\ }\hlstd{Lampara}\hlsym{\&\ }\hlstd{lampara}\hlsym{,\ }\hlstd{}\hlkwb{const\ }\hlstd{Columna}\hlsym{\&\ }\hlstd{columna}\hlsym{)\ \{}\\ +\hlline{102\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{Vector\ }\hlkwd{bisectriz}\hlstd{}\hlsym{(}\hlstd{columna}\hlsym{.}\hlstd{posicion}\hlsym{.}\hlstd{x\ }\hlsym{{-}\ }\hlstd{lampara}\hlsym{.}\hlstd{x}\hlsym{,\ }\hlstd{columna}\hlsym{.}\hlstd{posicion}\hlsym{.}\hlstd{y\ }\hlsym{{-}\ }\hlstd{lampara}\hlsym{.}\hlstd{y}\hlsym{);}\\ +\hlline{103\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{long\ double\ }\hlstd{p\ }\hlsym{=\ }\hlstd{}\hlkwd{asin}\hlstd{}\hlsym{(}\hlstd{columna}\hlsym{.}\hlstd{radio}\hlsym{/}\hlstd{bisectriz}\hlsym{.}\hlstd{}\hlkwd{norma}\hlstd{}\hlsym{());}\\ +\hlline{104\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{long\ double\ }\hlstd{alpha\ }\hlsym{=\ }\hlstd{bisectriz}\hlsym{.}\hlstd{}\hlkwd{angulo}\hlstd{}\hlsym{();}\\ +\hlline{105\ }\hlstd{\\ +\hlline{106\ }}\hlstd{\ \ \ \ }\hlstd{Vector\ }\hlkwd{d1}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{cos}\hlstd{}\hlsym{(}\hlstd{alpha\ }\hlsym{+\ }\hlstd{p}\hlsym{),\ }\hlstd{}\hlkwd{sin}\hlstd{}\hlsym{(}\hlstd{alpha\ }\hlsym{+\ }\hlstd{p}\hlsym{));}\\ +\hlline{107\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{Vector\ }\hlkwd{d2}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{cos}\hlstd{}\hlsym{(}\hlstd{alpha\ }\hlsym{{-}\ }\hlstd{p}\hlsym{),\ }\hlstd{}\hlkwd{sin}\hlstd{}\hlsym{(}\hlstd{alpha\ }\hlsym{{-}\ }\hlstd{p}\hlsym{));}\\ +\hlline{108\ }\hlstd{\\ +\hlline{109\ }}\hlstd{\ \ \ \ }\hlstd{MaybeDouble\ p1\ }\hlsym{=\ }\hlstd{}\hlkwd{intersect\textunderscore segments}\hlstd{}\hlsym{(}\hlstd{pared}\hlsym{,\ }\hlstd{}\hlkwd{Segmento}\hlstd{}\hlsym{(}\hlstd{lampara}\hlsym{,\ }\hlstd{}\hlkwd{Vector}\hlstd{}\hlsym{(}\hlstd{lampara}\hlsym{.}\hlstd{x\ }\hlsym{+\ }\hlstd{d1}\hlsym{.}\hlstd{x}\hlsym{,\ }\hlstd{lampara}\hlsym{.}\hlstd{y\ }\hlsym{+}\Righttorque\\ +\hlline{110\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{d1}\hlsym{.}\hlstd{y}\hlsym{)));}\\ +\hlline{111\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{MaybeDouble\ p2\ }\hlsym{=\ }\hlstd{}\hlkwd{intersect\textunderscore segments}\hlstd{}\hlsym{(}\hlstd{pared}\hlsym{,\ }\hlstd{}\hlkwd{Segmento}\hlstd{}\hlsym{(}\hlstd{lampara}\hlsym{,\ }\hlstd{}\hlkwd{Vector}\hlstd{}\hlsym{(}\hlstd{lampara}\hlsym{.}\hlstd{x\ }\hlsym{+\ }\hlstd{d2}\hlsym{.}\hlstd{x}\hlsym{,\ }\hlstd{lampara}\hlsym{.}\hlstd{y\ }\hlsym{+}\Righttorque\\ +\hlline{112\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{d2}\hlsym{.}\hlstd{y}\hlsym{)));}\\ +\hlline{113\ }\hlstd{\\ +\hlline{114\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{long\ double\ }\hlstd{unidad\ }\hlsym{=\ }\hlstd{}\hlkwd{largo}\hlstd{}\hlsym{(}\hlstd{pared}\hlsym{);}\\ +\hlline{115\ }\hlstd{\\ +\hlline{116\ }}\hlstd{\ \ \ \ }\hlstd{}\hlslc{//\ Se\ sabe\ que\ los\ puntos\ de\ interseccion\ estan\ ordenados\ correctamente}\\ +\hlline{117\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlslc{//\ porque\ el\ angulo\ de\ diferencia\ entre\ las\ semirectas\ es\ menor\ a\ 180,}\\ +\hlline{118\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlslc{//\ entonces\ no\ es\ necesario\ chequearlo.}\\ +\hlline{119\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{Intervalo\ res}\hlsym{;}\\ +\hlline{120\ }\hlstd{\\ +\hlline{121\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(!}\hlstd{p1}\hlsym{.}\hlstd{valido}\hlsym{)\ \{}\\ +\hlline{122\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(!}\hlstd{p2}\hlsym{.}\hlstd{valido}\hlsym{)\ \{}\\ +\hlline{123\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{}\hlkwd{Intervalo}\hlstd{}\hlsym{(}\hlstd{}\hlnum{0}\hlstd{}\hlsym{,\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{);}\\ +\hlline{124\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}\ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{125\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{res\ }\hlsym{=\ }\hlstd{}\hlkwd{Intervalo}\hlstd{}\hlsym{(}\hlstd{}\hlnum{0}\hlstd{}\hlsym{,\ }\hlstd{p2}\hlsym{.}\hlstd{valor}\hlsym{);}\\ +\hlline{126\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{127\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}\ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{128\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(!}\hlstd{p2}\hlsym{.}\hlstd{valido}\hlsym{)\ \{}\\ +\hlline{129\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{res\ }\hlsym{=\ }\hlstd{}\hlkwd{Intervalo}\hlstd{}\hlsym{(}\hlstd{p1}\hlsym{.}\hlstd{valor}\hlsym{,\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{);}\\ +\hlline{130\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}\ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{131\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{res\ }\hlsym{=\ }\hlstd{}\hlkwd{Intervalo}\hlstd{}\hlsym{(}\hlstd{p1}\hlsym{.}\hlstd{valor}\hlsym{,\ }\hlstd{p2}\hlsym{.}\hlstd{valor}\hlsym{);}\\ +\hlline{132\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{133\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{134\ }\hlstd{\\ +\hlline{135\ }}\hlstd{\ \ \ \ }\hlstd{res\ }\hlsym{=\ }\hlstd{}\hlkwd{interseccion\textunderscore intervalos}\hlstd{}\hlsym{(}\hlstd{res}\hlsym{,\ }\hlstd{}\hlkwd{Intervalo}\hlstd{}\hlsym{(}\hlstd{}\hlnum{0}\hlstd{}\hlsym{,}\hlstd{}\hlnum{1}\hlstd{}\hlsym{));}\\ +\hlline{136\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{}\hlkwd{Intervalo}\hlstd{}\hlsym{(}\hlstd{res}\hlsym{.}\hlstd{first\ }\hlsym{{*}\ }\hlstd{unidad}\hlsym{,\ }\hlstd{res}\hlsym{.}\hlstd{second\ }\hlsym{{*}\ }\hlstd{unidad}\hlsym{);}\\ +\hlline{137\ }\hlstd{}\hlsym{\}}\\ +\hlline{138\ }\hlstd{}\\ +\hlline{139\ }\hlkwb{void\ }\hlstd{}\hlkwd{invertir\textunderscore rango}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ }\hlstd{list}\hlsym{$<$}\hlstd{Intervalo}\hlsym{$>$\&\ }\hlstd{ints}\hlsym{,\ }\hlstd{}\hlkwb{long\ double\ }\hlstd{fin}\hlsym{,\ }\hlstd{list}\hlsym{$<$}\hlstd{Intervalo}\hlsym{$>$\&\ }\hlstd{out}\hlsym{)\ \{}\\ +\hlline{140\ }\hlstd{\\ +\hlline{141\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(!}\hlstd{ints}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{())\ \{}\\ +\hlline{142\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{out}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{Intervalo}\hlstd{}\hlsym{(}\hlstd{}\hlnum{0}\hlstd{}\hlsym{,}\hlstd{fin}\hlsym{));}\\ +\hlline{143\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{return}\hlstd{}\hlsym{;}\\ +\hlline{144\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{145\ }\hlstd{\\ +\hlline{146\ }\\ +\hlline{147\ }}\hlstd{\ \ \ \ }\hlstd{list}\hlsym{$<$}\hlstd{Intervalo}\hlsym{$>$::}\hlstd{const\textunderscore iterator\ it\ }\hlsym{=\ }\hlstd{ints}\hlsym{.}\hlstd{}\hlkwd{begin}\hlstd{}\hlsym{();}\\ +\hlline{148\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{it}\hlsym{{-}$>$}\hlstd{first\ }\hlsym{$>$\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ \{}\\ +\hlline{149\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{out}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{Intervalo}\hlstd{}\hlsym{(}\hlstd{}\hlnum{0}\hlstd{}\hlsym{,\ }\hlstd{it}\hlsym{{-}$>$}\hlstd{first}\hlsym{));}\\ +\hlline{150\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{151\ }\hlstd{\\ +\hlline{152\ }}\hlstd{\ \ \ \ }\hlstd{it}\hlsym{++;}\\ +\hlline{153\ }\hlstd{\\ +\hlline{154\ }}\hlstd{\ \ \ \ }\hlstd{list}\hlsym{$<$}\hlstd{Intervalo}\hlsym{$>$::}\hlstd{const\textunderscore iterator\ itprev\ }\hlsym{=\ }\hlstd{ints}\hlsym{.}\hlstd{}\hlkwd{begin}\hlstd{}\hlsym{();}\\ +\hlline{155\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{while\ }\hlstd{}\hlsym{(}\hlstd{it\ }\hlsym{!=\ }\hlstd{ints}\hlsym{.}\hlstd{}\hlkwd{end}\hlstd{}\hlsym{())\ \{}\\ +\hlline{156\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{out}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{Intervalo}\hlstd{}\hlsym{(}\hlstd{itprev}\hlsym{{-}$>$}\hlstd{second}\hlsym{,\ }\hlstd{it}\hlsym{{-}$>$}\hlstd{first}\hlsym{));}\\ +\hlline{157\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{it}\hlsym{++;}\\ +\hlline{158\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{itprev}\hlsym{++;}\\ +\hlline{159\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{160\ }\hlstd{\\ +\hlline{161\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{itprev}\hlsym{{-}$>$}\hlstd{second\ }\hlsym{$<$\ }\hlstd{fin}\hlsym{)\ \{}\\ +\hlline{162\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{out}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{Intervalo}\hlstd{}\hlsym{(}\hlstd{itprev}\hlsym{{-}$>$}\hlstd{second}\hlsym{,\ }\hlstd{fin}\hlsym{));}\\ +\hlline{163\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{164\ }\hlstd{}\hlsym{\}}\\ +\hlline{165\ }\hlstd{}\\ +\hlline{166\ }\\ +\hlline{167\ }\hlkwb{void\ }\hlstd{}\hlkwd{reduce\textunderscore union}\hlstd{}\hlsym{(}\hlstd{list}\hlsym{$<$}\hlstd{Intervalo}\hlsym{$>$\&\ }\hlstd{l\textunderscore o}\hlsym{,\ }\hlstd{list}\hlsym{$<$}\hlstd{Intervalo}\hlsym{$>$\&\ }\hlstd{out}\hlsym{)\ \{}\\ +\hlline{168\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlslc{//\ elimino\ repetidos\ para\ acelerar\ el\ sort}\\ +\hlline{169\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{list}\hlsym{$<$}\hlstd{Intervalo}\hlsym{$>$\ }\hlstd{l}\hlsym{;}\\ +\hlline{170\ }\hlstd{\\ +\hlline{171\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{for\ }\hlstd{}\hlsym{(}\hlstd{list}\hlsym{$<$}\hlstd{Intervalo}\hlsym{$>$::}\hlstd{const\textunderscore iterator\ itcito\ }\hlsym{=\ }\hlstd{l\textunderscore o}\hlsym{.}\hlstd{}\hlkwd{begin}\hlstd{}\hlsym{();\ }\hlstd{itcito\ }\hlsym{!=\ }\hlstd{l\textunderscore o}\hlsym{.}\hlstd{}\hlkwd{end}\hlstd{}\hlsym{();\ }\hlstd{itcito}\hlsym{++)\ \{}\\ +\hlline{172\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{itcito}\hlsym{{-}$>$}\hlstd{first\ }\hlsym{$<$\ }\hlstd{itcito}\hlsym{{-}$>$}\hlstd{second}\hlsym{)\ \{}\\ +\hlline{173\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{l}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{Intervalo}\hlstd{}\hlsym{(}\hlstd{itcito}\hlsym{{-}$>$}\hlstd{first}\hlsym{,\ }\hlstd{itcito}\hlsym{{-}$>$}\hlstd{second}\hlsym{));}\\ +\hlline{174\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}\ }\hlstd{}\hlkwa{else\ if\ }\hlstd{}\hlsym{(}\hlstd{itcito}\hlsym{{-}$>$}\hlstd{first\ }\hlsym{$>$\ }\hlstd{itcito}\hlsym{{-}$>$}\hlstd{second}\hlsym{)\ \{}\\ +\hlline{175\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{assert}\hlstd{}\hlsym{(}\hlstd{}\hlkwa{false}\hlstd{}\hlsym{);}\\ +\hlline{176\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{177\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{178\ }\hlstd{\\ +\hlline{179\ }\\ +\hlline{180\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(!}\hlstd{l}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{())\ }\hlstd{}\hlkwa{return}\hlstd{}\hlsym{;}\\ +\hlline{181\ }\hlstd{\\ +\hlline{182\ }}\hlstd{\ \ \ \ }\hlstd{l}\hlsym{.}\hlstd{}\hlkwd{sort}\hlstd{}\hlsym{();}\\ +\hlline{183\ }\hlstd{\\ +\hlline{184\ }}\hlstd{\ \ \ \ }\hlstd{list}\hlsym{$<$}\hlstd{Intervalo}\hlsym{$>$::}\hlstd{const\textunderscore iterator\ it\ }\hlsym{=\ }\hlstd{l}\hlsym{.}\hlstd{}\hlkwd{begin}\hlstd{}\hlsym{();}\\ +\hlline{185\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{Intervalo\ cand\ }\hlsym{=\ {*}}\hlstd{it}\hlsym{;}\\ +\hlline{186\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{Intervalo\ otro}\hlsym{;}\\ +\hlline{187\ }\hlstd{\\ +\hlline{188\ }}\hlstd{\ \ \ \ }\hlstd{it}\hlsym{++;}\\ +\hlline{189\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{while\ }\hlstd{}\hlsym{(}\hlstd{it\ }\hlsym{!=\ }\hlstd{l}\hlsym{.}\hlstd{}\hlkwd{end}\hlstd{}\hlsym{())\ \{}\\ +\hlline{190\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{otro\ }\hlsym{=\ {*}}\hlstd{it}\hlsym{;}\\ +\hlline{191\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{otro}\hlsym{.}\hlstd{first\ }\hlsym{$<$\ }\hlstd{otro}\hlsym{.}\hlstd{second}\hlsym{)\ \{}\\ +\hlline{192\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{otro}\hlsym{.}\hlstd{first\ }\hlsym{$>$\ }\hlstd{cand}\hlsym{.}\hlstd{second}\hlsym{)\ \{}\\ +\hlline{193\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{out}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{cand}\hlsym{);}\\ +\hlline{194\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{cand\ }\hlsym{=\ }\hlstd{otro}\hlsym{;}\\ +\hlline{195\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}\ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{196\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{otro}\hlsym{.}\hlstd{second\ }\hlsym{$>$\ }\hlstd{cand}\hlsym{.}\hlstd{second}\hlsym{)\ \{}\\ +\hlline{197\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{cand\ }\hlsym{=\ }\hlstd{}\hlkwd{Intervalo}\hlstd{}\hlsym{(}\hlstd{cand}\hlsym{.}\hlstd{first}\hlsym{,\ }\hlstd{otro}\hlsym{.}\hlstd{second}\hlsym{);}\\ +\hlline{198\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{199\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{200\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{201\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{it}\hlsym{++;}\\ +\hlline{202\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{203\ }\hlstd{\\ +\hlline{204\ }}\hlstd{\ \ \ \ }\hlstd{out}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{cand}\hlsym{);}\\ +\hlline{205\ }\hlstd{}\hlsym{\}}\\ +\hlline{206\ }\hlstd{}\\ +\hlline{207\ }\\ +\hlline{208\ }\hlkwb{long\ double\ }\hlstd{}\hlkwd{resolver}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ }\hlstd{list}\hlsym{$<$}\hlstd{Lampara}\hlsym{$>$\&\ }\hlstd{lamparas}\hlsym{,\ }\hlstd{}\hlkwb{const\ }\hlstd{list}\hlsym{$<$}\hlstd{Columna}\hlsym{$>$\&\ }\hlstd{columnas}\hlsym{,\ }\hlstd{}\hlkwb{int\ }\hlstd{max\textunderscore x}\hlsym{,\ }\hlstd{}\hlkwb{int\ }\Righttorque\\ +\hlline{209\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{max\textunderscore y}\hlsym{)\ \{}\\ +\hlline{210\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{list}\hlsym{$<$}\hlstd{Segmento}\hlsym{$>$\ }\hlstd{paredes}\hlsym{;}\\ +\hlline{211\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{paredes}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{Segmento}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{Vector}\hlstd{}\hlsym{(}\hlstd{}\hlnum{0}\hlstd{}\hlsym{,}\hlstd{}\hlnum{0}\hlstd{}\hlsym{),\ }\hlstd{}\hlkwd{Vector}\hlstd{}\hlsym{(}\hlstd{}\hlnum{0}\hlstd{}\hlsym{,\ }\hlstd{max\textunderscore y}\hlsym{)));}\\ +\hlline{212\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{paredes}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{Segmento}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{Vector}\hlstd{}\hlsym{(}\hlstd{}\hlnum{0}\hlstd{}\hlsym{,}\hlstd{max\textunderscore y}\hlsym{),\ }\hlstd{}\hlkwd{Vector}\hlstd{}\hlsym{(}\hlstd{max\textunderscore x}\hlsym{,\ }\hlstd{max\textunderscore y}\hlsym{)));}\\ +\hlline{213\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{paredes}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{Segmento}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{Vector}\hlstd{}\hlsym{(}\hlstd{max\textunderscore x}\hlsym{,}\hlstd{max\textunderscore y}\hlsym{),\ }\hlstd{}\hlkwd{Vector}\hlstd{}\hlsym{(}\hlstd{max\textunderscore x}\hlsym{,\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)));}\\ +\hlline{214\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{paredes}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{Segmento}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{Vector}\hlstd{}\hlsym{(}\hlstd{max\textunderscore x}\hlsym{,}\hlstd{}\hlnum{0}\hlstd{}\hlsym{),\ }\hlstd{}\hlkwd{Vector}\hlstd{}\hlsym{(}\hlstd{}\hlnum{0}\hlstd{}\hlsym{,\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)));}\\ +\hlline{215\ }\hlstd{\\ +\hlline{216\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{long\ double\ }\hlstd{total\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{217\ }\hlstd{\\ +\hlline{218\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{for\ }\hlstd{}\hlsym{(}\hlstd{list}\hlsym{$<$}\hlstd{Segmento}\hlsym{$>$::}\hlstd{iterator\ p\ }\hlsym{=\ }\hlstd{paredes}\hlsym{.}\hlstd{}\hlkwd{begin}\hlstd{}\hlsym{();\ }\hlstd{p\ }\hlsym{!=\ }\hlstd{paredes}\hlsym{.}\hlstd{}\hlkwd{end}\hlstd{}\hlsym{();\ }\hlstd{p}\hlsym{++)\ \{}\\ +\hlline{219\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{list}\hlsym{$<$}\hlstd{Intervalo}\hlsym{$>$\ }\hlstd{luces\textunderscore pared}\hlsym{;}\\ +\hlline{220\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{for\ }\hlstd{}\hlsym{(}\hlstd{list}\hlsym{$<$}\hlstd{Lampara}\hlsym{$>$::}\hlstd{const\textunderscore iterator\ l\ }\hlsym{=\ }\hlstd{lamparas}\hlsym{.}\hlstd{}\hlkwd{begin}\hlstd{}\hlsym{();\ }\hlstd{l\ }\hlsym{!=\ }\hlstd{lamparas}\hlsym{.}\hlstd{}\hlkwd{end}\hlstd{}\hlsym{();\ }\hlstd{l}\hlsym{++)\ \{}\\ +\hlline{221\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{list}\hlsym{$<$}\hlstd{Intervalo}\hlsym{$>$\ }\hlstd{zonas\textunderscore tapadas}\hlsym{;}\\ +\hlline{222\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{for\ }\hlstd{}\hlsym{(}\hlstd{list}\hlsym{$<$}\hlstd{Columna}\hlsym{$>$::}\hlstd{const\textunderscore iterator\ c\ }\hlsym{=\ }\hlstd{columnas}\hlsym{.}\hlstd{}\hlkwd{begin}\hlstd{}\hlsym{();\ }\hlstd{c\ }\hlsym{!=\ }\hlstd{columnas}\hlsym{.}\hlstd{}\hlkwd{end}\hlstd{}\hlsym{();\ }\hlstd{c}\hlsym{++)\ \{}\\ +\hlline{223\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{zonas\textunderscore tapadas}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{rango\textunderscore oscurecido}\hlstd{}\hlsym{({*}}\hlstd{p}\hlsym{,\ {*}}\hlstd{l}\hlsym{,\ {*}}\hlstd{c}\hlsym{));}\\ +\hlline{224\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{225\ }\hlstd{\\ +\hlline{226\ }}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{list}\hlsym{$<$}\hlstd{Intervalo}\hlsym{$>$\ }\hlstd{tapadas\textunderscore unidas}\hlsym{;}\\ +\hlline{227\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{list}\hlsym{$<$}\hlstd{Intervalo}\hlsym{$>$\ }\hlstd{zona\textunderscore iluminada}\hlsym{;}\\ +\hlline{228\ }\hlstd{\\ +\hlline{229\ }}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{reduce\textunderscore union}\hlstd{}\hlsym{(}\hlstd{zonas\textunderscore tapadas}\hlsym{,\ }\hlstd{tapadas\textunderscore unidas}\hlsym{);}\\ +\hlline{230\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{invertir\textunderscore rango}\hlstd{}\hlsym{(}\hlstd{tapadas\textunderscore unidas}\hlsym{,\ }\hlstd{}\hlkwd{largo}\hlstd{}\hlsym{({*}}\hlstd{p}\hlsym{),\ }\hlstd{zona\textunderscore iluminada}\hlsym{);}\\ +\hlline{231\ }\hlstd{\\ +\hlline{232\ }}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{luces\textunderscore pared}\hlsym{.}\hlstd{}\hlkwd{splice}\hlstd{}\hlsym{(}\hlstd{luces\textunderscore pared}\hlsym{.}\hlstd{}\hlkwd{end}\hlstd{}\hlsym{(),\ }\hlstd{zona\textunderscore iluminada}\hlsym{);}\\ +\hlline{233\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{234\ }\hlstd{\\ +\hlline{235\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{list}\hlsym{$<$}\hlstd{Intervalo}\hlsym{$>$\ }\hlstd{luces\textunderscore pared\textunderscore unidas}\hlsym{;}\\ +\hlline{236\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{reduce\textunderscore union}\hlstd{}\hlsym{(}\hlstd{luces\textunderscore pared}\hlsym{,\ }\hlstd{luces\textunderscore pared\textunderscore unidas}\hlsym{);}\\ +\hlline{237\ }\hlstd{\\ +\hlline{238\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{for\ }\hlstd{}\hlsym{(}\hlstd{list}\hlsym{$<$}\hlstd{Intervalo}\hlsym{$>$::}\hlstd{iterator\ it\ }\hlsym{=\ }\hlstd{luces\textunderscore pared\textunderscore unidas}\hlsym{.}\hlstd{}\hlkwd{begin}\hlstd{}\hlsym{();\ }\hlstd{it\ }\hlsym{!=\ }\hlstd{luces\textunderscore pared\textunderscore unidas}\hlsym{.}\hlstd{}\hlkwd{end}\hlstd{}\hlsym{(}\Righttorque\\ +\hlline{239\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{);\ }\hlstd{it}\hlsym{++)\ \{}\\ +\hlline{240\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{total\ }\hlsym{+=\ }\hlstd{}\hlkwd{largo}\hlstd{}\hlsym{({*}}\hlstd{it}\hlsym{);}\\ +\hlline{241\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{242\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{243\ }\hlstd{\\ +\hlline{244\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{total}\hlsym{;}\\ +\hlline{245\ }\hlstd{}\hlsym{\}}\\ +\hlline{246\ }\hlstd{}\\ +\hlline{247\ }\\ +\hlline{248\ }\hlkwb{int\ }\hlstd{}\hlkwd{main}\hlstd{}\hlsym{()\ \{}\\ +\hlline{249\ }\hlstd{\\ +\hlline{250\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{nl}\hlsym{,\ }\hlstd{nc}\hlsym{,\ }\hlstd{max\textunderscore x}\hlsym{,\ }\hlstd{max\textunderscore y}\hlsym{;}\\ +\hlline{251\ }\hlstd{\\ +\hlline{252\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{for\ }\hlstd{}\hlsym{(;;)\ \{}\\ +\hlline{253\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{scanf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%d\ \%d\ \%d\ \%d"}\hlstd{}\hlsym{,\ \&}\hlstd{nl}\hlsym{,\ \&}\hlstd{nc}\hlsym{,\ \&}\hlstd{max\textunderscore x}\hlsym{,\ \&}\hlstd{max\textunderscore y}\hlsym{);}\\ +\hlline{254\ }\hlstd{\\ +\hlline{255\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(!(}\hlstd{nl\ }\hlsym{\textbar \textbar \ }\hlstd{nc\ }\hlsym{\textbar \textbar \ }\hlstd{max\textunderscore x\ }\hlsym{\textbar \textbar \ }\hlstd{max\textunderscore y}\hlsym{))\ \{}\\ +\hlline{256\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{break}\hlstd{}\hlsym{;}\\ +\hlline{257\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{258\ }\hlstd{\\ +\hlline{259\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{list}\hlsym{$<$}\hlstd{Vector}\hlsym{$>$\ }\hlstd{lamparas}\hlsym{;}\\ +\hlline{260\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{list}\hlsym{$<$}\hlstd{Columna}\hlsym{$>$\ }\hlstd{columnas}\hlsym{;}\\ +\hlline{261\ }\hlstd{\\ +\hlline{262\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{x}\hlsym{,\ }\hlstd{y}\hlsym{,\ }\hlstd{r}\hlsym{;}\\ +\hlline{263\ }\hlstd{\\ +\hlline{264\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{forn}\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{nl}\hlsym{)\ \{}\\ +\hlline{265\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{scanf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%d\ \%d"}\hlstd{}\hlsym{,\ \&}\hlstd{x}\hlsym{,\ \&}\hlstd{y}\hlsym{);}\\ +\hlline{266\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{lamparas}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{Lampara}\hlstd{}\hlsym{(}\hlstd{x}\hlsym{,}\hlstd{y}\hlsym{));}\\ +\hlline{267\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{268\ }\hlstd{\\ +\hlline{269\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{forn}\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{nc}\hlsym{)\ \{}\\ +\hlline{270\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{scanf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%d\ \%d\ \%d"}\hlstd{}\hlsym{,\ \&}\hlstd{x}\hlsym{,\ \&}\hlstd{y}\hlsym{,\ \&}\hlstd{r}\hlsym{);}\\ +\hlline{271\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{columnas}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{Columna}\hlstd{}\hlsym{(}\hlstd{x}\hlsym{,\ }\hlstd{y}\hlsym{,\ }\hlstd{r}\hlsym{));}\\ +\hlline{272\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{273\ }\hlstd{\\ +\hlline{274\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{printf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%.4Lf}\hlesc{$\backslash$n}\hlstr{"}\hlstd{}\hlsym{,\ }\hlstd{}\hlkwd{resolver}\hlstd{}\hlsym{(}\hlstd{lamparas}\hlsym{,\ }\hlstd{columnas}\hlsym{,\ }\hlstd{max\textunderscore x}\hlsym{,\ }\hlstd{max\textunderscore y}\hlsym{));}\\ +\hlline{275\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{276\ }\hlstd{}\hlsym{\}}\hlstd{}\\ +\mbox{} +\normalfont +\shorthandon{"} diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/caratula.sty b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/caratula.sty new file mode 100644 index 0000000..7d4a979 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/caratula.sty @@ -0,0 +1,290 @@ +% ************************************************************************** +% +% Package 'caratula', version 0.3 (para componer caratulas de TPs del DC). +% +% En caso de dudas, problemas o sugerencias sobre este package escribir a +% Brian J. Cardiff (bcardif arroba gmail.com). +% Nico Rosner (nrosner arroba dc.uba.ar). +% +% ************************************************************************** + +% ----- Informacion sobre el package para el sistema ----------------------- + +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{caratula}[2005/08/09 v0.4 Para componer caratulas de TPs del DC] +\RequirePackage{ifthen} +\usepackage[pdftex]{graphicx} + +% ----- Imprimir un mensajito al procesar un .tex que use este package ----- + +\typeout{Cargando package 'caratula' v0.4 (2006/09/29)} + +% ----- Algunas variables -------------------------------------------------- + +\let\Materia\relax +\let\Submateria\relax +\let\Titulo\relax +\let\Subtitulo\relax +\let\Grupo\relax +\let\Fecha\relax +\let\Logoimagefile\relax +\let\Resumen\relax +\newcommand{\LabelIntegrantes}{} +\newboolean{showLU} +\newboolean{showDirectores} + +% ----- Comandos para que el usuario defina las variables ------------------ + +\def\materia#1{\def\Materia{#1}} +\def\submateria#1{\def\Submateria{#1}} +\def\titulo#1{\def\Titulo{#1}} +\def\subtitulo#1{\def\Subtitulo{#1}} +\def\grupo#1{\def\Grupo{#1}} +\def\fecha#1{\def\Fecha{#1}} +\def\logoimagefile#1{\def\Logoimagefile{#1}} +\def\resumen#1{\def\Resumen{#1}} + +% ----- Token list para los integrantes ------------------------------------ + +\newtoks\intlist\intlist={} + +\newtoks\intlistSinLU\intlistSinLU={} + +\newcounter{integrantesCount} +\setcounter{integrantesCount}{0} +\newtoks\intTabNombre\intTabNombre={} +\newtoks\intTabLU\intTabLU={} +\newtoks\intTabEmail\intTabEmail={} + +\newcounter{directoresCount} +\setcounter{directoresCount}{0} +\newtoks\direcTabNombre\direcTabNombre={} +\newtoks\direcTabEmail\direcTabEmail={} + +% ----- Comando para que el usuario agregue integrantes -------------------- + +\def\integrante#1#2#3{% + \intlist=\expandafter{\the\intlist\rule{0pt}{1.2em}#1&\tt #3\\[0.2em]}% + \intlistSinLU=\expandafter{\the\intlistSinLU\rule{0pt}{1.2em}#1 & \tt #3\\[0.2em]}% + % + \ifthenelse{\value{integrantesCount} > 0}{% + \intTabNombre=\expandafter{\the\intTabNombre & #1}% + \intTabLU=\expandafter{\the\intTabLU & #2}% + \intTabEmail=\expandafter{\the\intTabEmail & \tt #3}% + }{ + \intTabNombre=\expandafter{\the\intTabNombre #1}% + \intTabLU=\expandafter{\the\intTabLU #2}% + \intTabEmail=\expandafter{\the\intTabEmail \tt #3}% + }% + \addtocounter{integrantesCount}{1}% +} + +\def\director#1#2{% + \ifthenelse{\value{directoresCount} > 0}{% + \direcTabNombre=\expandafter{\the\direcTabNombre & #1}% + \direcTabEmail=\expandafter{\the\direcTabEmail & \tt #2}% + }{ + \direcTabNombre=\expandafter{\the\direcTabNombre #1}% + \direcTabEmail=\expandafter{\the\direcTabEmail \tt #2}% + }% + \addtocounter{directoresCount}{1}% +} + +% ----- Macro para generar la tabla de integrantes ------------------------- + +\newcommand{\tablaIntegrantes}{\ } + +\newcommand{\tablaIntegrantesVertical}{% +\ifthenelse{\boolean{showLU}}{% + \begin{tabular}[t]{| l @{\hspace{4ex}} c @{\hspace{4ex}} l|} + \hline + \multicolumn{1}{|c}{\rule{0pt}{1.2em} \LabelIntegrantes} & LU & \multicolumn{1}{c|}{Correo electr\'onico} \\[0.2em] + \hline \hline + \the\intlist + \hline + \end{tabular} +}{ + \begin{tabular}[t]{| l @{\hspace{4ex}} @{\hspace{4ex}} l|} + \hline + \multicolumn{1}{|c}{\rule{0pt}{1.2em} \LabelIntegrantes} & \multicolumn{1}{c|}{Correo electr\'onico} \\[0.2em] + \hline \hline + \the\intlistSinLU + \hline + \end{tabular} + }% +} + +\newcommand{\tablaIntegrantesHorizontal}{% + \begin{tabular}[t]{ *{\value{integrantesCount}}{c} } + \the\intTabNombre \\% +\ifthenelse{\boolean{showLU}}{ + \the\intTabLU \\% +}{} + \the\intTabEmail % + \end{tabular}% +} + +\newcommand{\tablaDirectores}{% +\ifthenelse{\boolean{showDirectores}}{% + \bigskip + Directores + + \smallskip + \begin{tabular}[t]{ *{\value{directoresCount}}{c} } + \the\direcTabNombre \\% + \the\direcTabEmail % + \end{tabular}% +}{}% +} + +% ----- Codigo para manejo de errores -------------------------------------- + +\def\se{\let\ifsetuperror\iftrue} +\def\ifsetuperror{% + \let\ifsetuperror\iffalse + \ifx\Materia\relax\se\errhelp={Te olvidaste de proveer una \materia{}.}\fi + \ifx\Titulo\relax\se\errhelp={Te olvidaste de proveer un \titulo{}.}\fi + \edef\mlist{\the\intlist}\ifx\mlist\empty\se% + \errhelp={Tenes que proveer al menos un \integrante{nombre}{lu}{email}.}\fi + \expandafter\ifsetuperror} + + +% ----- \maketitletxt correspondiente a la versión v0.2.1 (texto v0.2 + fecha ) --------- + +\def\maketitletxt{% + \ifsetuperror\errmessage{Faltan datos de la caratula! Ingresar 'h' para mas informacion.}\fi + \thispagestyle{empty} + \begin{center} + \vspace*{\stretch{2}} + {\LARGE\textbf{\Materia}}\\[1em] + \ifx\Submateria\relax\else{\Large \Submateria}\\[0.5em]\fi + \ifx\Fecha\relax\else{\Large \Fecha}\\[0.5em]\fi + \par\vspace{\stretch{1}} + {\large Departamento de Computaci\'on}\\[0.5em] + {\large Facultad de Ciencias Exactas y Naturales}\\[0.5em] + {\large Universidad de Buenos Aires} + \par\vspace{\stretch{3}} + {\Large \textbf{\Titulo}}\\[0.8em] + {\Large \Subtitulo} + \par\vspace{\stretch{3}} + \ifx\Grupo\relax\else\textbf{\Grupo}\par\bigskip\fi + \tablaIntegrantes + \end{center} + \vspace*{\stretch{3}} + \newpage} + +% ----- \maketitletxtlogo correspondiente v0.2.1 (texto con fecha y logo) --------- + +\def\maketitletxtlogo{% + \ifsetuperror\errmessage{Faltan datos de la caratula! Ingresar 'h' para mas informacion.}\fi + \thispagestyle{empty} + \begin{center} + \ifx\Logoimagefile\relax\else\includegraphics{\Logoimagefile}\fi \hfill \includegraphics{./figuras/logo_dc.jpg}\\[1em] + \vspace*{\stretch{2}} + {\LARGE\textbf{\Materia}}\\[1em] + \ifx\Submateria\relax\else{\Large \Submateria}\\[0.5em]\fi + \ifx\Fecha\relax\else{\large \Fecha}\\[0.5em]\fi + \par\vspace{\stretch{1}} + {\large Departamento de Computaci\'on}\\[0.5em] + {\large Facultad de Ciencias Exactas y Naturales}\\[0.5em] + {\large Universidad de Buenos Aires} + \par\vspace{\stretch{3}} + {\Large \textbf{\Titulo}}\\[0.8em] + {\Large \Subtitulo} + \par\vspace{\stretch{3}} + \ifx\Grupo\relax\else\textbf{\Grupo}\par\bigskip\fi + \tablaIntegrantes + \end{center} + \vspace*{\stretch{4}} + \newpage} + +% ----- \maketitlegraf correspondiente a la versión v0.3 (gráfica) ------------- + +\def\maketitlegraf{% + \ifsetuperror\errmessage{Faltan datos de la caratula! Ingresar 'h' para mas informacion.}\fi +% + \thispagestyle{empty} + + \ifx\Logoimagefile\relax\else\includegraphics{\Logoimagefile}\fi \hfill \includegraphics{./figuras/logo_dc.jpg} + + \vspace*{.12 \textheight} + + \noindent \textbf{\huge \Titulo} \medskip \\ + \ifx\Subtitulo\relax\else\noindent\textbf{\large \Subtitulo} \\ \fi% + \noindent \rule{\textwidth}{1 pt} + + {\noindent\large\Fecha \hspace*\fill \Materia} \\ + \ifx\Submateria\relax\else{\noindent \hspace*\fill \Submateria}\fi% + + \medskip% + \begin{center} + \ifx\Grupo\relax\else\textbf{\Grupo}\par\bigskip\fi + \tablaIntegrantes + + \tablaDirectores + \end{center}% + \vfill% + % \begin{abstract} + \small{\Resumen} + %\end{abstract} + + \begin{minipage}[t]{\textwidth} + \begin{minipage}[t]{.55 \textwidth} + \includegraphics{./figuras/logo_uba.jpg} + \end{minipage}%% + \begin{minipage}[b]{.5 \textwidth} + \textbf{\textsf{Facultad de Ciencias Exactas y Naturales}} \\ + \textsf{Universidad de Buenos Aires} \\ + {\scriptsize % + Ciudad Universitaria - (Pabell\'on I/Planta Baja) \\ + Intendente G\"uiraldes 2160 - C1428EGA \\ + Ciudad Aut\'onoma de Buenos Aires - Rep. Argentina \\ + Tel/Fax: (54 11) 4576-3359 \\ + http://www.fcen.uba.ar \\ + } + \end{minipage} + \end{minipage}% + + \newpage} + +% ----- Reemplazamos el comando \maketitle de LaTeX con el nuestro --------- +\renewcommand{\maketitle}{\maketitlegraf} + +% ----- Dependiendo de las opciones --------- +% +% opciones: +% txt : caratula solo texto. +% txtlogo : caratula txt con logo del DC y del grupo (opcional). +% graf : (default) caratula grafica con logo del DC, UBA y del grupo (opcional). +% +\@makeother\*% some package redefined it as a letter (as color.sty) +% +% Layout general de la caratula +% +\DeclareOption{txt}{\renewcommand{\maketitle}{\maketitletxt}} +\DeclareOption{txtlogo}{\renewcommand{\maketitle}{\maketitletxtlogo}} +\DeclareOption{graf}{\renewcommand{\maketitle}{\maketitlegraf}} +% +% Etiqueta Autores o Integrantes +% +\DeclareOption{integrante}{\renewcommand{\LabelIntegrantes}{Integrante}} +\DeclareOption{autor}{\renewcommand{\LabelIntegrantes}{Autor}} +% +% Formato tabla de integrantes +% +\DeclareOption{intVert}{\renewcommand{\tablaIntegrantes}{\tablaIntegrantesVertical}} +\DeclareOption{intHoriz}{\renewcommand{\tablaIntegrantes}{\tablaIntegrantesHorizontal}} +\DeclareOption{conLU}{\setboolean{showLU}{true}} +\DeclareOption{sinLU}{\setboolean{showLU}{false}} +\DeclareOption{showDirectores}{\setboolean{showDirectores}{true}} +\DeclareOption{hideDirectores}{\setboolean{showDirectores}{false}} +% +% Opciones predeterminadas +% +\ExecuteOptions{intVert}% +\ExecuteOptions{graf}% +\ExecuteOptions{integrante}% +\ExecuteOptions{conLU}% +\ExecuteOptions{hideDirectores}% +% +\ProcessOptions\relax diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/code_color.sty b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/code_color.sty new file mode 100644 index 0000000..b030e31 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/code_color.sty @@ -0,0 +1,20 @@ +% Style definition file generated by highlight 2.16, http://www.andre-simon.de/ + +% Highlighting theme definition: + +\newcommand{\hlstd}[1]{\textcolor[rgb]{0,0,0}{#1}} +\newcommand{\hlnum}[1]{\textcolor[rgb]{0,0,0}{#1}} +\newcommand{\hlesc}[1]{\textcolor[rgb]{0,0,0}{#1}} +\newcommand{\hlstr}[1]{\textcolor[rgb]{0,0,0}{#1}} +\newcommand{\hldstr}[1]{\textcolor[rgb]{0,0,0}{#1}} +\newcommand{\hlslc}[1]{\textcolor[rgb]{0.4,0.4,0.4}{\it{#1}}} +\newcommand{\hlcom}[1]{\textcolor[rgb]{0.4,0.4,0.4}{\it{#1}}} +\newcommand{\hldir}[1]{\textcolor[rgb]{0,0,0}{\bf{#1}}} +\newcommand{\hlsym}[1]{\textcolor[rgb]{0,0,0}{\bf{#1}}} +\newcommand{\hlline}[1]{\textcolor[rgb]{0.53,0.53,0.53}{#1}} +\newcommand{\hlkwa}[1]{\textcolor[rgb]{0,0,0}{\bf{#1}}} +\newcommand{\hlkwb}[1]{\textcolor[rgb]{0,0,0}{\bf{#1}}} +\newcommand{\hlkwc}[1]{\textcolor[rgb]{0,0,0}{\bf{#1}}} +\newcommand{\hlkwd}[1]{\textcolor[rgb]{0,0,0}{\bf{#1}}} +\definecolor{bgcolor}{rgb}{1,1,1} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/disgruntled.tex b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/disgruntled.tex new file mode 100644 index 0000000..7bffdb3 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/disgruntled.tex @@ -0,0 +1,417 @@ +\newcommand{\cosito}[0]{\textcolor{Orange}{\huge$\cdot$}} +\section{4289 - Disgruntled Judge} +\textbf{Problema:} +Dada una sucesión de números $x_1, x_3, ... , x_{2t-1}$, encontrar $x_2, x_4, ... , x_{2t}$, tal que: +$$\exists a, b \in \mathds{Z}, 0 \leq a,b \leq 10000, \forall 0 \leq i \leq 2t-1, x_{i+1} = a* x_{i} + b \mod 10001$$ + +\subsection{Resolución} +Para resolver el problema primero notamos que $10001 = 73*137$, lo cual puede ser útil para aplicar el teorema chino del resto. +Llamaremos $I_{i} = x_{2i-1}$ y $O_{i} = x_{2i}$. Notemos que como el enunciado nos dice que $0 \leq x_{i} \leq 10000$, resulta que los $x_{i}$ son restos de la división módulo 10001. Esto resulta importante porque nos permite trabajar con congruencia en vez de igualdad. + +Si el \textit{input} es sólo $I_1$, alcanza con tomar $O_1=I_1$, pues se puede tomar $a=0, b=I_1$. Análogamente, si el \textit{input} es sólo $I_1, I_2$, alcanza con tomar $O_k = I_2$, pues se puede usar $a=0, b = I_2$. + +Si la cantidad de \textit{inputs} ($n$) es mayor, hay que plantearlo de otra forma. + +Consideremos un caso tal que la cantidad de \textit{inputs} es mayor o igual a 3. Observando las ecuaciones de generación de los $x_i$ vemos que: + +$$a*I_1 + b \equiv O_1 \mod 10001$$ +$$a*0_1 + b \equiv I_2 \mod 10001$$ +$$a*I_2 + b \equiv O_2 \mod 10001$$ +$$a*O_2 + b \equiv I_3 \mod 10001$$ + +De aquí podemos obtener: + +$$a^2*I_1 + a*b + b \equiv I_2 \mod 10001$$ +$$a^2*I_2 + a*b + b \equiv I_3 \mod 10001$$ + +Restando ecuaciones, + +$$a^2*(I_1 - I_2) \equiv (I_2 - I_3) \mod 10001$$ + +Resolviendo esta ecuación podemos obtener candidatos para $a^2$, y de estos candidatos podemos obtener posibles valores para $a$. + +Notemos que si $(I_1 - I_2)\equiv 0 \mod 10001$, resulta que $I_1 = I_2$, ya que $0 \leq I_1,I_2 \leq 10001$. %TODO: lo explico mas esto? +En ese caso, alcanza con devolver $O_k=I_2$ + +Usando teorema chino del resto, obtenemos que: +$$a^2*(I_1 - I_2) \equiv (I_2 - I_3) \mod 137$$ +$$a^2*(I_1 - I_2) \equiv (I_2 - I_3) \mod 73$$ + +Supongamos que $(I_1 - I_2) \not\equiv 0 \mod 137 \wedge (I_1 - I_2) \not\equiv 0 \mod 73$ +Entonces, como ambos módulos son primos, existen $k_{73}, k_{137}$ inversos multiplicativos de $(I_1 - I_2)$ módulo 73 y 137 respectivamente, tales que: +$$a^2 \equiv (I_2 - I_3)*k_{137} \mod 137$$ +$$a^2 \equiv (I_2 - I_3)*k_{73} \mod 73$$ + +Para encontrar los $k$ se busca expresar a 1 como combinación lineal entre $(I_1 - I_2)$ y 137 o 73 según corresponda, lo cual es posible, ya que estamos suponiendo que $(I_1 - I_2)$ es coprimo con 137 y con 73. + +Luego buscamos $a$ tales que $a^2$ cumpla esas ecuaciones. Si $(I_1 - I_2) \equiv 0 \mod 137 \vee (I_1 - I_2) \equiv 0 \mod 73$ (es un ``o'' exclusivo, porque estamos considerando que no $(I_1 - I_2)$ no era múltiplo de $10001$), perdemos una de las ecuaciones, pero igual obtenemos posibles candidatos para $a^2$. + +Una vez que obtenemos un candidato para $a$, vemos si es viable. Para esto debe ser posible encontrar $b$ tal que: +$$a^2*I_1 + a*b + b \equiv I_2 \mod 10001$$ +Escrito de otra forma: +$$(a+1)*b \equiv I_2 - a^2*I_1 \mod 10001$$ + +Un caso donde podría no existir ningún $b$ que cumpla esta ecuación es si $(a+1) \equiv 0 \mod 10001$, pero el lado derecho de la ecuación no es equivalente a 0. Usando teorema chino del resto, se obtienen dos ecuaciones módulo 173 y 73, que permiten obtener un $b$ candidato. +En verdad no puede ser que $(a+1) \equiv 0 \mod 10001$, porque entonces resulta que $a^2 \equiv 1 \mod 10001$ y de $(a+1)*b \equiv I_2 - a^2*I_1 \mod 10001$ sale que $I_1 \equiv I_2 \mod 10001$, pero ese caso yo lo habíamos considerado antes por separado. +Sin embargo, si puede ocurrir que $(a+1) \equiv 0 \mod 73$ o $(a+1) \equiv 0 \mod 137$ y que no valga que el lado derecho también sea congruente a 0, por lo cual hay que chequear esas condiciones. + +Dado un valor de $k\neq 0$, existen a lo sumo dos $a$ distintos que cumplen: +$a \leq 0 \leq 73 \wedge a^2 \equiv k \mod 73$. En particular, existen o bien 2 $a$ que cumplen eso, o ninguno. El caso donde no existe ninguno no lo consideramos, ya que por enunciado sabemos que debe existir alguno. Si en vez de considerar el intervalo $[0,73]$ consideramos el intervalo $[0,\lfloor73/2\rfloor]$ existe un único $a$. El otro $a$ pertenece a la segunda mitad del intervalo y tiene la forma $a'=73-a$. +Algo similar ocurre para $137$. + +Podemos entonces tener dos arreglos, uno para cada factor primo, tales que, por ejemplo, $A_{73}[i] = k / k^2 \equiv i \mod 73 \wedge 0 < k < 73$, o $0$ si no existe tal $k$. + +En el caso en el que ninguna de las ecuaciones para $a^2$ se anula, usando lo visto antes, tenemos 4 posibles candidatos para $a$ (la combinación mediante teorema chino del resto de las dos soluciones módulo 73 y 137). Lo que hacemos entonces es probar alguno de esos que respete los \textit{inputs}, es decir que para todo $O_k$ en el rango, tiene que valer que $a*O_k+b \equiv I_{k+1} \mod 10001$. Una vez que encontramos uno, imprimimos los $O_k$. + +Si alguna de las ecuaciones se anula, tenemos muchos más candidatos. Por ejemplo, si se anula la ecuación de $137$, tenemos dos posibles valores de $a$ que son menores que $73$. Ahora, todo valor $a'$ que sea menor a $10001$ y congruente modulo $73$ a alguno de esos dos es otro posible candidato. Notemos que en este caso hay $2*137$ posibles candidatos. Es análogo para cuando la ecuación que se anula es la de $73$, en este caso hay $2*73$ candidatos + + +El siguiente pseudocódigo ilustra la resolución del problema: +\begin{algorithm}[H] +\begin{algorithmic} +\caption{Obtención de $a$ y $b$ para el caso en el que $n\geq 3$ } +\PARAMS{$I_1$,$I_2$,$I_3$} +\STATE q = $I_1-I_2$ +\STATE w = $I_2-I_3$ +\IF{$q \equiv 0 \mod 73 \wedge q \equiv 0 \mod 137$} +\STATE no importa $a$ ni $b$, se puede tomar $O_k = I_3$ +\RETURN +\ENDIF +\IF{$q \equiv 0 \mod 73$} +\STATE $a^2_{73} = w*q^{-1}_{73} \mod 73$ \COMMENT{ $q^{-1}_{73}$ es el inverso multiplicativo de $q \mod 73$} +\STATE obtener $a$ tal que $0 \leq a \leq \lfloor73/2\rfloor \wedge a^2 \equiv a^2_{73} \mod 73$ +\STATE $a'= 73 - a$ +\WHILE{no encontré solución} + \IF{ es posible encontrar un $b$ para ese $a$, y $a,b$ respetan los inputs} + \STATE esos son los que buscábamos + \RETURN + \ELSIF{ es posible encontrar un $b$ para $a'$ y $a',b$ respetan los inputs} + \STATE esos son los que buscábamos + \RETURN + \ELSE + \STATE $a=a+73$ + \STATE $a'=a'+73$ + \ENDIF +\ENDWHILE +\ELSIF{$q \equiv 0 \mod 137$} +\STATE realizar el mismo proceso que para 73 pero módulo 137 +\ELSE +\STATE $a^2_{73} = w*q^{-1}_{73} \mod 73$ +\STATE obtener $k$ tal que $0 \leq k \leq \lfloor73/2\rfloor \wedge k^2 \equiv a^2_{73} \mod 73$ +\STATE $a^2_{137} = w*q^{-1}_{137} \mod 137$ +\STATE obtener $j$ tal que $0 \leq j \lfloor\leq 137/2\rfloor \wedge j^2 \equiv a^2_{73} \mod 73$ +\STATE considerar los siguientes candidatos: \COMMENT{se obtienen gracias al teorema chino} +\STATE \cosito $k*137*137^{-1}_{73} + j*73*73^{-1}_{137} \mod 10001$ +\STATE \cosito $(73-k)*137*137^{-1}_{73} + j*73*73^{-1}_{137} \mod 10001$ +\STATE \cosito $k*137*137^{-1}_{73} + (137-j)*73*73^{-1}_{137} \mod 10001$ +\STATE \cosito $(73-k)*137*137^{-1}_{73} + (137-j)*73*73^{-1}_{137} \mod 10001$ +\STATE devolver alguno de los candidatos tal que sea posible encontrar un $b$ para el, y que ambos respeten los $I_i$. +\ENDIF +\end{algorithmic} +\end{algorithm} + +\begin{algorithm}[H] +\begin{algorithmic} +\caption{Obtención de $b$ dado un $a$, o fallar si no se puede} +\PARAMS{$a, I_1,I_2$} +\IF{$a+1 \equiv 0 \mod 73$} +\IF{$y - a^2*x \not\equiv 0 \mod 73$} +\STATE \textcolor{Orange}{Fallar} +\ELSE +\STATE $b = y - a^2*x * (a+1)^{-1}_{137} \mod 137$ +\RETURN +\ENDIF +\ELSIF{$a+1 \equiv 0 \mod 137$} +\IF{$y - a^2*x \not\equiv 0 \mod 137$} +\STATE \textcolor{Orange}{Fallar} +\ELSE +\STATE $b = y - a^2*x * (a+1)^{-1}_{73} \mod 73$ +\RETURN +\ENDIF +\ELSE +\STATE $b_{137} = y - a^2*x * (a+1)^{-1}_{137} \mod 137$ +\STATE $b_{73} = y - a^2*x * (a+1)^{-1}_{73} \mod 73$ +\STATE $b = b_{73}*137*137^{-1}_{73} + b_{137}*73*73^{-1}_{137} \mod 10001$ +\RETURN +\ENDIF +\end{algorithmic} +\end{algorithm} + +\subsection{Complejidad} +Con respecto a la complejidad, consideraremos que las operaciones aritméticas cuestan $O(1)$. Dado $m$, llamamos $\omega(m)$ a la cantidad de primos que dividen a $m$, es decir $\sharp\{ p / p \mid m \wedge p \in \mathds{P}\}$. Suponemos que conocemos esos factores primos, pues de lo contrario habría que considerar el costo de factorizar $m$. + +Para resolver el ejercicio, llenamos $\omega(m)$ arreglos, que sirven para obtener $a$, sabiendo el resto de $a^2$ para los distintos factores primos de $m$. Estos arreglos se pueden llenar en $O(m)$. +Luego se resuelven $O(\omega(m))$ ecuaciones, las cuales se pueden resolver en $O(\log m)$, ya que para hacerlo se necesita obtener los inversos multiplicativos que se pueden conseguir mediante el algoritmo para el $mcd$ como se vio en clase. + +A partir de esto, obtenemos $O(m)$ posibles candidatos (por ejemplo, si se anulan todas las ecuaciones menos una, la de $p_i$, quedan aproximadamente $O(m/p_i)$ candidatos). Para testear cada candidato, probamos que se cumplan todas las ecuaciones para los $I_i$, entonces si $n$ es la cantidad de inputs, chequeamos $O(n)$ ecuaciones. Por lo tanto, la complejidad de esta parte es $O(m*n)$. + +Leer la entrada es $O(n) \subseteq O(m*n)$. + +Uniendo todo, la complejidad es $O(\omega(m)*\log(m) + m*n)$. + +\subsection{Implementación} +\noindent +\ttfamily +\shorthandoff{"}\\ +\hlstd{}\hlline{\ 1\ }\hldir{\#include\ $<$stdlib.h$>$}\\ +\hlline{\ 2\ }\hlstd{}\hldir{\#include\ $<$stdlib.h$>$}\\ +\hlline{\ 3\ }\hlstd{}\hldir{\#include\ $<$stdio.h$>$}\\ +\hlline{\ 4\ }\hlstd{}\hldir{\#include\ $<$sys/types.h$>$}\\ +\hlline{\ 5\ }\hlstd{}\hldir{\#include\ $<$sys/stat.h$>$}\\ +\hlline{\ 6\ }\hlstd{}\hldir{\#include\ $<$fcntl.h$>$}\\ +\hlline{\ 7\ }\hlstd{}\hldir{\#include\ $<$cassert$>$}\\ +\hlline{\ 8\ }\hlstd{}\hldir{\#include\ $<$list$>$}\\ +\hlline{\ 9\ }\hlstd{}\hlkwa{using\ namespace\ }\hlstd{std}\hlsym{;}\\ +\hlline{10\ }\hlstd{}\hldir{\#define\ forn(i,n)\ for(int\ i\ =\ 0;\ i\ $<$\ n;\ ++i)}\\ +\hlline{11\ }\hlstd{}\hldir{\#define\ forsn(i,s,n)\ for(int\ i\ =\ (s);\ i\ $<$\ (n);\ i++)}\\ +\hlline{12\ }\hlstd{}\hldir{\#define\ foreachin(it,s)\ for(\textunderscore \textunderscore typeof\textunderscore \textunderscore ((s).begin())\ it\ =\ ((s).begin());\ it\ !=\ ((s).end());\ ++it)}\\ +\hlline{13\ }\hlstd{}\\ +\hlline{14\ }\hldir{\#define\ inverso\textunderscore de\textunderscore 73\textunderscore mod\textunderscore 137\ 122}\\ +\hlline{15\ }\hlstd{}\hldir{\#define\ inverso\textunderscore de\textunderscore 137\textunderscore mod\textunderscore 73\ 8}\\ +\hlline{16\ }\hlstd{}\hldir{\#define\ coef\textunderscore 137\ 1096\ }\hlslc{//\ 137{*}8}\\ +\hlline{17\ }\hldir{}\hlstd{}\hldir{\#define\ coef\textunderscore 73\ 8906\ }\hlslc{//\ 73{*}122}\\ +\hlline{18\ }\hldir{}\hlstd{}\\ +\hlline{19\ }\hlkwb{static\ int\ }\hlstd{cuad73}\hlsym{{[}}\hlstd{}\hlnum{73}\hlstd{}\hlsym{{]};}\\ +\hlline{20\ }\hlstd{}\hlkwb{static\ int\ }\hlstd{cuad137}\hlsym{{[}}\hlstd{}\hlnum{137}\hlstd{}\hlsym{{]};}\\ +\hlline{21\ }\hlstd{}\\ +\hlline{22\ }\hldir{\#define\ resto(x,y)\ ((((x)\ \%\ (y))\ +\ (y))\ \%\ (y))}\\ +\hlline{23\ }\hlstd{}\\ +\hlline{24\ }\hlslc{//\ si\ (a,b)\ =\ 1,\ deja\ en\ x\ el\ inverso\ multiplicativo\ de\ a\ ,mod\ b}\\ +\hlline{25\ }\hlstd{}\hlslc{//\ basicamente\ es\ la\ idea\ del\ algoritmo\ de\ euclides,\ pero\ iterativo}\\ +\hlline{26\ }\hlstd{}\hlslc{//\ mas\ info:\ www.math.hawaii.edu/$\sim$lee/discrete/combination.ps}\\ +\hlline{27\ }\hlstd{}\hlkwb{void\ }\hlstd{}\hlkwd{combinacion}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{int\ }\hlstd{a}\hlsym{,\ }\hlstd{}\hlkwb{int\ }\hlstd{b}\hlsym{,\ }\hlstd{}\hlkwb{int}\hlstd{}\hlsym{\&}\hlstd{x}\hlsym{)\ \{}\\ +\hlline{28\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{g0\ }\hlsym{=\ }\hlstd{a}\hlsym{;}\\ +\hlline{29\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{x0\ }\hlsym{=\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{30\ }\hlstd{}\hlslc{//}\hlstd{\ \ \ \ }\hlslc{int\ y0\ =\ 0;}\\ +\hlline{31\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{g1\ }\hlsym{=\ }\hlstd{b}\hlsym{;}\\ +\hlline{32\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{x1\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{33\ }\hlstd{}\hlslc{//}\hlstd{\ \ \ \ }\hlslc{int\ y1\ =\ 1;}\\ +\hlline{34\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{while\ }\hlstd{}\hlsym{(}\hlstd{g0\ }\hlsym{\%\ }\hlstd{g1\ }\hlsym{!=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ \{}\\ +\hlline{35\ }\hlstd{}\hlslc{//invariante:\ a{*}x\textunderscore 1+b{*}y\textunderscore 1=g1}\\ +\hlline{36\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{q\ }\hlsym{=\ }\hlstd{g0\ }\hlsym{/\ }\hlstd{g1}\hlsym{;}\\ +\hlline{37\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{temp\ }\hlsym{=\ }\hlstd{g1}\hlsym{;}\\ +\hlline{38\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{g1\ }\hlsym{=\ }\hlstd{g0\ }\hlsym{{-}\ }\hlstd{q\ }\hlsym{{*}\ }\hlstd{g1}\hlsym{;}\\ +\hlline{39\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{g0\ }\hlsym{=\ }\hlstd{temp}\hlsym{;}\\ +\hlline{40\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{temp\ }\hlsym{=\ }\hlstd{x1}\hlsym{;}\\ +\hlline{41\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{x1\ }\hlsym{=\ }\hlstd{x0\ }\hlsym{{-}\ }\hlstd{q\ }\hlsym{{*}\ }\hlstd{x1}\hlsym{;}\\ +\hlline{42\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{x0\ }\hlsym{=\ }\hlstd{temp}\hlsym{;}\\ +\hlline{43\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlcom{/{*}}\\ +\hlline{44\ }\hlcom{}\hlstd{\ \ \ \ \ \ \ \ \ }\hlcom{temp\ =\ y1;}\\ +\hlline{45\ }\hlcom{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlcom{y1\ =\ y0\ {-}\ q\ {*}\ y1;}\\ +\hlline{46\ }\hlcom{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlcom{y0\ =\ temp;}\\ +\hlline{47\ }\hlcom{}\hlstd{\ \ \ \ \ \ \ \ }\hlcom{{*}/}\hlstd{\\ +\hlline{48\ }}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{49\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{x}\hlsym{=}\hlstd{x1}\hlsym{;}\\ +\hlline{50\ }\hlstd{}\hlsym{\}}\\ +\hlline{51\ }\hlstd{}\\ +\hlline{52\ }\hlcom{/{*}\ utiliza\ la\ ecuacion:\ a\textasciicircum 2{*}x\ +a{*}b+b\ $\backslash$equiv\ y}\\ +\hlline{53\ }\hlcom{\ {*}\ para\ despejar\ b,\ si\ no\ es\ posible,\ es\ porque\ el\ a\ no\ era\ correcto}\\ +\hlline{54\ }\hlcom{\ {*}\ b{*}(a+1)\ $\backslash$equiv\ y\ {-}a\textasciicircum 2}\\ +\hlline{55\ }\hlcom{\ {*}/}\hlstd{}\\ +\hlline{56\ }\hlkwb{bool\ }\hlstd{}\hlkwd{obtener\textunderscore b}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{int\ }\hlstd{a}\hlsym{,\ }\hlstd{}\hlkwb{int\ }\hlstd{x}\hlsym{,\ }\hlstd{}\hlkwb{int\ }\hlstd{y}\hlsym{,}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{\&\ }\hlstd{b}\hlsym{)\ \{}\\ +\hlline{57\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{((}\hlstd{a}\hlsym{+}\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ \%\ }\hlstd{}\hlnum{73\ }\hlstd{}\hlsym{==\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ \{}\\ +\hlline{58\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlslc{//\ para\ poder\ encontrar\ un\ b,\ la\ parte\ derecha\ tb\ tiene\ que\ ser\ congruente\ a\ 0\ modulo\ 73}\\ +\hlline{59\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{y}\hlsym{{-}}\hlstd{}\hlkwd{resto}\hlstd{}\hlsym{(}\hlstd{a}\hlsym{{*}}\hlstd{a}\hlsym{,}\hlstd{}\hlnum{73}\hlstd{}\hlsym{){*}}\hlstd{x\ }\hlsym{\%}\hlstd{}\hlnum{73\ }\hlstd{}\hlsym{!=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)}\hlstd{}\hlkwa{return\ false}\hlstd{}\hlsym{;}\\ +\hlline{60\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{amas1inv}\hlsym{,\ }\hlstd{aux}\hlsym{;}\\ +\hlline{61\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{combinacion}\hlstd{}\hlsym{((}\hlstd{a}\hlsym{+}\hlstd{}\hlnum{1}\hlstd{}\hlsym{),}\hlstd{}\hlnum{137}\hlstd{}\hlsym{,}\hlstd{amas1inv}\hlsym{);}\\ +\hlline{62\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{amas1inv\ }\hlsym{=\ }\hlstd{}\hlkwd{resto}\hlstd{}\hlsym{(}\hlstd{amas1inv}\hlsym{,}\hlstd{}\hlnum{137}\hlstd{}\hlsym{);}\\ +\hlline{63\ }\hlstd{\\ +\hlline{64\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{acuad\ }\hlsym{=\ }\hlstd{a}\hlsym{{*}}\hlstd{a\ }\hlsym{\%}\hlstd{}\hlnum{137}\hlstd{}\hlsym{;}\\ +\hlline{65\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{aux\ }\hlsym{=\ }\hlstd{}\hlkwd{resto}\hlstd{}\hlsym{((}\hlstd{y\ }\hlsym{{-}\ }\hlstd{acuad}\hlsym{{*}}\hlstd{x}\hlsym{),}\hlstd{}\hlnum{137}\hlstd{}\hlsym{);}\\ +\hlline{66\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{b\ }\hlsym{=\ }\hlstd{aux}\hlsym{{*}}\hlstd{amas1inv}\hlsym{\%}\hlstd{}\hlnum{137}\hlstd{}\hlsym{;}\\ +\hlline{67\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{return\ true}\hlstd{}\hlsym{;}\\ +\hlline{68\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{69\ }\hlstd{\\ +\hlline{70\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{((}\hlstd{a}\hlsym{+}\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\%}\hlstd{}\hlnum{137\ }\hlstd{}\hlsym{==\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ \{}\\ +\hlline{71\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlslc{//\ para\ poder\ encontrar\ un\ b,\ la\ parte\ derecha\ tb\ tiene\ que\ ser\ congruente\ a\ 0\ modulo\ 137}\\ +\hlline{72\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{y}\hlsym{{-}}\hlstd{}\hlkwd{resto}\hlstd{}\hlsym{(}\hlstd{a}\hlsym{{*}}\hlstd{a}\hlsym{,}\hlstd{}\hlnum{137}\hlstd{}\hlsym{){*}}\hlstd{x\ }\hlsym{\%}\hlstd{}\hlnum{137\ }\hlstd{}\hlsym{!=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)}\hlstd{}\hlkwa{return\ false}\hlstd{}\hlsym{;}\\ +\hlline{73\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{amas1inv}\hlsym{,\ }\hlstd{aux}\hlsym{;}\\ +\hlline{74\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{combinacion}\hlstd{}\hlsym{((}\hlstd{a}\hlsym{+}\hlstd{}\hlnum{1}\hlstd{}\hlsym{),}\hlstd{}\hlnum{73}\hlstd{}\hlsym{,}\hlstd{amas1inv}\hlsym{);}\\ +\hlline{75\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{amas1inv\ }\hlsym{=\ }\hlstd{}\hlkwd{resto}\hlstd{}\hlsym{(}\hlstd{amas1inv}\hlsym{,}\hlstd{}\hlnum{73}\hlstd{}\hlsym{);}\\ +\hlline{76\ }\hlstd{\\ +\hlline{77\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{acuad\ }\hlsym{=\ }\hlstd{a}\hlsym{{*}}\hlstd{a\ }\hlsym{\%\ }\hlstd{}\hlnum{73}\hlstd{}\hlsym{;}\\ +\hlline{78\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{aux\ }\hlsym{=\ }\hlstd{}\hlkwd{resto}\hlstd{}\hlsym{((}\hlstd{y\ }\hlsym{{-}\ }\hlstd{acuad}\hlsym{{*}}\hlstd{x}\hlsym{),}\hlstd{}\hlnum{73}\hlstd{}\hlsym{);}\\ +\hlline{79\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{b\ }\hlsym{=\ }\hlstd{aux}\hlsym{{*}}\hlstd{amas1inv\ }\hlsym{\%}\hlstd{}\hlnum{73}\hlstd{}\hlsym{;}\\ +\hlline{80\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{return\ true}\hlstd{}\hlsym{;}\\ +\hlline{81\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{82\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{amas1inv137}\hlsym{,\ }\hlstd{aux}\hlsym{;}\\ +\hlline{83\ }\hlstd{\\ +\hlline{84\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{combinacion}\hlstd{}\hlsym{((}\hlstd{a}\hlsym{+}\hlstd{}\hlnum{1}\hlstd{}\hlsym{),}\hlstd{}\hlnum{137}\hlstd{}\hlsym{,}\hlstd{amas1inv137}\hlsym{);}\\ +\hlline{85\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{amas1inv137\ }\hlsym{=\ }\hlstd{}\hlkwd{resto}\hlstd{}\hlsym{(}\hlstd{amas1inv137}\hlsym{,}\hlstd{}\hlnum{137}\hlstd{}\hlsym{);}\\ +\hlline{86\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{acuad137\ }\hlsym{=\ }\hlstd{a}\hlsym{{*}}\hlstd{a\ }\hlsym{\%\ }\hlstd{}\hlnum{137}\hlstd{}\hlsym{;}\\ +\hlline{87\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{aux137\ }\hlsym{=\ }\hlstd{}\hlkwd{resto}\hlstd{}\hlsym{((}\hlstd{y\ }\hlsym{{-}\ }\hlstd{acuad137}\hlsym{{*}}\hlstd{x}\hlsym{),}\hlstd{}\hlnum{137}\hlstd{}\hlsym{);}\\ +\hlline{88\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{b137}\hlsym{=\ }\hlstd{aux137}\hlsym{{*}}\hlstd{amas1inv137\ }\hlsym{\%\ }\hlstd{}\hlnum{137}\hlstd{}\hlsym{;}\\ +\hlline{89\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{amas1inv73}\hlsym{;}\\ +\hlline{90\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{combinacion}\hlstd{}\hlsym{((}\hlstd{a}\hlsym{+}\hlstd{}\hlnum{1}\hlstd{}\hlsym{),}\hlstd{}\hlnum{73}\hlstd{}\hlsym{,}\hlstd{amas1inv73}\hlsym{);}\\ +\hlline{91\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{amas1inv73\ }\hlsym{=\ }\hlstd{}\hlkwd{resto}\hlstd{}\hlsym{(}\hlstd{amas1inv73}\hlsym{,}\hlstd{}\hlnum{73}\hlstd{}\hlsym{);}\\ +\hlline{92\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{acuad73\ }\hlsym{=\ }\hlstd{a}\hlsym{{*}}\hlstd{a\ }\hlsym{\%}\hlstd{}\hlnum{73}\hlstd{}\hlsym{;}\\ +\hlline{93\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{aux73\ }\hlsym{=\ }\hlstd{}\hlkwd{resto}\hlstd{}\hlsym{((}\hlstd{y\ }\hlsym{{-}\ }\hlstd{acuad73}\hlsym{{*}}\hlstd{x}\hlsym{),}\hlstd{}\hlnum{73}\hlstd{}\hlsym{);}\\ +\hlline{94\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{b73}\hlsym{=\ }\hlstd{aux73}\hlsym{{*}}\hlstd{amas1inv73\ }\hlsym{\%}\hlstd{}\hlnum{73}\hlstd{}\hlsym{;}\\ +\hlline{95\ }\hlstd{\\ +\hlline{96\ }}\hlstd{\ \ \ \ }\hlstd{}\hlslc{//usamos\ teorema\ chino\ del\ resto,\ para\ encontrar\ b}\\ +\hlline{97\ }\hlstd{\\ +\hlline{98\ }}\hlstd{\ \ \ \ }\hlstd{b\ }\hlsym{=\ ((}\hlstd{b73}\hlsym{{*}}\hlstd{coef\textunderscore 137}\hlsym{)+(}\hlstd{b137}\hlsym{{*}}\hlstd{coef\textunderscore 73}\hlsym{))\ \%\ }\hlstd{}\hlnum{10001}\hlstd{}\hlsym{;}\\ +\hlline{99\ }\hlstd{\\ +\hlline{100\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{return\ true}\hlstd{}\hlsym{;}\\ +\hlline{101\ }\hlstd{}\\ +\hlline{102\ }\hlsym{\}}\\ +\hlline{103\ }\hlstd{}\\ +\hlline{104\ }\hlkwb{static\ int\ }\hlstd{numeros}\hlsym{{[}}\hlstd{}\hlnum{101}\hlstd{}\hlsym{{]};}\\ +\hlline{105\ }\hlstd{}\\ +\hlline{106\ }\hlkwb{bool\ }\hlstd{}\hlkwd{testear\textunderscore candidato}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{int\ }\hlstd{a}\hlsym{,\ }\hlstd{}\hlkwb{int\ }\hlstd{b}\hlsym{,\ }\hlstd{}\hlkwb{int\ }\hlstd{cant}\hlsym{,}\hlstd{list}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$\&\ }\hlstd{res}\hlsym{)\ \{}\\ +\hlline{107\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{forn}\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,}\hlstd{cant}\hlsym{)\ \{}\\ +\hlline{108\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{f\ }\hlsym{=\ (}\hlstd{a}\hlsym{{*}}\hlstd{numeros}\hlsym{{[}}\hlstd{i}\hlsym{{]}+}\hlstd{b}\hlsym{)\%\ }\hlstd{}\hlnum{10001}\hlstd{}\hlsym{;}\\ +\hlline{109\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{res}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{f}\hlsym{);}\\ +\hlline{110\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{numeros}\hlsym{{[}}\hlstd{i}\hlsym{+}\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]}\ $<$\ }\hlstd{cant\ }\hlsym{\&\&\ (}\hlstd{a}\hlsym{{*}}\hlstd{f}\hlsym{+}\hlstd{b}\hlsym{)\%\ }\hlstd{}\hlnum{10001\ }\hlstd{}\hlsym{!=\ }\hlstd{numeros}\hlsym{{[}}\hlstd{i}\hlsym{+}\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]})\ \{}\\ +\hlline{111\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{break}\hlstd{}\hlsym{;}\\ +\hlline{112\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{113\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{114\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{res}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{()\ ==\ }\hlstd{cant}\hlsym{;}\\ +\hlline{115\ }\hlstd{}\hlsym{\}}\\ +\hlline{116\ }\hlstd{}\\ +\hlline{117\ }\hlkwb{void\ }\hlstd{}\hlkwd{llenar\textunderscore res}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{int\ }\hlstd{a}\hlsym{,}\hlstd{}\hlkwb{int\ }\hlstd{a1}\hlsym{,}\hlstd{}\hlkwb{int\ }\hlstd{x}\hlsym{,\ }\hlstd{}\hlkwb{int\ }\hlstd{y}\hlsym{,}\hlstd{}\hlkwb{int\ }\hlstd{cant}\hlsym{,}\hlstd{list}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$\&\ }\hlstd{res}\hlsym{,}\hlstd{}\hlkwb{int\ }\hlstd{q}\hlsym{)\ \{}\\ +\hlline{118\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{b}\hlsym{;}\\ +\hlline{119\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{candidatos}\hlsym{{[}}\hlstd{}\hlnum{2}\hlstd{}\hlsym{{]}\ =\ \{}\hlstd{a}\hlsym{,}\hlstd{a1}\hlsym{\};}\\ +\hlline{120\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{t\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{121\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{while\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwa{true}\hlstd{}\hlsym{)\ \{}\\ +\hlline{122\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwd{obtener\textunderscore b}\hlstd{}\hlsym{(}\hlstd{candidatos}\hlsym{{[}}\hlstd{t}\hlsym{{]},}\hlstd{x}\hlsym{,}\hlstd{y}\hlsym{,}\hlstd{b}\hlsym{))\ \{}\\ +\hlline{123\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwd{testear\textunderscore candidato}\hlstd{}\hlsym{(}\hlstd{candidatos}\hlsym{{[}}\hlstd{t}\hlsym{{]},}\hlstd{b}\hlsym{,}\hlstd{cant}\hlsym{,}\hlstd{res}\hlsym{))}\hlstd{}\hlkwa{break}\hlstd{}\hlsym{;}\\ +\hlline{124\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{125\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{res}\hlsym{.}\hlstd{}\hlkwd{clear}\hlstd{}\hlsym{();}\\ +\hlline{126\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{t}\hlsym{++;}\\ +\hlline{127\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{t}\hlsym{$>$}\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ \{}\\ +\hlline{128\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{candidatos}\hlsym{{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}=}\hlstd{candidatos}\hlsym{{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}+}\hlstd{q}\hlsym{;}\\ +\hlline{129\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{candidatos}\hlsym{{[}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]}=}\hlstd{candidatos}\hlsym{{[}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]}+}\hlstd{q}\hlsym{;}\\ +\hlline{130\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{t}\hlsym{=}\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{131\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{132\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{133\ }\hlstd{}\hlsym{\}}\\ +\hlline{134\ }\hlstd{}\\ +\hlline{135\ }\hlkwb{void\ }\hlstd{}\hlkwd{resolver}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ int\ }\hlstd{cuadk}\hlsym{{[}{]},}\hlstd{}\hlkwb{int\ }\hlstd{k}\hlsym{,}\hlstd{}\hlkwb{int\ }\hlstd{x}\hlsym{,}\hlstd{}\hlkwb{int\ }\hlstd{y}\hlsym{,}\hlstd{}\hlkwb{int\ }\hlstd{qk}\hlsym{,\ }\hlstd{}\hlkwb{int\ }\hlstd{wk}\hlsym{,}\hlstd{}\hlkwb{int\ }\hlstd{cant}\hlsym{)\ \{}\\ +\hlline{136\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{qkinv}\hlsym{;}\\ +\hlline{137\ }\hlstd{\\ +\hlline{138\ }}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{combinacion}\hlstd{}\hlsym{(}\hlstd{qk}\hlsym{,}\hlstd{k}\hlsym{,}\hlstd{qkinv}\hlsym{);}\\ +\hlline{139\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{qkinv\ }\hlsym{=\ }\hlstd{}\hlkwd{resto}\hlstd{}\hlsym{(}\hlstd{qkinv}\hlsym{,}\hlstd{k}\hlsym{);}\\ +\hlline{140\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{acuad\ }\hlsym{=\ (}\hlstd{wk}\hlsym{{*}}\hlstd{qkinv}\hlsym{)\%}\hlstd{k}\hlsym{;}\\ +\hlline{141\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{a}\hlsym{,}\hlstd{a1}\hlsym{;}\\ +\hlline{142\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{a\ }\hlsym{=\ }\hlstd{cuadk}\hlsym{{[}}\hlstd{acuad}\hlsym{{]};}\\ +\hlline{143\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{a1}\hlsym{=\ }\hlstd{k\ }\hlsym{{-}}\hlstd{cuadk}\hlsym{{[}}\hlstd{acuad}\hlsym{{]};}\\ +\hlline{144\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{list}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$\ }\hlstd{res}\hlsym{;}\\ +\hlline{145\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{llenar\textunderscore res}\hlstd{}\hlsym{(}\hlstd{a}\hlsym{,}\hlstd{a1}\hlsym{,}\hlstd{x}\hlsym{,}\hlstd{y}\hlsym{,}\hlstd{cant}\hlsym{,}\hlstd{res}\hlsym{,}\hlstd{k}\hlsym{);}\\ +\hlline{146\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{foreachin}\hlstd{}\hlsym{(}\hlstd{it}\hlsym{,}\hlstd{res}\hlsym{)\ \{}\\ +\hlline{147\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{printf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%d}\hlesc{$\backslash$n}\hlstr{"}\hlstd{}\hlsym{,{*}}\hlstd{it}\hlsym{);}\\ +\hlline{148\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{149\ }\hlstd{}\hlsym{\}}\\ +\hlline{150\ }\hlstd{}\\ +\hlline{151\ }\\ +\hlline{152\ }\hlkwb{int\ }\hlstd{}\hlkwd{main}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{int\ }\hlstd{argc}\hlsym{,\ }\hlstd{}\hlkwb{char}\hlstd{}\hlsym{{*}{*}\ }\hlstd{argv}\hlsym{)\ \{}\\ +\hlline{153\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlslc{//\ cuad73{[}k{]}\ =\ a\ /\ a\textasciicircum 2\ \%\ 73\ ==\ k}\\ +\hlline{154\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlslc{//\ notar\ que\ alcanza\ mirar\ hasta\ 37\ (73/2+1)}\\ +\hlline{155\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlslc{//\ porque\ j\textasciicircum 2\ \%\ 73\ ==\ (73\ {-}\ j)\textasciicircum 2}\\ +\hlline{156\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlslc{//\ ademas\ no\ hay\ a1,a2\ entre\ {[}0,73/2+1)\ tal\ que\ a1\textasciicircum 2\ \%\ 73\ ==\ a2\textasciicircum 2\ \%\ 73}\\ +\hlline{157\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{forn}\hlstd{}\hlsym{(}\hlstd{each}\hlsym{,}\hlstd{}\hlnum{37}\hlstd{}\hlsym{)\ \{}\\ +\hlline{158\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{cuad73}\hlsym{{[}(}\hlstd{each}\hlsym{{*}}\hlstd{each}\hlsym{)\%}\hlstd{}\hlnum{73}\hlstd{}\hlsym{{]}\ =\ }\hlstd{each}\hlsym{;}\\ +\hlline{159\ }\hlstd{\\ +\hlline{160\ }}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{161\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlslc{//\ simil\ a\ lo\ anterior}\\ +\hlline{162\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{forn}\hlstd{}\hlsym{(}\hlstd{each}\hlsym{,}\hlstd{}\hlnum{68}\hlstd{}\hlsym{)\ \{}\\ +\hlline{163\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{cuad137}\hlsym{{[}(}\hlstd{each}\hlsym{{*}}\hlstd{each}\hlsym{)\%}\hlstd{}\hlnum{137}\hlstd{}\hlsym{{]}=}\hlstd{each}\hlsym{;}\\ +\hlline{164\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{165\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{cant}\hlsym{;}\\ +\hlline{166\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{scanf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%d"}\hlstd{}\hlsym{,\&}\hlstd{cant}\hlsym{);}\\ +\hlline{167\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{while\ }\hlstd{}\hlsym{(}\hlstd{cant\ }\hlsym{$>$\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ \{}\\ +\hlline{168\ }\hlstd{\\ +\hlline{169\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{forn}\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,}\hlstd{cant}\hlsym{)\ \{}\\ +\hlline{170\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{scanf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%d"}\hlstd{}\hlsym{,\&}\hlstd{numeros}\hlsym{{[}}\hlstd{i}\hlsym{{]});}\\ +\hlline{171\ }\hlstd{\\ +\hlline{172\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{173\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{cant\ }\hlsym{$<$\ }\hlstd{}\hlnum{3}\hlstd{}\hlsym{)\ \{}\\ +\hlline{174\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{forn}\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{cant}\hlsym{)\ \{}\\ +\hlline{175\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{printf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%d}\hlesc{$\backslash$n}\hlstr{"}\hlstd{}\hlsym{,}\hlstd{numeros}\hlsym{{[}}\hlstd{cant}\hlsym{{-}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]});}\\ +\hlline{176\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{177\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{178\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{179\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{x}\hlsym{,}\hlstd{y}\hlsym{,}\hlstd{z}\hlsym{;}\\ +\hlline{180\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{x}\hlsym{=}\hlstd{numeros}\hlsym{{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]};}\\ +\hlline{181\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{y}\hlsym{=}\hlstd{numeros}\hlsym{{[}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]};}\\ +\hlline{182\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{z}\hlsym{=}\hlstd{numeros}\hlsym{{[}}\hlstd{}\hlnum{2}\hlstd{}\hlsym{{]};}\\ +\hlline{183\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{q}\hlsym{,}\hlstd{w}\hlsym{;}\\ +\hlline{184\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlcom{/{*}\ Idea:}\\ +\hlline{185\ }\hlcom{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ }\hlcom{a{*}x\ +\ b\ $\backslash$equiv\ 0\textunderscore 1}\\ +\hlline{186\ }\hlcom{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ }\hlcom{a{*}O\textunderscore 1\ +\ b\ $\backslash$equiv\ y}\\ +\hlline{187\ }\hlcom{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ }\hlcom{a{*}y\ +\ b\ $\backslash$equiv\ O\textunderscore 2}\\ +\hlline{188\ }\hlcom{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ }\hlcom{a{*}O\textunderscore 2\ +b\ $\backslash$equiv\ z}\\ +\hlline{189\ }\hlcom{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ }\hlcom{{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}}\\ +\hlline{190\ }\hlcom{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ }\hlcom{a\textasciicircum 2{*}x+ab+b\ $\backslash$equiv\ y}\\ +\hlline{191\ }\hlcom{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ }\hlcom{a\textasciicircum 2{*}y+ab+b\ $\backslash$equiv\ z}\\ +\hlline{192\ }\hlcom{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ }\hlcom{{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}{-}}\\ +\hlline{193\ }\hlcom{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ }\hlcom{a\textasciicircum 2(x{-}y)\ $\backslash$equiv\ (y{-}z)}\\ +\hlline{194\ }\hlcom{}\\ +\hlline{195\ }\hlcom{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ }\hlcom{Resolver\ esa\ ecuacion\ modulo\ 137\ y\ 73\ y\ obtener\ candidatos\ para\ a.}\\ +\hlline{196\ }\hlcom{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ }\hlcom{obtener\ un\ b\ para\ alguno\ de\ los\ candidatos.\ usar\ esa\ pareja\ (a,b)}\\ +\hlline{197\ }\hlcom{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ }\hlcom{{*}/}\hlstd{\\ +\hlline{198\ }}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{q\ }\hlsym{=\ (}\hlstd{x}\hlsym{{-}}\hlstd{y}\hlsym{);}\\ +\hlline{199\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{w\ }\hlsym{=\ (}\hlstd{y}\hlsym{{-}}\hlstd{z}\hlsym{);}\\ +\hlline{200\ }\hlstd{\\ +\hlline{201\ }}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{q137\ }\hlsym{=\ }\hlstd{}\hlkwd{resto}\hlstd{}\hlsym{(}\hlstd{q}\hlsym{,}\hlstd{}\hlnum{137}\hlstd{}\hlsym{);}\\ +\hlline{202\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{q73\ }\hlsym{=\ }\hlstd{}\hlkwd{resto}\hlstd{}\hlsym{(}\hlstd{q}\hlsym{,}\hlstd{}\hlnum{73}\hlstd{}\hlsym{);}\\ +\hlline{203\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{w137\ }\hlsym{=\ }\hlstd{}\hlkwd{resto}\hlstd{}\hlsym{(}\hlstd{w}\hlsym{,}\hlstd{}\hlnum{137}\hlstd{}\hlsym{);}\\ +\hlline{204\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{w73\ }\hlsym{=\ }\hlstd{}\hlkwd{resto}\hlstd{}\hlsym{(}\hlstd{w}\hlsym{,}\hlstd{}\hlnum{73}\hlstd{}\hlsym{);}\\ +\hlline{205\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{q137\ }\hlsym{==\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ \{}\\ +\hlline{206\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{q73\ }\hlsym{==\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ \{}\\ +\hlline{207\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{forn}\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,}\hlstd{cant}\hlsym{)\ \{}\\ +\hlline{208\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{printf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%d}\hlesc{$\backslash$n}\hlstr{"}\hlstd{}\hlsym{,}\hlstd{numeros}\hlsym{{[}}\hlstd{cant}\hlsym{{-}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{{]});}\\ +\hlline{209\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{210\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{211\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{212\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{resolver}\hlstd{}\hlsym{(}\hlstd{cuad73}\hlsym{,}\hlstd{}\hlnum{73}\hlstd{}\hlsym{,}\hlstd{x}\hlsym{,}\hlstd{y}\hlsym{,}\hlstd{q73}\hlsym{,}\hlstd{w73}\hlsym{,}\hlstd{cant}\hlsym{);}\\ +\hlline{213\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{214\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{215\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{216\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{q73\ }\hlsym{==\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ \{}\\ +\hlline{217\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{resolver}\hlstd{}\hlsym{(}\hlstd{cuad137}\hlsym{,}\hlstd{}\hlnum{137}\hlstd{}\hlsym{,}\hlstd{x}\hlsym{,}\hlstd{y}\hlsym{,}\hlstd{q137}\hlsym{,}\hlstd{w137}\hlsym{,}\hlstd{cant}\hlsym{);}\\ +\hlline{218\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{219\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{else\ }\hlstd{}\hlsym{\{}\\ +\hlline{220\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{q137inv}\hlsym{,}\hlstd{q73inv}\hlsym{;}\\ +\hlline{221\ }\hlstd{\\ +\hlline{222\ }}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{combinacion}\hlstd{}\hlsym{(}\hlstd{q137}\hlsym{,}\hlstd{}\hlnum{137}\hlstd{}\hlsym{,}\hlstd{q137inv}\hlsym{);}\\ +\hlline{223\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{q137inv\ }\hlsym{=\ }\hlstd{}\hlkwd{resto}\hlstd{}\hlsym{(}\hlstd{q137inv}\hlsym{,}\hlstd{}\hlnum{137}\hlstd{}\hlsym{);}\\ +\hlline{224\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{acuad137\ }\hlsym{=\ (}\hlstd{w137}\hlsym{{*}}\hlstd{q137inv}\hlsym{)\%}\hlstd{}\hlnum{137}\hlstd{}\hlsym{;}\\ +\hlline{225\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{combinacion}\hlstd{}\hlsym{(}\hlstd{q73}\hlsym{,}\hlstd{}\hlnum{73}\hlstd{}\hlsym{,}\hlstd{q73inv}\hlsym{);}\\ +\hlline{226\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{q73inv\ }\hlsym{=\ }\hlstd{}\hlkwd{resto}\hlstd{}\hlsym{(}\hlstd{q73inv}\hlsym{,}\hlstd{}\hlnum{73}\hlstd{}\hlsym{);}\\ +\hlline{227\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{acuad73\ }\hlsym{=\ (}\hlstd{w73}\hlsym{{*}}\hlstd{q73inv}\hlsym{)\%}\hlstd{}\hlnum{73}\hlstd{}\hlsym{;}\\ +\hlline{228\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{a}\hlsym{,}\hlstd{b}\hlsym{;}\\ +\hlline{229\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{j\ }\hlsym{=\ }\hlstd{cuad73}\hlsym{{[}}\hlstd{acuad73}\hlsym{{]};}\\ +\hlline{230\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{k\ }\hlsym{=\ }\hlstd{cuad137}\hlsym{{[}}\hlstd{acuad137}\hlsym{{]};}\\ +\hlline{231\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{list}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$\ }\hlstd{res}\hlsym{;}\\ +\hlline{232\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{candidatos}\hlsym{{[}}\hlstd{}\hlnum{4}\hlstd{}\hlsym{{]}\ =\ \{\ }\hlstd{}\hlkwd{resto}\hlstd{}\hlsym{(}\hlstd{j}\hlsym{{*}}\hlstd{coef\textunderscore 137\ }\hlsym{+\ }\hlstd{k}\hlsym{{*}\ }\hlstd{coef\textunderscore 73}\hlsym{,}\hlstd{}\hlnum{10001}\hlstd{}\hlsym{),\ }\hlstd{}\hlkwd{resto}\hlstd{}\hlsym{((}\hlstd{}\hlnum{73}\hlstd{}\hlsym{{-}}\hlstd{j}\hlsym{)}\Righttorque\\ +\hlline{233\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{{*}}\hlstd{coef\textunderscore 137\ }\hlsym{+\ }\hlstd{k}\hlsym{{*}\ }\hlstd{coef\textunderscore 73}\hlsym{,}\hlstd{}\hlnum{10001}\hlstd{}\hlsym{),}\\ +\hlline{234\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{resto}\hlstd{}\hlsym{((}\hlstd{}\hlnum{73}\hlstd{}\hlsym{{-}}\hlstd{j}\hlsym{){*}}\hlstd{coef\textunderscore 137\ }\hlsym{+\ (}\hlstd{}\hlnum{137}\hlstd{}\hlsym{{-}}\hlstd{k}\hlsym{){*}\ }\hlstd{coef\textunderscore 73}\hlsym{,}\hlstd{}\hlnum{10001}\hlstd{}\hlsym{),\ }\hlstd{}\hlkwd{resto}\hlstd{}\hlsym{(}\Righttorque\\ +\hlline{235\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{j}\hlsym{{*}}\hlstd{coef\textunderscore 137\ }\hlsym{+\ (}\hlstd{}\hlnum{137}\hlstd{}\hlsym{{-}}\hlstd{k}\hlsym{){*}\ }\hlstd{coef\textunderscore 73}\hlsym{,}\hlstd{}\hlnum{10001}\hlstd{}\hlsym{)}\\ +\hlline{236\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\};}\\ +\hlline{237\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{forn}\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{}\hlnum{4}\hlstd{}\hlsym{)\ \{}\\ +\hlline{238\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{a\ }\hlsym{=}\hlstd{candidatos}\hlsym{{[}}\hlstd{i}\hlsym{{]}\ ;}\\ +\hlline{239\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwd{obtener\textunderscore b}\hlstd{}\hlsym{(}\hlstd{a}\hlsym{,}\hlstd{x}\hlsym{,}\hlstd{y}\hlsym{,}\hlstd{b}\hlsym{))\ \{}\\ +\hlline{240\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwd{testear\textunderscore candidato}\hlstd{}\hlsym{(}\hlstd{a}\hlsym{,}\hlstd{b}\hlsym{,}\hlstd{cant}\hlsym{,}\hlstd{res}\hlsym{))\ \{}\\ +\hlline{241\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{break}\hlstd{}\hlsym{;}\\ +\hlline{242\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{243\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{244\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{res}\hlsym{.}\hlstd{}\hlkwd{clear}\hlstd{}\hlsym{();}\\ +\hlline{245\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{246\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{foreachin}\hlstd{}\hlsym{(}\hlstd{it}\hlsym{,}\hlstd{res}\hlsym{)\ \{}\\ +\hlline{247\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{printf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%d}\hlesc{$\backslash$n}\hlstr{"}\hlstd{}\hlsym{,{*}}\hlstd{it}\hlsym{);}\\ +\hlline{248\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{249\ }\hlstd{\\ +\hlline{250\ }}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{251\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{252\ }\hlstd{\\ +\hlline{253\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{254\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{}\hlkwd{scanf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%d}\hlesc{$\backslash$n}\hlstr{"}\hlstd{}\hlsym{,\&}\hlstd{cant}\hlsym{)!=}\hlstd{}\hlnum{1}\hlstd{}\hlsym{)}\hlstd{}\hlkwa{break}\hlstd{}\hlsym{;}\\ +\hlline{255\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{256\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{}\hlsym{(}\hlstd{EXIT\textunderscore SUCCESS}\hlsym{);}\\ +\hlline{257\ }\hlstd{}\hlsym{\}}\\ +\hlline{258\ }\hlstd{}\\ +\mbox{} +\normalfont +\shorthandon{"} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/figuras/ballroom.png b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/figuras/ballroom.png new file mode 100644 index 0000000000000000000000000000000000000000..1f03968063d1618856cb57275a27ddb3226e51ab GIT binary patch literal 42778 zcwRhu2UHVX*L4z_f`CyeQZ)onI#Q*ogc6DxIqH{K8QE63xL5yccDM<8!0iH;6INC>e~id`r`s` zU%ll9yM6n%oTs06!1b$mH#z@X?iur10x;MK7#4HhDkSsI$nDHb>w&h#v84N#^zI&m zpFDXuGy(VPE_1xZtN*UCoIe+G`laoqW0&8WlpyXJCrWXj5-z=9B!k5(H26euDrnCGr7C%c z2Y793Vocn7YxHNisyx6^yMmjGS8WW*Hvef!pJC;vx8_*>8h*KIrM(0N)<=%vF1!0v z)?W0L;}aiDzpQ-^nLS|^Tj$YWml6-fX8m)bx$wM^{j*y!^kAy7lcNSlbq4r7%dhv0 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+\hlline{\ 6\ }\hlstd{}\\ +\hlline{\ 7\ }\hlkwa{using\ namespace\ }\hlstd{std}\hlsym{;}\\ +\hlline{\ 8\ }\hlstd{}\\ +\hlline{\ 9\ }\hlkwc{typedef\ }\hlstd{}\hlkwb{unsigned\ long\ long\ int\ }\hlstd{lluint}\hlsym{;}\\ +\hlline{10\ }\hlstd{}\\ +\hlline{11\ }\hlkwc{typedef\ }\hlstd{vector}\hlsym{$<$}\hlstd{lluint}\hlsym{$>$\ }\hlstd{Row}\hlsym{;}\\ +\hlline{12\ }\hlstd{}\hlkwc{typedef\ }\hlstd{vector}\hlsym{$<$}\hlstd{Row}\hlsym{$>$\ }\hlstd{Mat}\hlsym{;}\\ +\hlline{13\ }\hlstd{}\\ +\hlline{14\ }\hldir{\#define\ forsn(i,\ s,\ n)\ for\ (int\ i\ =\ (s);\ i\ $<$\ (n);\ i++)}\\ +\hlline{15\ }\hlstd{}\hldir{\#define\ forn(i,\ n)\ forsn\ (i,\ 0,\ n)}\\ +\hlline{16\ }\hlstd{}\\ +\hlline{17\ }\hlkwb{void\ }\hlstd{}\hlkwd{mat\textunderscore mult}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ }\hlstd{Mat}\hlsym{\&\ }\hlstd{m1}\hlsym{,\ }\hlstd{}\hlkwb{const\ }\hlstd{Mat}\hlsym{\&\ }\hlstd{m2}\hlsym{,\ }\hlstd{Mat}\hlsym{\&\ }\hlstd{res}\hlsym{)\ \{}\\ +\hlline{18\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ int\ }\hlstd{n\ }\hlsym{=\ }\hlstd{m1}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{();}\\ +\hlline{19\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ int\ }\hlstd{m\ }\hlsym{=\ }\hlstd{m2}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{();}\\ +\hlline{20\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ int\ }\hlstd{p\ }\hlsym{=\ }\hlstd{m2}\hlsym{{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{();}\\ +\hlline{21\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{assert}\hlstd{}\hlsym{(}\hlstd{m1}\hlsym{{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{()\ ==\ }\hlstd{m\ }\hlsym{\&\&\ }\hlstd{res}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{()\ ==\ }\hlstd{n\ }\hlsym{\&\&\ }\hlstd{res}\hlsym{{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{()\ ==\ }\hlstd{p}\hlsym{);}\\ +\hlline{22\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{n}\hlsym{)\ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{j}\hlsym{,\ }\hlstd{p}\hlsym{)\ \{}\\ +\hlline{23\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{lluint\ s\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{24\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{k}\hlsym{,\ }\hlstd{m}\hlsym{)\ }\hlstd{s\ }\hlsym{+=\ }\hlstd{m1}\hlsym{{[}}\hlstd{i}\hlsym{{]}{[}}\hlstd{k}\hlsym{{]}\ {*}\ }\hlstd{m2}\hlsym{{[}}\hlstd{k}\hlsym{{]}{[}}\hlstd{j}\hlsym{{]};}\\ +\hlline{25\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{res}\hlsym{{[}}\hlstd{i}\hlsym{{]}{[}}\hlstd{j}\hlsym{{]}\ =\ }\hlstd{s}\hlsym{;}\\ +\hlline{26\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{27\ }\hlstd{}\hlsym{\}}\\ +\hlline{28\ }\hlstd{}\\ +\hlline{29\ }\hlkwb{void\ }\hlstd{}\hlkwd{mat\textunderscore identity}\hlstd{}\hlsym{(}\hlstd{Mat}\hlsym{\&\ }\hlstd{mt}\hlsym{)\ \{}\\ +\hlline{30\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ int\ }\hlstd{n\ }\hlsym{=\ }\hlstd{mt}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{();}\\ +\hlline{31\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{assert}\hlstd{}\hlsym{(}\hlstd{n\ }\hlsym{==\ }\hlstd{mt}\hlsym{{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{());}\\ +\hlline{32\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{n}\hlsym{)\ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{j}\hlsym{,\ }\hlstd{n}\hlsym{)\ \{}\\ +\hlline{33\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{mt}\hlsym{{[}}\hlstd{i}\hlsym{{]}{[}}\hlstd{j}\hlsym{{]}\ =\ }\hlstd{i\ }\hlsym{==\ }\hlstd{j}\hlsym{;}\\ +\hlline{34\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{35\ }\hlstd{}\hlsym{\}}\\ +\hlline{36\ }\hlstd{}\\ +\hlline{37\ }\hlkwb{void\ }\hlstd{}\hlkwd{mat\textunderscore copy}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ }\hlstd{Mat}\hlsym{\&\ }\hlstd{in}\hlsym{,\ }\hlstd{Mat}\hlsym{\&\ }\hlstd{out}\hlsym{)\ \{}\\ +\hlline{38\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ int\ }\hlstd{n\ }\hlsym{=\ }\hlstd{in}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{();}\\ +\hlline{39\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ int\ }\hlstd{m\ }\hlsym{=\ }\hlstd{in}\hlsym{{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{();}\\ +\hlline{40\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{assert}\hlstd{}\hlsym{(}\hlstd{out}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{()\ ==\ }\hlstd{in}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{()\ \&\&\ }\hlstd{out}\hlsym{{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{()\ ==\ }\hlstd{in}\hlsym{{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{());}\\ +\hlline{41\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{n}\hlsym{)\ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{j}\hlsym{,\ }\hlstd{m}\hlsym{)\ }\hlstd{out}\hlsym{{[}}\hlstd{i}\hlsym{{]}{[}}\hlstd{j}\hlsym{{]}\ =\ }\hlstd{in}\hlsym{{[}}\hlstd{i}\hlsym{{]}{[}}\hlstd{j}\hlsym{{]};}\\ +\hlline{42\ }\hlstd{}\hlsym{\}}\\ +\hlline{43\ }\hlstd{}\\ +\hlline{44\ }\hlkwb{void\ }\hlstd{}\hlkwd{mat\textunderscore pow}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ }\hlstd{Mat}\hlsym{\&\ }\hlstd{mt}\hlsym{,\ }\hlstd{}\hlkwb{int\ }\hlstd{pow}\hlsym{,\ }\hlstd{Mat}\hlsym{\&\ }\hlstd{res}\hlsym{)\ \{}\\ +\hlline{45\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ int\ }\hlstd{n\ }\hlsym{=\ }\hlstd{mt}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{();}\\ +\hlline{46\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{vector}\hlsym{$<$}\hlstd{Mat}\hlsym{$>$\ }\hlstd{}\hlkwd{acc}\hlstd{}\hlsym{(}\hlstd{}\hlnum{2}\hlstd{}\hlsym{,\ }\hlstd{}\hlkwd{Mat}\hlstd{}\hlsym{(}\hlstd{n}\hlsym{,\ }\hlstd{}\hlkwd{Row}\hlstd{}\hlsym{(}\hlstd{n}\hlsym{,\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)));}\\ +\hlline{47\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{mat\textunderscore identity}\hlstd{}\hlsym{(}\hlstd{res}\hlsym{);}\\ +\hlline{48\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{mat\textunderscore copy}\hlstd{}\hlsym{(}\hlstd{mt}\hlsym{,\ }\hlstd{acc}\hlsym{{[}}\hlstd{}\hlkwa{false}\hlstd{}\hlsym{{]});}\\ +\hlline{49\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{bool\ }\hlstd{cur\ }\hlsym{=\ }\hlstd{}\hlkwa{false}\hlstd{}\hlsym{;}\\ +\hlline{50\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{for\ }\hlstd{}\hlsym{(;;)\ \{}\\ +\hlline{51\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{pow\ }\hlsym{\&\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ \{}\\ +\hlline{52\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{mat\textunderscore copy}\hlstd{}\hlsym{(}\hlstd{res}\hlsym{,\ }\hlstd{acc}\hlsym{{[}!}\hlstd{cur}\hlsym{{]});}\\ +\hlline{53\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{mat\textunderscore mult}\hlstd{}\hlsym{(}\hlstd{acc}\hlsym{{[}!}\hlstd{cur}\hlsym{{]},\ }\hlstd{acc}\hlsym{{[}}\hlstd{cur}\hlsym{{]},\ }\hlstd{res}\hlsym{);}\\ +\hlline{54\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{55\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{pow\ }\hlsym{$>$$>$=\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{56\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{pow\ }\hlsym{==\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{)\ }\hlstd{}\hlkwa{break}\hlstd{}\hlsym{;}\\ +\hlline{57\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{mat\textunderscore mult}\hlstd{}\hlsym{(}\hlstd{acc}\hlsym{{[}}\hlstd{cur}\hlsym{{]},\ }\hlstd{acc}\hlsym{{[}}\hlstd{cur}\hlsym{{]},\ }\hlstd{acc}\hlsym{{[}!}\hlstd{cur}\hlsym{{]});}\\ +\hlline{58\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{cur\ }\hlsym{=\ !}\hlstd{cur}\hlsym{;}\\ +\hlline{59\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{60\ }\hlstd{}\hlsym{\}}\\ +\hlline{61\ }\hlstd{}\\ +\hlline{62\ }\hlkwb{void\ }\hlstd{}\hlkwd{mat\textunderscore print}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ }\hlstd{Mat}\hlsym{\&\ }\hlstd{mt}\hlsym{)\ \{}\\ +\hlline{63\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ int\ }\hlstd{n\ }\hlsym{=\ }\hlstd{mt}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{();}\\ +\hlline{64\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ int\ }\hlstd{m\ }\hlsym{=\ }\hlstd{mt}\hlsym{{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{();}\\ +\hlline{65\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{n}\hlsym{)\ \{}\\ +\hlline{66\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{j}\hlsym{,\ }\hlstd{m}\hlsym{)\ \{}\\ +\hlline{67\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{mt}\hlsym{{[}}\hlstd{i}\hlsym{{]}{[}}\hlstd{j}\hlsym{{]}\ $<$$<$\ }\hlstd{}\hlstr{"\ "}\hlstd{}\hlsym{;}\\ +\hlline{68\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{69\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{endl}\hlsym{;}\\ +\hlline{70\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{71\ }\hlstd{}\hlsym{\}}\\ +\hlline{72\ }\hlstd{}\\ +\hlline{73\ }\hldir{\#define\ MIN\textunderscore CHAR\ 32}\\ +\hlline{74\ }\hlstd{}\hldir{\#define\ MAX\textunderscore CHAR\ 127}\\ +\hlline{75\ }\hlstd{}\hldir{\#define\ N}\hlstd{\ \ }\hldir{(MAX\textunderscore CHAR\ {-}\ MIN\textunderscore CHAR\ +\ 1)}\\ +\hlline{76\ }\hlstd{}\\ +\hlline{77\ }\hldir{\#define\ in\textunderscore range(Char)\ (MIN\textunderscore CHAR\ $<$=\ (Char)\ $<$=\ MAX\textunderscore CHAR)}\\ +\hlline{78\ }\hlstd{}\hldir{\#define\ charcode(Char)\ ((Char)\ {-}\ MIN\textunderscore CHAR)}\\ +\hlline{79\ }\hlstd{}\\ +\hlline{80\ }\hldir{\#define\ Max\textunderscore rule\ 1024}\\ +\hlline{81\ }\hlstd{}\hlkwb{int\ }\hlstd{}\hlkwd{main}\hlstd{}\hlsym{()\ \{}\\ +\hlline{82\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{ncases}\hlsym{;}\\ +\hlline{83\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{char\ }\hlstd{buf}\hlsym{{[}}\hlstd{Max\textunderscore rule}\hlsym{{]};}\\ +\hlline{84\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{char\ }\hlstd{chr}\hlsym{;}\\ +\hlline{85\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{scanf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%u}\hlesc{$\backslash$n}\hlstr{"}\hlstd{}\hlsym{,\ \&}\hlstd{ncases}\hlsym{);}\\ +\hlline{86\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{ci}\hlsym{,\ }\hlstd{ncases}\hlsym{)\ \{}\\ +\hlline{87\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{nrules}\hlsym{;}\\ +\hlline{88\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{scanf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%u}\hlesc{$\backslash$n}\hlstr{"}\hlstd{}\hlsym{,\ \&}\hlstd{nrules}\hlsym{);}\\ +\hlline{89\ }\hlstd{\\ +\hlline{90\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlslc{//\ rules{[}i{]}{[}j{]}\ =\ cantidad\ de\ ocurrencias\ de\ Ai\ en\ la\ regla\ Aj\ {-}$>$\ ...}\\ +\hlline{91\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{Mat\ }\hlkwd{rules}\hlstd{}\hlsym{(}\hlstd{N}\hlsym{,\ }\hlstd{}\hlkwd{Row}\hlstd{}\hlsym{(}\hlstd{N}\hlsym{,\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{));}\\ +\hlline{92\ }\hlstd{\\ +\hlline{93\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{mat\textunderscore identity}\hlstd{}\hlsym{(}\hlstd{rules}\hlsym{);}\\ +\hlline{94\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{ri}\hlsym{,\ }\hlstd{nrules}\hlsym{)\ \{}\\ +\hlline{95\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{scanf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%c{-}$>$\%s}\hlesc{$\backslash$n}\hlstr{"}\hlstd{}\hlsym{,\ \&}\hlstd{chr}\hlsym{,\ }\hlstd{buf}\hlsym{);}\\ +\hlline{96\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{assert}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{in\textunderscore range}\hlstd{}\hlsym{(}\hlstd{chr}\hlsym{));}\\ +\hlline{97\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{N}\hlsym{)\ }\hlstd{rules}\hlsym{{[}}\hlstd{i}\hlsym{{]}{[}}\hlstd{}\hlkwd{charcode}\hlstd{}\hlsym{(}\hlstd{chr}\hlsym{){]}\ =\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{98\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{const\ int\ }\hlstd{rule\textunderscore len\ }\hlsym{=\ }\hlstd{}\hlkwd{strlen}\hlstd{}\hlsym{(}\hlstd{buf}\hlsym{);}\\ +\hlline{99\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{rule\textunderscore len}\hlsym{)\ \{}\\ +\hlline{100\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{assert}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{in\textunderscore range}\hlstd{}\hlsym{(}\hlstd{buf}\hlsym{{[}}\hlstd{i}\hlsym{{]}));}\\ +\hlline{101\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{rules}\hlsym{{[}}\hlstd{}\hlkwd{charcode}\hlstd{}\hlsym{(}\hlstd{buf}\hlsym{{[}}\hlstd{i}\hlsym{{]}){]}{[}}\hlstd{}\hlkwd{charcode}\hlstd{}\hlsym{(}\hlstd{chr}\hlsym{){]}++;}\\ +\hlline{102\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{103\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{104\ }\hlstd{\\ +\hlline{105\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{nqueries}\hlsym{;}\\ +\hlline{106\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{pow}\hlsym{;}\\ +\hlline{107\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{scanf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%u}\hlesc{$\backslash$n}\hlstr{"}\hlstd{}\hlsym{,\ \&}\hlstd{nqueries}\hlsym{);}\\ +\hlline{108\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{qi}\hlsym{,\ }\hlstd{nqueries}\hlsym{)\ \{}\\ +\hlline{109\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{Mat\ }\hlkwd{input}\hlstd{}\hlsym{(}\hlstd{N}\hlsym{,\ }\hlstd{}\hlkwd{Row}\hlstd{}\hlsym{(}\hlstd{}\hlnum{1}\hlstd{}\hlsym{,\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{));}\\ +\hlline{110\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{scanf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%s\ \%c\ \%u}\hlesc{$\backslash$n}\hlstr{"}\hlstd{}\hlsym{,\ }\hlstd{buf}\hlsym{,\ \&}\hlstd{chr}\hlsym{,\ \&}\hlstd{pow}\hlsym{);}\\ +\hlline{111\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlslc{//\ procesar\ regla}\\ +\hlline{112\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{const\ int\ }\hlstd{input\textunderscore len\ }\hlsym{=\ }\hlstd{}\hlkwd{strlen}\hlstd{}\hlsym{(}\hlstd{buf}\hlsym{);}\\ +\hlline{113\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{input\textunderscore len}\hlsym{)\ \{}\\ +\hlline{114\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{assert}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{in\textunderscore range}\hlstd{}\hlsym{(}\hlstd{buf}\hlsym{{[}}\hlstd{i}\hlsym{{]}));}\\ +\hlline{115\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{input}\hlsym{{[}}\hlstd{}\hlkwd{charcode}\hlstd{}\hlsym{(}\hlstd{buf}\hlsym{{[}}\hlstd{i}\hlsym{{]}){]}{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}++;}\\ +\hlline{116\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{117\ }\hlstd{\\ +\hlline{118\ }}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{Mat\ }\hlkwd{pow\textunderscore rules}\hlstd{}\hlsym{(}\hlstd{N}\hlsym{,\ }\hlstd{}\hlkwd{Row}\hlstd{}\hlsym{(}\hlstd{N}\hlsym{,\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{));}\\ +\hlline{119\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{mat\textunderscore pow}\hlstd{}\hlsym{(}\hlstd{rules}\hlsym{,\ }\hlstd{pow}\hlsym{,\ }\hlstd{pow\textunderscore rules}\hlsym{);}\\ +\hlline{120\ }\hlstd{\\ +\hlline{121\ }}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{Mat\ }\hlkwd{result}\hlstd{}\hlsym{(}\hlstd{N}\hlsym{,\ }\hlstd{}\hlkwd{Row}\hlstd{}\hlsym{(}\hlstd{}\hlnum{1}\hlstd{}\hlsym{,\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{));}\\ +\hlline{122\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{mat\textunderscore mult}\hlstd{}\hlsym{(}\hlstd{pow\textunderscore rules}\hlsym{,\ }\hlstd{input}\hlsym{,\ }\hlstd{result}\hlsym{);}\\ +\hlline{123\ }\hlstd{\\ +\hlline{124\ }}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{cout\ }\hlsym{$<$$<$\ }\hlstd{result}\hlsym{{[}}\hlstd{}\hlkwd{charcode}\hlstd{}\hlsym{(}\hlstd{chr}\hlsym{){]}{[}}\hlstd{}\hlnum{0}\hlstd{}\hlsym{{]}\ $<$$<$\ }\hlstd{endl}\hlsym{;}\\ +\hlline{125\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{126\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{127\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{128\ }\hlstd{}\hlsym{\}}\hlstd{}\\ +\mbox{} +\normalfont +\shorthandon{"} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/informe.tex b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/informe.tex new file mode 100644 index 0000000..2b670bb --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/informe.tex @@ -0,0 +1,118 @@ +%% SECCION documentclass %% +%%---------------------------------------------------------------------------%% +\documentclass{article} + +%%---------------------------------------------------------------------------%% +%% SECCION usepackage %% +%%---------------------------------------------------------------------------%% +\usepackage{amsmath, amsthm} +\usepackage[spanish,activeacute]{babel} +\usepackage{caratula} +\usepackage{a4wide} +\usepackage{hyperref} +\usepackage{fancyhdr} +\usepackage{dsfont} +% \usepackage{moreverb} +\usepackage{graphicx} % Para el logo magico! +\usepackage{capt-of} +\usepackage{afterpage} +\usepackage{float} +\usepackage{amssymb} +\usepackage{amsmath} +\usepackage[latin1]{inputenc} +\usepackage{subfigure} +\usepackage{algorithm} +\usepackage{algorithmic} +\usepackage[dvipsnames,usenames]{color} +\usepackage{amsfonts} +\usepackage{code_color} +\usepackage{amsthm} +\usepackage{marvosym} +%\usepackage{minipage} + +%%---------------------------------------------------------------------------%% +%% SECCION opciones %% +%%---------------------------------------------------------------------------%% +\parskip = 11 pt +\headheight = 13.1pt +\pagestyle {fancy} +\definecolor{orange}{rgb}{1,0.5,0} + +\addtolength{\headwidth}{1.0in} + +\addtolength{\oddsidemargin}{-0.5in} +\addtolength{\textwidth}{1.0in} +\addtolength{\topmargin}{-0.8in} +\addtolength{\textheight}{0.7in} + +%%%---------------------------------------------------------------------------%% +%%% SECCION listings %% +%%%---------------------------------------------------------------------------%% +%\usepackage{listings} +%\lstset{ +% language=C++, +% basicstyle=\ttfamily \small, +% keepspaces=true, +% flexiblecolumns=false, +% basewidth={0.5em,0.45em}, +% keywordstyle=\ttfamily \bfseries \hlkwa, +% tabsize=4 +%} + +\newcommand{\Nat}{\mathbb{N}} +\newcommand{\Int}{\mathbb{Z}} +\newcommand{\Real}{\mathbb{R}} +\newcommand{\tq}{\ensuremath{\,|\,}} +\newcommand{\imp}{\ensuremath{\Rightarrow}} + +%%---------------------------------------------------------------------------%% +%% SECCION document %% +%%---------------------------------------------------------------------------%% +\begin{document} +\renewcommand{\chaptername}{Parte } +\input{trans_algorithmic.tex} +%%---- Caratula -------------------------------------------------------------%% +\materia{Problemas, algoritmos y programación (2010)} +\titulo{Trabajo Pr'actico nº 4} + + +\integrante{Barenbaum, Pablo}{124/04}{foones@gmail.com} +\integrante{Mart'inez, Federico}{17/06}{federicoemartinez@gmail.com} +\integrante{Sainz-Tr'apaga, Gonzalo}{454/06}{gonzalo@sainztrapaga.com.ar} +\grupo{Grupo 1} +\resumen{ +El siguiente informe presenta la resolución a los 4 problemas correspondientes al cuarto trabajo pr\'actico de la materia Problemas, Algoritmos y Programación en el primer cuatrimestre del 2010. En el mismo se encuentra la explicación del algoritmo utilizado para resolver cada problema, así como también la implementación en C++ de los mismos. +} + +% TOC, usa estilos locos +\maketitle +\pagestyle{empty} +{ +\fancypagestyle{plain} + { + \fancyhead{} + \fancyfoot{} + \renewcommand{\headrulewidth}{0.0pt} + } % clear header and footer of plain page because of ToC +%\tableofcontents +} + +\newpage +% arreglos los estilos para el resto del documento, y +% reseteo los numeros de pagina para que queden bien +\pagenumbering{arabic} +\fancypagestyle{plain} { + \fancyhead[LO]{Barenbaum, Martínez, Sainz Trápaga} + \fancyhead[C]{} + \fancyhead[RO]{P\'agina \thepage\ de \pageref{LastPage}} + \fancyfoot{} + \renewcommand{\headrulewidth}{0.4pt} +} +\pagestyle{plain} +\input{disgruntled} +\input{gnu} +\input{walk} +\input{ballroom} +\label{LastPage} +\end{document} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/trans_algorithmic.tex b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/trans_algorithmic.tex new file mode 100644 index 0000000..9ce8c65 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/trans_algorithmic.tex @@ -0,0 +1,15 @@ +\renewcommand{\algorithmicrequire}{\textcolor{blue}{\textbf{Requiere:}}} +\renewcommand{\algorithmicensure}{\textbf{Devuelve:}} +\renewcommand{\algorithmicend}{\textbf{Fin}} +\renewcommand{\algorithmicif}{\textcolor{blue}{\textbf{Si}}} +\renewcommand{\algorithmicthen}{\textcolor{blue}{}} %%\textbf{entonces}}} +\renewcommand{\algorithmicelse}{\textcolor{red}{\textbf{Si no}}} +\renewcommand{\algorithmicelsif }{\textcolor{blue}{\textbf{Si no y}}} +\renewcommand{\algorithmicendif}{\textcolor{blue}{\textbf{Fin si}}} +\renewcommand{\algorithmicfor}{\textcolor{ForestGreen}{\textbf{Para}}} +\renewcommand{\algorithmicendfor}{\textcolor{ForestGreen}{\textbf{Fin para}}} +\renewcommand{\algorithmicwhile}{\textcolor{ForestGreen}{\textbf{Mientras}}} +\renewcommand{\algorithmicendwhile}{\textcolor{ForestGreen}{\textbf{Fin mientras}}} +\renewcommand{\algorithmicdo}{\textcolor{ForestGreen}{}} %%\textbf{hacer}}} +\renewcommand{\algorithmicreturn}{\textbf{Devolver}} +\floatname{algorithm}{Algoritmo} diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/walk.tex b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/walk.tex new file mode 100644 index 0000000..b45dbea --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/doc/walk.tex @@ -0,0 +1,270 @@ +\newcommand{\Null}{\textsc{null}} +\section{3980 - Walk} +\textbf{Problema:} +Se tiene un conjunto de pol\'igonos (en $\Int^2$) que representan curvas de nivel. +No hay intersecciones entre segmentos de dos pol\'igonos distintos, ni entre dos +segmentos de un mismo pol\'igono. Dados dos puntos A y B (que no est\'an contenidos +en el borde de ninguna de las curvas de nivel), determinar la m\'inima altura que +se debe subir/bajar para llegar desde A hasta B, asumiendo que las \'areas entre +las curvas de nivel son \'optimas. + +\subsection{Resoluci\'on} + +\subsubsection{Modelo del problema} +Dado que no hay intersecciones entre dos segmentos de un pol\'igono, +todos los pol\'igonos tienen un ``interior'' y un ``exterior'' +claramente definido. + +Adem\'as, dado que no hay intersecciones entre dos pol\'igonos distintos, +se puede observar que hay un bosque de pol\'igonos impl\'icito en el problema. +Dados dos pol\'igonos $p$ y $q$, notamos $q \subset p$ si todos los v\'ertices +de $q$ est\'an en el interior de $p$. Los hijos de un pol\'igono $p$ se definen +de la siguiente manera: + +$hijos(p) = \{q \tq q \subset p \,\land \not\exists p'.(q \subset p' \subset p) \}$ + +Es decir, los hijos de un pol\'igono son aquellos que est\'an inmediatamente +adentro. Las hojas son los pol\'igonos que no contienen a ning\'un otro pol\'igono. +En la implementaci\'on, se trabaja directamente con el bosque de pol\'igonos. +Para simplificar la demostraci\'on, se puede considerar que se tiene un \'arbol +de pol\'igonos, agregando como ra\'iz un pol\'igono suficientemente grande que contenga +a todos los dem\'as. (Esto no cambia la soluci\'on porque el camino que +requiere menos subidas/bajadas no atraviesa esta curva de nivel). + +Dado un punto $x \in \Real^2$, notamos $x \in p$ sii $x$ est\'a +adentro del pol\'igono $p$. +El \'arbol se interpreta de la siguiente manera: el nodo del \'arbol +asociado al pol\'igono $p$ representa todos los puntos +$\{x \tq x \in p \,\land x \not\in hijos(p)\}$. +Un camino en el \'arbol representa un +camino entre puntos del plano (cocientando a los puntos mediante +la relaci\'on de equivalencia $x \equiv y$ sii $\forall p. (x \in p \iff y \in p)$). +Atravesar el eje que conecta al nodo $p$ con su hijo $q$ +equivale a cruzar la curva de nivel representada por $q$. + +Dado un punto $x$ se define $L(x)$ como el pol\'igono m\'as chico que +lo contiene: + +$L(x) = p \text{ tal que } x \in p \,\land \not\exists q. (q < p \,\land\, x \in q)$ + +Dado un punto $x$, se puede ver que $x$ est\'a +adentro de todos los pol\'igonos en el camino que va desde la ra\'iz del +\'arbol hasta $L(x)$, y que adem\'as no est\'a contenido en ning\'un otro nodo. + +Atravesar una curva de nivel siempre agrega un costo no negativo +de subida o de bajada. Por lo tanto, el \'unico camino +simple entre $L(A)$ y $L(B)$, que es m\'inimo en cantidad de ejes, +tambi\'en debe ser m\'inimo en cantidad de distancia subida/bajada. + +\subsubsection{Cuestiones de implementaci\'on} + +Para encontrar el camino simple entre $L(A)$ y $L(B)$ se usa +la siguiente propiedad de los pol\'igonos: $p \subset q \imp area(p) < area(q)$. +Esto es verdad porque no hay intersecciones de ning\'un tipo. +Por lo tanto, si se ordenan los pol\'igonos por \'area creciente +y se los recorre en ese orden, se visitan los nodos del \'arbol +de manera tal que, al momento de visitar el nodo $p$, +todos los nodos en $hijos(p)$ ya fueron visitados. + +\begin{algorithm}[H] +\begin{algorithmic} +\caption{Encontrar el camino entre $L(A)$ y $L(B)$} +\STATE Ordenar los pol\'igonos por \'area. +\STATE $ramaA := []$ +\STATE $ramaB := []$ +\FOR{cada pol\'igono $p$, por \'area creciente} + \IF{$A \in p \land B \in p$} + \STATE terminar, devolver $(ramaA, ramaB)$ + \ELSIF{$A \in p$} + \STATE agregar $p$ a $ramaA$ + \ELSIF{$B \in p$} + \STATE agregar $p$ a $ramaB$ + \ENDIF +\ENDFOR +\end{algorithmic} +\end{algorithm} + +Sea $L(A,B)$ el pol\'igono m\'as chico que contiene a $A$ y a $B$, es decir:\\ +$L(A,B) = p \text{ tal que } A \in p \,\land B \in p \,\land \not\exists q.(q < p \,\land A \in q \,\land B \in q)$ + +El algoritmo se basa en el hecho de que el camino simple desde $L(A)$ +hasta $L(B)$ es el camino que va desde $L(A)$ hasta $L(A,B)$ m\'as el camino +que va desde $L(A,B)$ hasta $L(B)$. +El invariante es que, despu\'es de la iteraci\'on correspondiente al pol\'igono $p$, +$ramaA$ contiene los nodos del camino simple que va desde $L(A,B)$ hasta $L(A)$ +y cuya \'area no exceda el \'area de $p$. (Y an\'alogamente para $B$). + +En la implementaci\'on no se construye la lista, sino que directamente +se suman las distancias ascendidas o descendidas. + +\subsubsection{Complejidad} + +La entrada consta de $P$ pol\'igonos. Cada pol\'igono puede tener +una cantidad variable de v\'ertices. La cantidad total de v\'ertices +es $V$. + +Primero se calcula el \'area de cada pol\'igono, usando el m\'etodo +usual (sumar los productos vectoriales y tomar m\'odulo). +Esto requiere calcular productos vectoriales usando cada +v\'ertice una cantidad constante de veces. Se hace para cada +v\'ertice de cada pol\'igono y por lo tanto la complejidad +temporal es $O(V)$. + +Una vez calculadas las \'areas, ordenar los pol\'igonos por \'area +tiene complejidad $O(P \log P)$. + +Para verificar si un punto $x$ est\'a contenido en un pol\'igono, +se elige un punto $y$ afuera del pol\'igono, y se determina si +la cantidad de veces que el segmento $\bar{xy}$ se +cruza con un segmento del pol\'igono es par o impar, usando +nuevamente productos vectoriales. +Esto requiere mirar cada punto del pol\'igono una cantidad +constante de veces. En peor caso, $L(A,B)$ es la ra\'iz +del \'arbol y se visitan todos los pol\'igonos una vez. +El costo es $O(P + V) \subseteq O(V)$. + +La complejidad temporal de todo el algoritmo es entonces +$O(P \log P + V)$. + +\subsection{Implementación} + +\noindent +\ttfamily +\shorthandoff{"}\\ +\hlstd{}\hlline{\ 1\ }\hldir{\#include\ $<$iostream$>$}\\ +\hlline{\ 2\ }\hlstd{}\hldir{\#include\ $<$algorithm$>$}\\ +\hlline{\ 3\ }\hlstd{}\hldir{\#include\ $<$vector$>$}\\ +\hlline{\ 4\ }\hlstd{}\hldir{\#include\ $<$cassert$>$}\\ +\hlline{\ 5\ }\hlstd{}\hldir{\#include\ $<$cstdio$>$}\\ +\hlline{\ 6\ }\hlstd{}\\ +\hlline{\ 7\ }\hlkwa{using\ namespace\ }\hlstd{std}\hlsym{;}\\ +\hlline{\ 8\ }\hlstd{}\\ +\hlline{\ 9\ }\hlkwc{typedef\ }\hlstd{pair}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{,\ }\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$\ }\hlstd{Coord}\hlsym{;}\\ +\hlline{10\ }\hlstd{}\hlkwc{typedef\ }\hlstd{vector}\hlsym{$<$}\hlstd{Coord}\hlsym{$>$\ }\hlstd{Poly}\hlsym{;}\\ +\hlline{11\ }\hlstd{}\\ +\hlline{12\ }\hldir{\#define\ x\ first}\\ +\hlline{13\ }\hlstd{}\hldir{\#define\ y\ second}\\ +\hlline{14\ }\hlstd{}\\ +\hlline{15\ }\hldir{\#define\ forsn(i,\ s,\ n)\ for\ (int\ i\ =\ (s);\ i\ $<$\ (n);\ i++)}\\ +\hlline{16\ }\hlstd{}\hldir{\#define\ forn(i,\ n)\ forsn\ (i,\ 0,\ n)}\\ +\hlline{17\ }\hlstd{}\\ +\hlline{18\ }\hldir{\#define\ coord\textunderscore sub(c1,\ c2)\ Coord((c1).x\ {-}\ (c2).x,\ (c1).y\ {-}\ (c2).y)}\\ +\hlline{19\ }\hlstd{}\\ +\hlline{20\ }\hlkwb{bool\ }\hlstd{}\hlkwd{cross\textunderscore prod\textunderscore sign}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ }\hlstd{Coord}\hlsym{\&\ }\hlstd{p}\hlsym{,\ }\hlstd{}\hlkwb{const\ }\hlstd{Coord}\hlsym{\&\ }\hlstd{q}\hlsym{)\ \{}\\ +\hlline{21\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ long\ long\ int\ }\hlstd{pxqy\ }\hlsym{=\ ((}\hlstd{}\hlkwb{long\ long\ int}\hlstd{}\hlsym{)}\hlstd{p}\hlsym{.}\hlstd{x}\hlsym{)\ {*}\ }\hlstd{q}\hlsym{.}\hlstd{y}\hlsym{;}\\ +\hlline{22\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ long\ long\ int\ }\hlstd{qxpy\ }\hlsym{=\ ((}\hlstd{}\hlkwb{long\ long\ int}\hlstd{}\hlsym{)}\hlstd{q}\hlsym{.}\hlstd{x}\hlsym{)\ {*}\ }\hlstd{p}\hlsym{.}\hlstd{y}\hlsym{;}\\ +\hlline{23\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{pxqy\ }\hlsym{$>$=\ }\hlstd{qxpy}\hlsym{;}\\ +\hlline{24\ }\hlstd{}\hlsym{\}}\\ +\hlline{25\ }\hlstd{}\\ +\hlline{26\ }\hlkwb{bool\ }\hlstd{}\hlkwd{se\textunderscore cruzan}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ }\hlstd{Coord}\hlsym{\&\ }\hlstd{s0}\hlsym{,\ }\hlstd{}\hlkwb{const\ }\hlstd{Coord}\hlsym{\&\ }\hlstd{s1}\hlsym{,\ }\hlstd{}\hlkwb{const\ }\hlstd{Coord}\hlsym{\&\ }\hlstd{t0}\hlsym{,\ }\hlstd{}\hlkwb{const\ }\hlstd{Coord}\hlsym{\&\ }\hlstd{t1}\hlsym{)\ \{}\\ +\hlline{27\ }\hlstd{}\hldir{\#define\ se\textunderscore cruzan1(a,\ b,\ c,\ d)\ (cross\textunderscore prod\textunderscore sign(coord\textunderscore sub(a,\ c),\ coord\textunderscore sub(d,\ c))\ !=\ cross\textunderscore prod\textunderscore sign(}\Righttorque\\ +\hlline{28\ }\hldir{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hldir{coord\textunderscore sub(b,\ c),\ coord\textunderscore sub(d,\ c)))}\\ +\hlline{29\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{}\hlkwd{se\textunderscore cruzan1}\hlstd{}\hlsym{(}\hlstd{s0}\hlsym{,\ }\hlstd{s1}\hlsym{,\ }\hlstd{t0}\hlsym{,\ }\hlstd{t1}\hlsym{)\ \&\&\ }\hlstd{}\hlkwd{se\textunderscore cruzan1}\hlstd{}\hlsym{(}\hlstd{t0}\hlsym{,\ }\hlstd{t1}\hlsym{,\ }\hlstd{s0}\hlsym{,\ }\hlstd{s1}\hlsym{);}\\ +\hlline{30\ }\hlstd{}\hldir{\#undef\ se\textunderscore cruzan1}\\ +\hlline{31\ }\hlstd{}\hlsym{\}}\\ +\hlline{32\ }\hlstd{}\\ +\hlline{33\ }\hlkwb{bool\ }\hlstd{}\hlkwd{esta\textunderscore adentro}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ }\hlstd{Coord}\hlsym{\&\ }\hlstd{punto}\hlsym{,\ }\hlstd{}\hlkwb{const\ }\hlstd{Poly}\hlsym{\&\ }\hlstd{poly}\hlsym{)\ \{}\\ +\hlline{34\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlslc{//\ buscar\ un\ punto\ afuera}\\ +\hlline{35\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{maxx\ }\hlsym{=\ }\hlstd{punto}\hlsym{.}\hlstd{x}\hlsym{;}\\ +\hlline{36\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ (}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{)}\hlstd{poly}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{())\ \{}\\ +\hlline{37\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{maxx\ }\hlsym{=\ }\hlstd{}\hlkwd{max}\hlstd{}\hlsym{(}\hlstd{maxx}\hlsym{,\ }\hlstd{poly}\hlsym{{[}}\hlstd{i}\hlsym{{]}.}\hlstd{x}\hlsym{);}\\ +\hlline{38\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{39\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{maxx}\hlsym{++;}\\ +\hlline{40\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ }\hlstd{Coord\ }\hlkwd{externo}\hlstd{}\hlsym{(}\hlstd{maxx}\hlsym{,\ }\hlstd{punto}\hlsym{.}\hlstd{y\ }\hlsym{+\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{);}\\ +\hlline{41\ }\hlstd{\\ +\hlline{42\ }}\hlstd{\ \ \ \ }\hlstd{}\hlslc{//\ ver\ si\ la\ cantidad\ de\ cruces\ es\ par\ o\ impar}\\ +\hlline{43\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ int\ }\hlstd{n\ }\hlsym{=\ }\hlstd{poly}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{();}\\ +\hlline{44\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{bool\ }\hlstd{adentro\ }\hlsym{=\ }\hlstd{}\hlkwa{false}\hlstd{}\hlsym{;}\\ +\hlline{45\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{n}\hlsym{)\ }\hlstd{adentro\ \textasciicircum }\hlsym{=\ }\hlstd{}\hlkwd{se\textunderscore cruzan}\hlstd{}\hlsym{(}\hlstd{punto}\hlsym{,\ }\hlstd{externo}\hlsym{,\ }\hlstd{poly}\hlsym{{[}}\hlstd{i}\hlsym{{]},\ }\hlstd{poly}\hlsym{{[}(}\hlstd{i\ }\hlsym{+\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ \%\ }\hlstd{n}\hlsym{{]});}\\ +\hlline{46\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{adentro}\hlsym{;}\\ +\hlline{47\ }\hlstd{}\hlsym{\}}\\ +\hlline{48\ }\hlstd{}\\ +\hlline{49\ }\hlkwb{long\ long\ int\ }\hlstd{}\hlkwd{doble\textunderscore area}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ }\hlstd{Poly}\hlsym{\&\ }\hlstd{poly}\hlsym{)\ \{}\\ +\hlline{50\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ int\ }\hlstd{n\ }\hlsym{=\ }\hlstd{poly}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{();}\\ +\hlline{51\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{long\ long\ int\ }\hlstd{s\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{52\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{n}\hlsym{)\ \{}\\ +\hlline{53\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{const\ int\ }\hlstd{j\ }\hlsym{=\ (}\hlstd{i\ }\hlsym{+\ }\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ \%\ }\hlstd{n}\hlsym{;}\\ +\hlline{54\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{s\ }\hlsym{+=\ ((}\hlstd{}\hlkwb{long\ long\ int}\hlstd{}\hlsym{)}\hlstd{poly}\hlsym{{[}}\hlstd{i}\hlsym{{]}.}\hlstd{x}\hlsym{)\ {*}\ }\hlstd{poly}\hlsym{{[}}\hlstd{j}\hlsym{{]}.}\hlstd{y\ }\hlsym{{-}\ ((}\hlstd{}\hlkwb{long\ long\ int}\hlstd{}\hlsym{)}\hlstd{poly}\hlsym{{[}}\hlstd{i}\hlsym{{]}.}\hlstd{y}\hlsym{)\ {*}\ }\hlstd{poly}\hlsym{{[}}\hlstd{j}\hlsym{{]}.}\hlstd{x}\hlsym{;}\\ +\hlline{55\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{56\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{s\ }\hlsym{$<$\ }\hlstd{}\hlnum{0\ }\hlstd{?\ }\hlsym{{-}}\hlstd{s\ }\hlsym{:\ }\hlstd{s}\hlsym{;}\\ +\hlline{57\ }\hlstd{}\hlsym{\}}\\ +\hlline{58\ }\hlstd{}\\ +\hlline{59\ }\hlkwc{typedef\ }\hlstd{vector}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$\ }\hlstd{vint}\hlsym{;}\\ +\hlline{60\ }\hlstd{}\hlkwc{typedef\ }\hlstd{vector}\hlsym{$<$}\hlstd{}\hlkwb{long\ long\ int}\hlstd{}\hlsym{$>$\ }\hlstd{vllint}\hlsym{;}\\ +\hlline{61\ }\hlstd{\\ +\hlline{62\ }vllint\ \textunderscore \textunderscore area2}\hlsym{;}\\ +\hlline{63\ }\hlstd{}\hlkwb{bool\ }\hlstd{}\hlkwd{cmp\textunderscore area2}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{int\ }\hlstd{i}\hlsym{,\ }\hlstd{}\hlkwb{int\ }\hlstd{j}\hlsym{)\ \{}\\ +\hlline{64\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{\textunderscore \textunderscore area2}\hlsym{{[}}\hlstd{i}\hlsym{{]}\ $<$\ }\hlstd{\textunderscore \textunderscore area2}\hlsym{{[}}\hlstd{j}\hlsym{{]};}\\ +\hlline{65\ }\hlstd{}\hlsym{\}}\\ +\hlline{66\ }\hlstd{}\hlkwb{void\ }\hlstd{}\hlkwd{minwalk}\hlstd{}\hlsym{(}\hlstd{}\hlkwb{const\ }\hlstd{vector}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$\&\ }\hlstd{heights}\hlsym{,\ }\hlstd{}\hlkwb{const\ }\hlstd{vector}\hlsym{$<$}\hlstd{Poly}\hlsym{$>$\&\ }\hlstd{curves}\hlsym{,\ }\hlstd{}\hlkwb{const\ }\hlstd{Coord}\hlsym{\&\ }\hlstd{pos\textunderscore alice}\hlsym{,\ }\hlstd{}\hlkwb{const\ }\Righttorque\\ +\hlline{67\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{Coord}\hlsym{\&\ }\hlstd{pos\textunderscore bob}\hlsym{)\ \{}\\ +\hlline{68\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ int\ }\hlstd{n\ }\hlsym{=\ }\hlstd{curves}\hlsym{.}\hlstd{}\hlkwd{size}\hlstd{}\hlsym{();}\\ +\hlline{69\ }\hlstd{\\ +\hlline{70\ }}\hlstd{\ \ \ \ }\hlstd{}\hlslc{//\ ordenar\ los\ poligonos\ por\ area}\\ +\hlline{71\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{\textunderscore \textunderscore area2\ }\hlsym{=\ }\hlstd{}\hlkwd{vllint}\hlstd{}\hlsym{(}\hlstd{n}\hlsym{);}\\ +\hlline{72\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{pi}\hlsym{,\ }\hlstd{n}\hlsym{)\ \{}\\ +\hlline{73\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{\textunderscore \textunderscore area2}\hlsym{{[}}\hlstd{pi}\hlsym{{]}\ =\ }\hlstd{}\hlkwd{doble\textunderscore area}\hlstd{}\hlsym{(}\hlstd{curves}\hlsym{{[}}\hlstd{pi}\hlsym{{]});}\\ +\hlline{74\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{75\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{vint\ }\hlkwd{ind}\hlstd{}\hlsym{(}\hlstd{n}\hlsym{,\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{);}\\ +\hlline{76\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{n}\hlsym{)\ }\hlstd{ind}\hlsym{{[}}\hlstd{i}\hlsym{{]}\ =\ }\hlstd{i}\hlsym{;}\\ +\hlline{77\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{sort}\hlstd{}\hlsym{(}\hlstd{ind}\hlsym{.}\hlstd{}\hlkwd{begin}\hlstd{}\hlsym{(),\ }\hlstd{ind}\hlsym{.}\hlstd{}\hlkwd{end}\hlstd{}\hlsym{(),\ }\hlstd{cmp\textunderscore area2}\hlsym{);}\\ +\hlline{78\ }\hlstd{\\ +\hlline{79\ }}\hlstd{\ \ \ \ }\hlstd{}\hlslc{//\ visitarlos\ en\ ese\ orden\ y\ calcular\ cuanto\ sube\ /\ baja}\\ +\hlline{80\ }\hlstd{}\hldir{\#define\ up\textunderscore down(H1,\ H2)\ if\ (H1\ $<$\ H2)\ \{\ cost\textunderscore up\ +=\ H2\ {-}\ H1;\ \}\ else\ \{\ cost\textunderscore down\ +=\ H1\ {-}\ H2;\ \}}\\ +\hlline{81\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{last\textunderscore height\textunderscore alice\ }\hlsym{=\ {-}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{,\ }\hlstd{last\textunderscore height\textunderscore bob\ }\hlsym{=\ {-}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{;}\\ +\hlline{82\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{cost\textunderscore up\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{,\ }\hlstd{cost\textunderscore down\ }\hlsym{=\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{83\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{i}\hlsym{,\ }\hlstd{n}\hlsym{)\ \{}\\ +\hlline{84\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{const\ int\ }\hlstd{j\ }\hlsym{=\ }\hlstd{ind}\hlsym{{[}}\hlstd{i}\hlsym{{]};}\\ +\hlline{85\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{const\ bool\ }\hlstd{contains\textunderscore alice\ }\hlsym{=\ }\hlstd{}\hlkwd{esta\textunderscore adentro}\hlstd{}\hlsym{(}\hlstd{pos\textunderscore alice}\hlsym{,\ }\hlstd{curves}\hlsym{{[}}\hlstd{j}\hlsym{{]});}\\ +\hlline{86\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{const\ bool\ }\hlstd{contains\textunderscore bob\ }\hlsym{=\ }\hlstd{}\hlkwd{esta\textunderscore adentro}\hlstd{}\hlsym{(}\hlstd{pos\textunderscore bob}\hlsym{,\ }\hlstd{curves}\hlsym{{[}}\hlstd{j}\hlsym{{]});}\\ +\hlline{87\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{contains\textunderscore alice\ }\hlsym{\&\&\ }\hlstd{contains\textunderscore bob}\hlsym{)\ \{}\\ +\hlline{88\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{break}\hlstd{}\hlsym{;}\\ +\hlline{89\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}\ }\hlstd{}\hlkwa{else\ if\ }\hlstd{}\hlsym{(}\hlstd{contains\textunderscore alice}\hlsym{)\ \{}\\ +\hlline{90\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{last\textunderscore height\textunderscore alice\ }\hlsym{!=\ {-}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ \{}\\ +\hlline{91\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{up\textunderscore down}\hlstd{}\hlsym{(}\hlstd{last\textunderscore height\textunderscore alice}\hlsym{,\ }\hlstd{heights}\hlsym{{[}}\hlstd{j}\hlsym{{]});}\\ +\hlline{92\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{93\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{last\textunderscore height\textunderscore alice\ }\hlsym{=\ }\hlstd{heights}\hlsym{{[}}\hlstd{j}\hlsym{{]};}\\ +\hlline{94\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}\ }\hlstd{}\hlkwa{else\ if\ }\hlstd{}\hlsym{(}\hlstd{contains\textunderscore bob}\hlsym{)\ \{}\\ +\hlline{95\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{last\textunderscore height\textunderscore bob\ }\hlsym{!=\ {-}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ \{}\\ +\hlline{96\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{up\textunderscore down}\hlstd{}\hlsym{(}\hlstd{heights}\hlsym{{[}}\hlstd{j}\hlsym{{]},\ }\hlstd{last\textunderscore height\textunderscore bob}\hlsym{);}\\ +\hlline{97\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{98\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{last\textunderscore height\textunderscore bob\ }\hlsym{=\ }\hlstd{heights}\hlsym{{[}}\hlstd{j}\hlsym{{]};}\\ +\hlline{99\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{100\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{101\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{if\ }\hlstd{}\hlsym{(}\hlstd{last\textunderscore height\textunderscore alice\ }\hlsym{!=\ {-}}\hlstd{}\hlnum{1\ }\hlstd{}\hlsym{\&\&\ }\hlstd{last\textunderscore height\textunderscore bob\ }\hlsym{!=\ {-}}\hlstd{}\hlnum{1}\hlstd{}\hlsym{)\ \{}\\ +\hlline{102\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{up\textunderscore down}\hlstd{}\hlsym{(}\hlstd{last\textunderscore height\textunderscore alice}\hlsym{,\ }\hlstd{last\textunderscore height\textunderscore bob}\hlsym{);}\\ +\hlline{103\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{104\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{printf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%i\ \%i}\hlesc{$\backslash$n}\hlstr{"}\hlstd{}\hlsym{,\ }\hlstd{cost\textunderscore up}\hlsym{,\ }\hlstd{cost\textunderscore down}\hlsym{);}\\ +\hlline{105\ }\hlstd{}\hlsym{\}}\\ +\hlline{106\ }\hlstd{}\\ +\hlline{107\ }\hlkwb{int\ }\hlstd{}\hlkwd{main}\hlstd{}\hlsym{()\ \{}\\ +\hlline{108\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ }\hlstd{Coord\ }\hlkwd{pos\textunderscore alice}\hlstd{}\hlsym{(}\hlstd{}\hlnum{0}\hlstd{}\hlsym{,\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{);}\\ +\hlline{109\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{const\ }\hlstd{Coord\ }\hlkwd{pos\textunderscore bob}\hlstd{}\hlsym{(}\hlstd{}\hlnum{100000}\hlstd{}\hlsym{,\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{);}\\ +\hlline{110\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{ncases}\hlsym{;}\\ +\hlline{111\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{scanf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%i}\hlesc{$\backslash$n}\hlstr{"}\hlstd{}\hlsym{,\ \&}\hlstd{ncases}\hlsym{);}\\ +\hlline{112\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{ci}\hlsym{,\ }\hlstd{ncases}\hlsym{)\ \{}\\ +\hlline{113\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{npolys}\hlsym{;}\\ +\hlline{114\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{scanf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%i}\hlesc{$\backslash$n}\hlstr{"}\hlstd{}\hlsym{,\ \&}\hlstd{npolys}\hlsym{);}\\ +\hlline{115\ }\hlstd{\\ +\hlline{116\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{vector}\hlsym{$<$}\hlstd{Poly}\hlsym{$>$\ }\hlstd{polys}\hlsym{;}\\ +\hlline{117\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{vector}\hlsym{$<$}\hlstd{}\hlkwb{int}\hlstd{}\hlsym{$>$\ }\hlstd{heights}\hlsym{;}\\ +\hlline{118\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{pi}\hlsym{,\ }\hlstd{npolys}\hlsym{)\ \{}\\ +\hlline{119\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{curve\textunderscore height}\hlsym{,\ }\hlstd{nverts}\hlsym{;}\\ +\hlline{120\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{scanf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%i\ \%i"}\hlstd{}\hlsym{,\ \&}\hlstd{curve\textunderscore height}\hlsym{,\ \&}\hlstd{nverts}\hlsym{);}\\ +\hlline{121\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{polys}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{Poly}\hlstd{}\hlsym{());}\\ +\hlline{122\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{forn\ }\hlstd{}\hlsym{(}\hlstd{vi}\hlsym{,\ }\hlstd{nverts}\hlsym{)\ \{}\\ +\hlline{123\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwb{int\ }\hlstd{vert\textunderscore x}\hlsym{,\ }\hlstd{vert\textunderscore y}\hlsym{;}\\ +\hlline{124\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{scanf}\hlstd{}\hlsym{(}\hlstd{}\hlstr{"\%i\ \%i"}\hlstd{}\hlsym{,\ \&}\hlstd{vert\textunderscore x}\hlsym{,\ \&}\hlstd{vert\textunderscore y}\hlsym{);}\\ +\hlline{125\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{polys}\hlsym{{[}}\hlstd{pi}\hlsym{{]}.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{}\hlkwd{Coord}\hlstd{}\hlsym{(}\hlstd{vert\textunderscore x}\hlsym{,\ }\hlstd{vert\textunderscore y}\hlsym{));}\\ +\hlline{126\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{127\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ \ \ \ \ }\hlstd{heights}\hlsym{.}\hlstd{}\hlkwd{push\textunderscore back}\hlstd{}\hlsym{(}\hlstd{curve\textunderscore height}\hlsym{);}\\ +\hlline{128\ }\hlstd{}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{129\ }\hlstd{\\ +\hlline{130\ }}\hlstd{\ \ \ \ \ \ \ \ }\hlstd{}\hlkwd{minwalk}\hlstd{}\hlsym{(}\hlstd{heights}\hlsym{,\ }\hlstd{polys}\hlsym{,\ }\hlstd{pos\textunderscore alice}\hlsym{,\ }\hlstd{pos\textunderscore bob}\hlsym{);}\\ +\hlline{131\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlsym{\}}\\ +\hlline{132\ }\hlstd{}\hlstd{\ \ \ \ }\hlstd{}\hlkwa{return\ }\hlstd{}\hlnum{0}\hlstd{}\hlsym{;}\\ +\hlline{133\ }\hlstd{}\hlsym{\}}\\ +\hlline{134\ }\hlstd{}\\ +\mbox{} +\normalfont +\shorthandon{"} diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/gnu/gnu.cpp b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/gnu/gnu.cpp new file mode 100644 index 0000000..1c77f99 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/gnu/gnu.cpp @@ -0,0 +1,128 @@ +#include +#include +#include +#include +#include + +using namespace std; + +typedef unsigned long long int lluint; + +typedef vector Row; +typedef vector Mat; + +#define forsn(i, s, n) for (int i = (s); i < (n); i++) +#define forn(i, n) forsn (i, 0, n) + +void mat_mult(const Mat& m1, const Mat& m2, Mat& res) { + const int n = m1.size(); + const int m = m2.size(); + const int p = m2[0].size(); + assert(m1[0].size() == m && res.size() == n && res[0].size() == p); + forn (i, n) forn (j, p) { + lluint s = 0; + forn (k, m) s += m1[i][k] * m2[k][j]; + res[i][j] = s; + } +} + +void mat_identity(Mat& mt) { + const int n = mt.size(); + assert(n == mt[0].size()); + forn (i, n) forn (j, n) { + mt[i][j] = i == j; + } +} + +void mat_copy(const Mat& in, Mat& out) { + const int n = in.size(); + const int m = in[0].size(); + assert(out.size() == in.size() && out[0].size() == in[0].size()); + forn (i, n) forn (j, m) out[i][j] = in[i][j]; +} + +void mat_pow(const Mat& mt, int pow, Mat& res) { + const int n = mt.size(); + vector acc(2, Mat(n, Row(n, 0))); + mat_identity(res); + mat_copy(mt, acc[false]); + bool cur = false; + for (;;) { + if (pow & 1) { + mat_copy(res, acc[!cur]); + mat_mult(acc[!cur], acc[cur], res); + } + pow >>= 1; + if (pow == 0) break; + mat_mult(acc[cur], acc[cur], acc[!cur]); + cur = !cur; + } +} + +void mat_print(const Mat& mt) { + const int n = mt.size(); + const int m = mt[0].size(); + forn (i, n) { + forn (j, m) { + cout << mt[i][j] << " "; + } + cout << endl; + } +} + +#define MIN_CHAR 32 +#define MAX_CHAR 127 +#define N (MAX_CHAR - MIN_CHAR + 1) + +#define in_range(Char) (MIN_CHAR <= (Char) <= MAX_CHAR) +#define charcode(Char) ((Char) - MIN_CHAR) + +#define Max_rule 1024 +int main() { + int ncases; + char buf[Max_rule]; + char chr; + scanf("%u\n", &ncases); + forn (ci, ncases) { + int nrules; + scanf("%u\n", &nrules); + + // rules[i][j] = cantidad de ocurrencias de Ai en la regla Aj -> ... + Mat rules(N, Row(N, 0)); + + mat_identity(rules); + forn (ri, nrules) { + scanf("%c->%s\n", &chr, buf); + assert(in_range(chr)); + forn (i, N) rules[i][charcode(chr)] = 0; + const int rule_len = strlen(buf); + forn (i, rule_len) { + assert(in_range(buf[i])); + rules[charcode(buf[i])][charcode(chr)]++; + } + } + + int nqueries; + int pow; + scanf("%u\n", &nqueries); + forn (qi, nqueries) { + Mat input(N, Row(1, 0)); + scanf("%s %c %u\n", buf, &chr, &pow); + // procesar regla + const int input_len = strlen(buf); + forn (i, input_len) { + assert(in_range(buf[i])); + input[charcode(buf[i])][0]++; + } + + Mat pow_rules(N, Row(N, 0)); + mat_pow(rules, pow, pow_rules); + + Mat result(N, Row(1, 0)); + mat_mult(pow_rules, input, result); + + cout << result[charcode(chr)][0] << endl; + } + } + return 0; +} diff --git a/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/walk/walk.cpp b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/walk/walk.cpp new file mode 100644 index 0000000..a80b14d --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/help/gomox.ar-pap-2010-d9b17e5cb110/tpd/walk/walk.cpp @@ -0,0 +1,132 @@ +#include +#include +#include +#include +#include + +using namespace std; + +typedef pair Coord; +typedef vector Poly; + +#define x first +#define y second + +#define forsn(i, s, n) for (int i = (s); i < (n); i++) +#define forn(i, n) forsn (i, 0, n) + +#define coord_sub(c1, c2) Coord((c1).x - (c2).x, (c1).y - (c2).y) + +bool cross_prod_sign(const Coord& p, const Coord& q) { + const long long int pxqy = ((long long int)p.x) * q.y; + const long long int qxpy = ((long long int)q.x) * p.y; + return pxqy >= qxpy; +} + +bool se_cruzan(const Coord& s0, const Coord& s1, const Coord& t0, const Coord& t1) { +#define se_cruzan1(a, b, c, d) (cross_prod_sign(coord_sub(a, c), coord_sub(d, c)) != cross_prod_sign(coord_sub(b, c), coord_sub(d, c))) + return se_cruzan1(s0, s1, t0, t1) && se_cruzan1(t0, t1, s0, s1); +#undef se_cruzan1 +} + +bool esta_adentro(const Coord& punto, const Poly& poly) { + // buscar un punto afuera + int maxx = punto.x; + forn (i, (int)poly.size()) { + maxx = max(maxx, poly[i].x); + } + maxx++; + const Coord externo(maxx, punto.y + 1); + + // ver si la cantidad de cruces es par o impar + const int n = poly.size(); + bool adentro = false; + forn (i, n) adentro ^= se_cruzan(punto, externo, poly[i], poly[(i + 1) % n]); + return adentro; +} + +long long int doble_area(const Poly& poly) { + const int n = poly.size(); + long long int s = 0; + forn (i, n) { + const int j = (i + 1) % n; + s += ((long long int)poly[i].x) * poly[j].y - ((long long int)poly[i].y) * poly[j].x; + } + return s < 0 ? -s : s; +} + +typedef vector vint; +typedef vector vllint; + +vllint __area2; +bool cmp_area2(int i, int j) { + return __area2[i] < __area2[j]; +} +void minwalk(const vector& heights, const vector& curves, const Coord& pos_alice, const Coord& pos_bob) { + const int n = curves.size(); + + // ordenar los poligonos por area + __area2 = vllint(n); + forn (pi, n) { + __area2[pi] = doble_area(curves[pi]); + } + vint ind(n, 0); + forn (i, n) ind[i] = i; + sort(ind.begin(), ind.end(), cmp_area2); + + // visitarlos en ese orden y calcular cuanto sube / baja +#define up_down(H1, H2) if (H1 < H2) { cost_up += H2 - H1; } else { cost_down += H1 - H2; } + int last_height_alice = -1, last_height_bob = -1; + int cost_up = 0, cost_down = 0; + forn (i, n) { + const int j = ind[i]; + const bool contains_alice = esta_adentro(pos_alice, curves[j]); + const bool contains_bob = esta_adentro(pos_bob, curves[j]); + if (contains_alice && contains_bob) { + break; + } else if (contains_alice) { + if (last_height_alice != -1) { + up_down(last_height_alice, heights[j]); + } + last_height_alice = heights[j]; + } else if (contains_bob) { + if (last_height_bob != -1) { + up_down(heights[j], last_height_bob); + } + last_height_bob = heights[j]; + } + } + if (last_height_alice != -1 && last_height_bob != -1) { + up_down(last_height_alice, last_height_bob); + } + printf("%i %i\n", cost_up, cost_down); +} + +int main() { + const Coord pos_alice(0, 0); + const Coord pos_bob(100000, 0); + int ncases; + scanf("%i\n", &ncases); + forn (ci, ncases) { + int npolys; + scanf("%i\n", &npolys); + + vector polys; + vector heights; + forn (pi, npolys) { + int curve_height, nverts; + scanf("%i %i", &curve_height, &nverts); + polys.push_back(Poly()); + forn (vi, nverts) { + int vert_x, vert_y; + scanf("%i %i", &vert_x, &vert_y); + polys[pi].push_back(Coord(vert_x, vert_y)); + } + heights.push_back(curve_height); + } + + minwalk(heights, polys, pos_alice, pos_bob); + } + return 0; +} + diff --git a/ICPC Live Archive/3928 - Ballroom lights/in.txt b/ICPC Live Archive/3928 - Ballroom lights/in.txt new file mode 100644 index 0000000..3b38bfd --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/in.txt @@ -0,0 +1,57 @@ +2 1 8 8 +6 6 +2 6 +4 4 2 + +1 4 7 7 +3 3 +2 4 1 +4 2 1 +2 2 1 +4 4 1 + +2 2 9 7 +1 2 +5 5 +3 3 2 +7 5 1 + +1 1 100 100 +50 50 +50 20 10 + +2 2 9 7 +1 2 +5 5 +3 3 2 +7 5 1 + +1 2 8 6 +4 2 +2 2 1 +6 2 1 + +1 2 8 6 +4 1 +2 2 1 +6 2 1 + +1 2 8 6 +4 5 +2 2 1 +6 2 1 + +2 2 8 6 +4 1 +7 5 +2 2 1 +6 2 1 + +3 2 8 6 +4 1 +7 5 +1 5 +2 2 1 +6 2 1 + +0 0 0 0 \ No newline at end of file diff --git a/ICPC Live Archive/3928 - Ballroom lights/myout b/ICPC Live Archive/3928 - Ballroom lights/myout new file mode 100644 index 0000000..0c30097 --- /dev/null +++ b/ICPC Live Archive/3928 - Ballroom lights/myout @@ -0,0 +1,59 @@ +1875.1300 +1816.7069 +1859.9603 +1701.0056 +1694.2440 +1679.8729 +770.9998 +806.9729 +829.8151 +45096.2100 +45627.3044 +45986.0000 +44189.1357 +258418.9386 +176007.9887 +405422.9695 +438061.9559 +464596.0000 +586985.4217 +2024135.7681 +3165697.7588 +3325798.2753 +3711064.9684 +3674825.1969 +3336387.0389 +3724588.8082 +3017409.8248 +2088219.1250 +3856748.4938 +3512718.3803 +3581697.8205 +184939.5647 +287754.1893 +268002.7207 +2.1726 +38.9101 +31.3493 +10.5684 +31.1358 +44.5655 +15.0000 +26.0685 +20.5117 +53.7338 +64.9581 +50.0813 +133.1443 +158.4993 +142.2758 +28.0000 +0.0000 +25.8214 +10.0000 +18.0566 +0.0000 +22.0000 +14.0000 +22.5142 +25.6203 diff --git 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x; return s.str(); +} + +template int toInt(const T &x){ +stringstream s; s << x; int r; s >> r; return r; +} + +#define For(i, a, b) for (int i=(a); i<(b); ++i) +#define foreach(x, v) for (typeof (v).begin() x = (v).begin(); x != (v).end(); ++x) +#define D(x) cout << #x " = " << (x) << endl + +const double EPS = 1e-9; +int cmp(double x, double y, double tol = EPS){ + return (x <= y + tol) ? (x + tol < y) ? -1 : 0 : 1; +} + +const int MAXN = 105; + +int A[MAXN], B[MAXN]; + +vector g[MAXN]; + +bool segundo_de_mayor_a_menor(pair a, pair b){ + if (a.second != b.second) return a.second > b.second; + return a.first < b.first; +} + + +pair f(int u, int dad = -1){ + vector< pair > p; + for (int i = 0; i < g[u].size(); ++i){ + int v = g[u][i]; + if (v == dad) continue; + + p.push_back( f(v, u) ); + } + + sort(p.begin(), p.end(), segundo_de_mayor_a_menor); + + int total = A[u]; + int tengo = A[u] - B[u]; + for (int i = 0; i < p.size(); ++i){ + if (tengo > p[i].first){ + tengo -= p[i].first - p[i].second; + }else{ + total += p[i].first - tengo; + tengo = p[i].second; + } + } + //printf(" f(u=%d) = <%d, %d>\n", u, total, tengo); + return make_pair(total, tengo); +} + +int main(){ + int n, Caso = 1; + while (cin >> n){ + if (n == 0) break; + cout << "Case " << Caso++ << ": "; + + for (int i = 0; i < n; ++i){ + int x, y, z; + cin >> x >> y >> z; + A[i] = x; + B[i] = y + z; + A[i] = max(A[i], B[i]); + + g[i].clear(); + } + + for (int i = 0; i < n - 1; ++i){ + int u, v; + cin >> u >> v; + u--, v--; + g[u].push_back(v); + g[v].push_back(u); + } + + //for (int i = 0; i < n; ++i){ + // printf("Nodo %d: A = %d, B = %d\n", i, A[i], B[i]); + //} + + int ans = INT_MAX; + for (int i = 0; i < n; ++i){ + + pair p = f(i); + //printf("Empezando en %d: <%d, %d>\n", i, p.first, p.second); + + + ans = min(ans, p.first); + + } + + cout << ans << endl; + } + return 0; +} diff --git a/ICPC Live Archive/4788 - Castles/in.txt b/ICPC Live Archive/4788 - Castles/in.txt new file mode 100644 index 0000000..5f93dcb --- /dev/null +++ b/ICPC Live Archive/4788 - Castles/in.txt @@ -0,0 +1,39 @@ +3 +5 5 5 +10 5 5 +5 1 1 +1 3 +2 3 +5 +10 5 10 +20 10 5 +10 10 5 +5 5 5 +20 0 10 +1 2 +1 3 +1 4 +3 5 + +6 +1 3 4 +20 5 10 +6 10 3 +12 2 0 +100 100 13 +17 0 11 +1 2 +2 3 +2 4 +1 5 +5 6 + +1 +2 2 3 + + +1 + +1000 0 0 +0 + diff --git a/ICPC Live Archive/4794 - Sharing Chocolate/4794 b/ICPC Live Archive/4794 - Sharing Chocolate/4794 new file mode 100755 index 0000000000000000000000000000000000000000..14f87ac6411fbf0a22d9a7d35b381aa561a1bd15 GIT binary patch literal 25464 zcwX&X4|r77mA~^R$s}Yl0kK8-V^E-=7LpJ!0o@IM-gYQpBP12E`j|{6Fq)aj@#*aLj0oP|US8>E5jH zvGS^KV)+lKc=Z*dE1~*|D*psRHmO)@Ck@n2RxT@Frb@`??Vj7O z@bt=M53~~lf8r&Ib)MSIpqE&0^LSIso2%l}Na{-zUA5R~PM=uqciR)>&E@h;DqdaB zOcHyEqPs>my*i&KL0&$WH$}y(Z3FGCRK<&8jcp`(R=NH3QC=+%+iiu47sV=@&!*<% z*t z`T+ZQ|6PP^glE}3ke)@~3sS~KWbzwC5XeR*lGIn}-GnqHiO(UduW)={;P-kK)Ho{_ zRBfxN;^|Wf)8hr*@mIpu#s6}kx32o(KY#QT_CW_>W5CTxvOo~FIVRqzs9feYyA4Zd{tNj z=dFRp;n!ZFp{9$u$XSDp!_r%@oPO<QyQpR?SZY#*>AEjj30y+!C?)KONzV^7UJUr9rpAjp%Z^r%{PjjD5+TI0V>=ev zdPn|(ejr3myGSJR z+A9wbs{8;}$^<3k20m!&)Sdjj!K%Ar4ZJyMv^JeIS({3T|1TJlz5!EUpi8<7Bwj^< zS1c2SVIXUVfK*6VEV%-NHV9I+Wxg=%)ekPjsNrhM+-`_o%K(sea;ttYvr8BNB_e|v z5I}u{!azU>BOBIHHq5kM53RcaTE7EY|FAVs(GJSCOV2~qtdVYLtuXZGVHWIxI>6l+ zmKv~ef~+w?51X+&e0xD!R2pyKAq`1?vH?&i@4DH%& zjX*ReEfxB_3${02CjM6kzo2CPf|9u}S>~q3ZsJR)xz4CC&7nsMEl2OWj3Q`PNxz$v zM9z0YmZPDWeLF&yZ=*!ZQIOhnYQw$JW@!jC?hE+a0u_6M!d`2ewRQ3i*7Ip|Zo-FA zAIuF3`z$XAZ6%$)>@J}NlP?@i!{&|6@ZODjmVq=4>--4CPPh<6XvIE6+qUYl-K2mp5Uh|u_jx_g!(bX% z2dllu8tAd=LRKC0^5j>!&?PsXr9z>T4|fUYXcd30Low&9b~Nq7(o?YF4H7U0(Cz)6 zn*?ms9fv5U5Ba?Tp*JY>P7wN*3VWGi)*T_=4c1n38+6UFRkWl8tPYLW z(u^B|VB@}((0swQZ9zYD@L8+0pAP&4#q&c`sA2w*bOQn2`z4yaR?(4(>`Fr+iVik_g* zhBnn56wW{s?Mq=(@7$o+RC||jN@Y{0m`$}yD=f^WLfoc8QJV^Jn>rp8j!zIm2{yG7 z=AL8svra9~rJee7ct{sfq;QTDCwDGjAIsG`YHuvhWV#7iIF!Zf8 zhwZ?LbO3ADS}_FEk24MvX12Ogf z{ZwxHCR{1``DF^e5 z*J_PYc8W&6Wh!fA=;Q%u+63%aIwuY;2v(d!X({IBKVL5!EiTJosBLOIx8;#vK#oWV zr(^R2v-(K~zBhr+w|)=NFcN&T9Nv(ixlB%ZE8JQZfyHsK@v3z9`;o{_A+o(OLVRYB z-wUeXI&5$PFu&joymZ~tHORCs$^t21W8a$~+n5eQuo{5{6~2r!;O(RF-1wFCxGj6bYN2Qz7V(tQB& zWn=B23c-qSK%ZQaQs?+Rm%8-=xiRHpd6Kp1G;9?bha@v-pV;_HhWz;I;`()`ahCK$ zlWNMvPU(wo*rgU4NTo&-z6y19n6i8S0*ls}!`A&XhX6sd0$-CbRbLVhY3V zGMJvkHmHr}rm#^Zn$@X49jgz4U!=#EEzy>IIX&8vjp?eEq|ah(P-#U5Z%j9nCQ08; zS9MLk(lvpKKD0KPH&!Wu>D`*m#u*IbD?^p-!y3=~H)>Xa*QH2$B4A!m^3qNV5gn8W zrE~_jVzuDX~*q>6iwXlS2?_*?2Wj)t* zBCSF`s~QX&YcE3|_eg(Y0=g-9f!s)Rglos&Po$TyT1`T?k%}%*L|>9F>*OZgV4_7F z(y>-*U3&?#cUuE*OTno4OHz;ALW4S4%0=mWiWJ^ibWFP_)iT8|N>3{Qc}(p{KBjiC zF||W_jOM85V2z^Z!ET&gXnXQ;%TUq7tsoax>t**Y`&ug7WX3kkjmc`)jcDkIcTG(oK|BQd&i6HKki9eSp#$O5K#!QR<=8M`=B! z4U|4a>BE#hLg{u&AEmUJ(#I&>N$KO1wov*6rMoEIP3c}rpQN;n(x)liN9lJc-B0PW zlpdh;IZE3p{XV4!DLq8#VM>2Q=@CkgQrbc3F-nh9dV+twQo4PrQEDy*%wcjPcYss(pDk=h+id>^#LoR@l6byxCPt z^2qEecmgH&IK1S}T2f8cv`$|D`?_W8BeQRS=dLX{jxCx%X7=o&D@3r8@Nj-l^k=zUDxkD)(e=t&IW5&wl24B@Wl!lM{EjG+b$(Q@5N zs0u@mV`w9Ua1ew|Aw8Q#R~O{x62+H+9*yVo1Nc&Y>r_1YC}fjNlFxGJ&_C$7ndpXL zLwsKjF>Jk-kRvmQe(p@_>!X`U^b>XPn8rj9-9u&Th^`?w{U865MM!RThG`e7KyD>W zpILuq%gsp~PmGwHllz$7h(()aKOw}Ui$R0L@D2_5X1LE@VffoL;E%xF$mM@tmjZ8u z)d6WTARhPchq(NC8stxgq;`&0A0*Xt{O2{`4?xoWW02nqNyTH3 zZv>O+e^)!c2=GG#44}M7*$H#y#2j(Eh7ihpY19OPuS82c>0j8Vd*J{8I05cS3_~$j? 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(x + tol < y) ? -1 : 0 : 1; +} + +const int MAXN = 15; +const int MAXR = 105; +const int MAXS = MAXR * MAXR; + +int a[MAXN]; +int sum[1 << MAXN]; +int popcount[1 << MAXN]; +int memo[MAXR][1 << MAXN]; +vector masks[MAXS]; + +int n; + +bool f(int r, int c, int mask){ + //printf("f(r=%d, c=%d, mask=%x, sum[mask]=%d)\n", r, c, mask, sum[mask]); + if (sum[mask] != r * c) return false; + + // r * c == sum[mask] + if (popcount[mask] == 1) return true; + + + if (memo[r][mask] != -1) return memo[r][mask]; + + for (int i=1; i &optionsleft = masks[ rleft * c ]; + for (int k = 0; k < optionsleft.size(); ++k){ + int lsubset = optionsleft[k]; + if (~mask & lsubset) continue; + int rsubset = mask & ~lsubset; + + //printf("lsubset = %X, rsubset = %X\n", lsubset, rsubset); + assert((lsubset | rsubset) == mask); + assert((lsubset & rsubset) == 0); + assert(sum[lsubset] == rleft * c); + + if (sum[rsubset] == rright * c){ + bool maybe = f(rleft, c, lsubset) && f(rright, c, rsubset); + if (maybe){ + memo[r][mask] = memo[c][mask] = 1; + return 1; + } + } + } + } + + for (int j=1; j &optionsleft = masks[ cleft * r ]; + for (int k = 0; k < optionsleft.size(); ++k){ + int lsubset = optionsleft[k]; + if (~mask & lsubset) continue; + int rsubset = mask & ~lsubset; + assert((lsubset | rsubset) == mask); + assert((lsubset & rsubset) == 0); + assert(sum[lsubset] == cleft * r); + + if (sum[rsubset] == cright * r){ + bool maybe = f(r, cleft, lsubset) && f(r, cright, rsubset); + if (maybe){ + memo[r][mask] = memo[c][mask] = 1; + return 1; + } + } + } + } + + + + memo[r][mask] = memo[c][mask] = 0; + return 0; +} + +int main(){ + int Case = 0; + while (scanf("%d", &n) == 1){ + if (n == 0) break; + printf("Case %d: ", ++Case); + + int r, c; + scanf("%d %d", &r, &c); + for (int i = 0; i < n; ++i){ + scanf("%d", &a[i]); + } + + for (int i = 0; i <= r * c; ++i){ + masks[i].clear(); + } + + for (int mask = 0; mask < (1 << n); ++mask){ + sum[mask] = popcount[mask] = 0; + for (int k = 0; k < n; ++k){ + if (mask & (1 << k)){ + sum[mask] += a[k]; + popcount[mask]++; + } + } + + masks[sum[mask]].push_back(mask); + + for (int i = 0; i < MAXR; ++i){ + memo[i][mask] = -1; + } + } + + // for (int mask = 0; mask < (1 << n); ++mask){ + // printf("Mask = %X\n", mask); + // printf(" popcount = %d\n", popcount[mask]); + // printf(" sum = %d\n", sum[mask]); + // } + + bool ans = f(r, c, (1 << n) - 1); + printf("%s\n", ans ? "Yes" : "No"); + } + return 0; +} diff --git a/ICPC Live Archive/4794 - Sharing Chocolate/in.txt b/ICPC Live Archive/4794 - Sharing Chocolate/in.txt new file mode 100644 index 0000000..248cd27 --- /dev/null +++ b/ICPC Live Archive/4794 - Sharing Chocolate/in.txt @@ -0,0 +1,73 @@ +2 +6 1 +3 3 + +5 +100 1 +25 25 25 25 25 + +5 +100 1 +20 20 20 20 20 + +5 +100 1 +20 20 20 19 21 + +1 +1 1 +1 + +2 +2 1 +1 1 + +10 +10 1 +1 1 1 1 1 1 1 1 1 1 + +15 +15 1 +1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 + +15 +100 1 +6 6 6 6 6 6 6 6 6 6 6 6 6 6 16 + +2 +1 2 +1 1 + +15 +1 100 +6 6 6 6 6 6 6 6 6 6 6 6 6 6 16 + +4 +2 2 +1 1 1 1 + +2 +2 2 +3 1 + +4 +3 4 +6 3 2 1 + +2 +2 3 +1 5 + +10 +100 100 +100 100 100 100 100 100 100 100 100 100 + +10 +100 100 +1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 + +10 +100 100 +1000 1000 1000 1000 1000 1000 1000 1000 999 1001 + +0 diff --git a/ICPC Live Archive/4794 - Sharing Chocolate/tille b/ICPC Live Archive/4794 - Sharing Chocolate/tille new file mode 100755 index 0000000000000000000000000000000000000000..8937466f390b5ab38790b571060adb4f4cefeedb GIT binary patch literal 34144 zcwX&&4SZD9mH3^HkPre15CWpoAc#Q`k`OR_r~xuKDS@U0ETZ^GCId{(S0^(O_%+>V zfHFIzOI>QID=uqY#gA>_uf21JNTZB(?Wi<-Xzz7!PJT8)U#o^$TKZ{EE5NG9U$ z|M&mp{qoMc=iYP9J@?#m@4N5jyf=Tk@X^%#>Pey!{ahI?Qkke z$(&nk%WaFl$HER%cvjefa@Lwr&Jx?QC81@+UtnMmIHg*Zddhc4G)!9 zIf?UMtHbq2h^~zE1I3gz&dOS+n}y4}U&wn-hld#n7(G?VkeoPDEOoyYtq1<4<*1Bs}gI-E~nY%8!yeu7_z@i_D zQdNUSb9t0i-fBmfysQE)FG+{%+c}Vh9*R<3DP6hN;|`OTUBKmK>u|lVVLO-Va7C#s zizRPmf#?Tw5ZB8?``xa?6{VugQ>Mp5gAIqw!4m=kz-bWcM`q2oJ#O?_BP&LbBe14zet#ePQbd^u3 zSXWsg%5l0xJs!wEvUYsBY2pw5t|C>jCYVYnh*v@>$+eCgj zkXun}JDhc%3deQVO`bj(?BFVo%x7W^1oeES>*_qts>yTpeEmoN(SP(G{YU@NfBe65 zEVcVi*_+O$`5G?zyxmO=7fs&l?`h}`1Q_#RIImB*O+>nmXK*F56<`9R~C(qmc4N3N9Z<_By(;?Hr_bqnQCwAX! zXRP+7gGu(L8O-|`rqu7lLf&^&{Sa#U6a|)oQp@bVh8DZeyW8$tx(np&Qm=(t?SVGC z&(>-8+jjG0JBWv~p;Nsb_4Gr{whk!nglpRo+c}f{sI3*%K69Pj?`X zT*q`Y8(M#oo4R+!ITS%wRLdjDd8jpYZ|m5OjjgG_K#8e)L2A?CWw&!XOSA0ud5`&) zw)qwwF80}4pz-I_!qM3HhTUL|bLtz2VD3yv9JQ&`{ONw1I?HzK$7ytJ`^h-E9`;-g zSGxmyszv=j$mlzQg4E5B4%k#G?V!>_@EBm9@j~i-ts7dsd(Mmj3q!}O*hS=b5$g)x zQ@KcqU8L9jp0mqLNV9*}*MWfVcP9}3q647a*W8X5|9-rvw<9xHU>j8983nn!sPK1G z_%#%E4IO~ZI*ZNfdObmFqThDbXFJ)oBLR~qXW7nrFM}(!jZ1z5nElLTQ_p~MXLSY7 zVZo?S;zx-XnoD|&3@!9YN&cm(ul?YK?|irQ*Kt<}Huq~CkC z$k+P&FJZ{3?|c;qM6T0!aN=vem+j39clycZ&;*pLuI5sAs(VI})K+yDB)WcQ#Xj1& zlPGuWltf#Q$Vd2@#IW*KwK7-^72rj^ex%+E9h!NDn!@ry)e}MUoHv?h#}r|nZBz8- zX$dh;qx$|xY{>qV0mN;M1`9oZQEwrAwZ0=0-?BG1BcGo;q<=rkRtvvENhDD9lW?fz zUPyHPlO^0roX#;amZ2Kec_YINWz8Um4Yb0<*0s-!i0ZSQ2zAksBe{!q>hdfj^)5O( zwD2@aWfm@K>4`8ey^^}&M078`7}5=9e?rD&(G7zqV>dMOZfI`RcfWNJ1 ziH(@$U)ZVjhnoE*c15JBrL#68tLCp*gZk{3Bp(aZuSbx4s_PR-cLhul`h!T{7!jjC zxP;v!!n))~>3ZV?efM%xSbnJQUN9Q%|4tG{>zJhX-L?>;F;rt5Z&W8`ZDdBHeffpn zXc7Du88!b!`RaxXBpnOXSJFv3)$|8QcO7F9Oh%+T(_@*8Bs8Rlne3+Fc)#c*C+v_; 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+ +vector partiendo( int x, int y, vector a ); +vector deformar( int i, int h, int j, vector a ); +int cortes=0; + +int main(){ + int n, x, y, h, cont=0; + while( scanf("%d",&n) && n!=0 ){ + cortes=0; cont++; + vector parts; + h=n; cin >> x >> y; + int num=0; + while(h--){ cin >> num; parts.push_back(num); } + parts=partiendo( x, y, parts ); + if( parts.size()==0 && cortes-1 partiendo( int x, int y, vector a ){ + + if( a.size() == 0 ) return a; + for( int i=0; i< a.size() ; i++ ){ + int b=0; + + for( int h=i; h< a.size() ; h++ ){ + if( h==i ) b+=a[h]; + else if( a[i]==a[h] ) b+=a[h]; + if( b%x==0 && y-(b/x)>-1 ){ cortes+=(h-i)+1; return partiendo( x, y-(b/x), deformar(i,h,-5,a) ); } + if( b%y==0 && x-(b/y)>-1 ){ cortes+=(h-i)+1; return partiendo( x-(b/y), y, deformar(i,h,-5,a) ); } + + for( int j=h+1; j< a.size() ; j++ ){ + + int s=b; + if( a[i]==a[j] ) s=b+a[j]; + if( s%x==0 && y-(s/x)>-1 ){ cortes+=(h-i)+2; return partiendo( x, y-(s/x), deformar(i,h,j,a) ); } + if( s%y==0 && x-(s/y)>-1 ){ cortes+=(h-i)+2; return partiendo( x-(s/y), y, deformar(i,h,j,a) ); } + + } + } + } + return a; + +} + + +vector deformar( int i, int h, int j, vector a ){ + vector f; + for( int g=0; gh && g!=j ) f.push_back(a[g]); + return f; +} + diff --git a/ICPC Live Archive/4807 - Cocircular Points/4807.2.cpp b/ICPC Live Archive/4807 - Cocircular Points/4807.2.cpp new file mode 100644 index 0000000..945ee70 --- /dev/null +++ b/ICPC Live Archive/4807 - Cocircular Points/4807.2.cpp @@ -0,0 +1,115 @@ +// Accepted +using namespace std; +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#define foreach(x, v) for (typeof (v).begin() x=(v).begin(); x !=(v).end(); ++x) +#define For(i, a, b) for (int i=(a); i<(b); ++i) +#define D(x) cout << #x " is " << x << endl + +const double EPS = 1e-9; +int cmp(double x, double y = 0, double tol = EPS) { + return (x <= y + tol) ? (x + tol < y) ? -1 : 0 : 1; +} + +struct point { + double x, y; + point(double x, double y) : x(x), y(y) {} + point(){} + bool operator < (const point &p) const { + int t = cmp(this->x, p.x); + if (t != 0) return t < 0; + return cmp(this->y, p.y) < 0; + } + bool operator == (const point &p) const { + return cmp(this->x, p.x) == 0 and cmp(this->y, p.y) == 0; + } +}; + +point center(const point &p, const point &q, const point &r) { + double ax = q.x - p.x; + double ay = q.y - p.y; + double bx = r.x - p.x; + double by = r.y - p.y; + double d = ax*by - bx*ay; + + if (cmp(d, 0) == 0) { + printf("Points are collinear!\n"); + assert(false); + } + + double cx = (q.x + p.x) / 2; + double cy = (q.y + p.y) / 2; + double dx = (r.x + p.x) / 2; + double dy = (r.y + p.y) / 2; + + double t1 = bx*dx + by*dy; + double t2 = ax*cx + ay*cy; + + double x = (by*t2 - ay*t1) / d; + double y = (ax*t1 - bx*t2) / d; + + return point(x, y); +} + +point points[105]; +point centers[105]; + +int main(){ + int n; + while (scanf("%d", &n) == 1) { + if (n == 0) break; + + for (int i = 0; i < n; ++i) { + scanf("%lf %lf", &points[i].x, &points[i].y); + } + + if (n <= 2) { + printf("%d\n", n); + continue; + } + + int ans = 2; + for (int i = 0; i < n; ++i) { + for (int j = i + 1; j < n; ++j) { + int last = 0; + for (int k = 0; k < n; ++k) { + if (k == i or k == j) continue; + double x0 = points[i].x - points[k].x; + double y0 = points[i].y - points[k].y; + double x1 = points[j].x - points[k].x; + double y1 = points[j].y - points[k].y; + if ( cmp(x0*y1 - y0*x1, 0) == 0 ) continue; // collinear + centers[last++] = center(points[i], points[j], points[k]); + } + sort(centers, centers + last); + for (int k = 0; k < last; ) { + int same = k; + while (same < last and centers[k] == centers[same]) same++; + ans = max(ans, same - k + 2); + k = same; + } + } + } + printf("%d\n", ans); + } + return 0; +} \ No newline at end of file diff --git a/ICPC Live Archive/4807 - Cocircular Points/4807.cpp b/ICPC Live Archive/4807 - Cocircular Points/4807.cpp new file mode 100644 index 0000000..b6c9b8e --- /dev/null +++ b/ICPC Live Archive/4807 - Cocircular Points/4807.cpp @@ -0,0 +1,107 @@ +// Accepted +using namespace std; +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#define foreach(x, v) for (typeof (v).begin() x=(v).begin(); x !=(v).end(); ++x) +#define For(i, a, b) for (int i=(a); i<(b); ++i) +#define D(x) cout << #x " is " << x << endl + +const double EPS = 1e-9; +int cmp(double x, double y = 0, double tol = EPS) { + return (x <= y + tol) ? (x + tol < y) ? -1 : 0 : 1; +} + +struct point { + double x, y; + point(double x, double y) : x(x), y(y) {} + point(){} + bool operator < (const point &p) const { + int t = cmp(this->x, p.x); + if (t != 0) return t < 0; + return cmp(this->y, p.y) < 0; + } +}; + +point center(const point &p, const point &q, const point &r) { + double ax = q.x - p.x; + double ay = q.y - p.y; + double bx = r.x - p.x; + double by = r.y - p.y; + double d = ax*by - bx*ay; + + if (cmp(d, 0) == 0) { + printf("p = <%lf, %lf>, q = <%lf, %lf>, r = <%lf, %lf>\n", p.x, p.y, q.x, q.y, r.x, r.y); + printf("Points are collinear!\n"); + assert(false); + } + + double cx = (q.x + p.x) / 2; + double cy = (q.y + p.y) / 2; + double dx = (r.x + p.x) / 2; + double dy = (r.y + p.y) / 2; + + double t1 = bx*dx + by*dy; + double t2 = ax*cx + ay*cy; + + double x = (by*t2 - ay*t1) / d; + double y = (ax*t1 - bx*t2) / d; + + return point(x, y); +} + +point points[105]; + +int main(){ + int n; + while (scanf("%d", &n) == 1) { + if (n == 0) break; + + for (int i = 0; i < n; ++i) { + scanf("%lf %lf", &points[i].x, &points[i].y); + } + + if (n <= 2) { + printf("%d\n", n); + continue; + } + + int ans = 2; + for (int i = 0; i < n; ++i) { + for (int j = i + 1; j < n; ++j) { + map times; + for (int k = 0; k < n; ++k) { + if (k == i or k == j) continue; + double x0 = points[i].x - points[k].x; + double y0 = points[i].y - points[k].y; + double x1 = points[j].x - points[k].x; + double y1 = points[j].y - points[k].y; + if ( cmp(x0*y1 - y0*x1, 0) == 0 ) continue; // collinear + point c = center(points[i], points[j], points[k]); + times[c]++; + ans = max(ans, times[c] + 2); + } + } + } + printf("%d\n", ans); + } + return 0; +} \ No newline at end of file diff --git a/ICPC Live Archive/4807 - Cocircular Points/a.out b/ICPC Live Archive/4807 - Cocircular Points/a.out new file mode 100755 index 0000000000000000000000000000000000000000..19dcf2664c1c61dfceab021e83f5fb226ab9b811 GIT binary patch literal 22228 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/dev/null +++ b/ICPC Live Archive/4807 - Cocircular Points/in.txt @@ -0,0 +1,18 @@ +7 +-10 0 +0 -10 +10 0 +0 10 +-20 10 +-10 20 +-2 4 +4 +-10000 10000 +10000 10000 +10000 -10000 +-10000 -9999 +3 +-1 0 +0 0 +1 0 +0 diff --git a/ICPC Live Archive/4808 - Digits Count/4808.2.cpp b/ICPC Live Archive/4808 - Digits Count/4808.2.cpp new file mode 100644 index 0000000..be81a04 --- /dev/null +++ b/ICPC Live Archive/4808 - Digits Count/4808.2.cpp @@ -0,0 +1,68 @@ +using namespace std; +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#define foreach(x, v) for (typeof (v).begin() x=(v).begin(); x !=(v).end(); ++x) +#define For(i, a, b) for (int i=(a); i<(b); ++i) +#define D(x) cout << #x " is " << x << endl + +int count(int x, int digit) { + int power = 1, ans = 0; + int left = x, right = 0; + while (left > 0) { + int current = left % 10; + left /= 10; + ans += left * power; + if (current == digit) { + ans += right + 1; + } else if (current > digit) { + ans += power; + } + power *= 10; + right = x % power; + } + if (digit == 0) { + ans -= (power - 1) / 9; + } + return ans; +} + +int main(){ + int a, b; + while (cin >> a >> b) { + if (a == 0 and b == 0) break; + int ans[10]; + + for (int d = 0; d <= 9; ++d) { + ans[d] = count(b, d); + if (a - 1 > 0) ans[d] -= count(a - 1, d); + } + + for (int i = 0; i <= 9; ++i) { + if (i > 0) printf(" "); + printf("%d", ans[i]); + } + printf("\n"); + + + } + return 0; +} \ No newline at end of file diff --git a/ICPC Live Archive/4808 - Digits Count/4808.cpp b/ICPC Live Archive/4808 - Digits Count/4808.cpp new file mode 100644 index 0000000..2aaea15 --- /dev/null +++ b/ICPC Live Archive/4808 - Digits Count/4808.cpp @@ -0,0 +1,127 @@ +using namespace std; +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#define foreach(x, v) for (typeof (v).begin() x=(v).begin(); x !=(v).end(); ++x) +#define For(i, a, b) for (int i=(a); i<(b); ++i) +#define D(x) cout << #x " is " << x << endl + +vector num; + + +void print(const vector &v) { + for (int i = 0; i < v.size(); ++i) { + if (i > 0) printf(" "); + printf("%d", v[i]); + } + printf("\n"); +} + +int ten(int e) { + assert(e >= 0); + int ans = 1; + while (e--) ans *= 10; + return ans; +} + +int assemble(int i) { + assert(i >= -1); + int ans = 0; + for (int k = i; k >= 0; --k) { + ans = 10 * ans + num[k]; + } + return ans; +} + +vector memo[10][2]; + +vector f(int i, bool m) { + if (i < 0) { + return vector(10, 0); + } + + if (memo[i][m].size() > 0) return memo[i][m]; + + vector ans(10, 0); + + int limit = (m ? 9 : num[i] - 1); + for (int k = 0; k <= limit; ++k) { + vector s = f(i - 1, true); + s[k] += ten(i); + for (int j = 0; j < 10; ++j) ans[j] += s[j]; + } + + if (!m) { + vector s = f(i - 1, false); + s[num[i]] += assemble(i - 1) + 1; + for (int j = 0; j < 10; ++j) ans[j] += s[j]; + } + memo[i][m] = ans; + return ans; +} + +vector f(int x) { + num.clear(); + while (x > 0) num.push_back(x % 10), x /= 10; + for (int i = 0; i <= 10; ++i) { + memo[i][0].clear(), memo[i][1].clear(); + } + vector ans = f(num.size() - 1, false); + ans[0] -= (ten(num.size()) - 1) / 9; + // for (int i = num.size() - 1; i >= 0; --i) { + // assert(ans[0] >= ten(i)); + // ans[0] -= ten(i); + // } + return ans; +} + +void bruteforce(int a) { + vector ans(10, 0); + for (int i = 1; i <= a; ++i){ + int x = i; + while (x > 0) ans[x % 10]++, x /= 10; + } + printf("Bruteforced answer for i=%d: ", a); + print(ans); +} + +int main(){ + // vector a = f(1); + // print(a); + // for (int i = 1; i <= 100; ++i) { + // printf("i = %d: ", i); + // print(f(i)); + // } + int a, b; + while (cin >> a >> b) { + if (a == 0 and b == 0) break; + vector ans = f(b); + if (a - 1 > 0) { + vector remove = f(a - 1); + 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