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1 " These macros 'solve' any maze produced by the a-maze-ing maze.c program.
2 "
3 " First, a bit of maze theory.
4 " If you were put into a maze, a guaranteed method of finding your way
5 " out of the maze is to put your left hand onto a wall and just keep walking,
6 " never taking your hand off the wall. This technique is only guaranteed to
7 " work if the maze does not have any 'islands', or if the 'exit' is on the
8 " same island as your starting point. These conditions hold for the mazes
9 " under consideration.
10 "
11 " Assuming that the maze is made up of horizontal and vertical walls spaced
12 " one step apart and that you can move either north, south, east or west,
13 " then you can automate this procedure by carrying out the following steps.
14 "
15 " 1. Put yourself somewhere in the maze near a wall.
16 " 2. Check if you have a wall on your left. If so, go to step 4.
17 " 3. There is no wall on your left, so turn on the spot to your left and step
18 " forward by one step and repeat step 2.
19 " 4. Check what is directly in front of you. If it is a wall, turn on the
20 " spot to your right by 90 degrees and repeat step 4.
21 " 5. There is no wall in front of you, so step forward one step and
22 " go to step 2.
23 "
24 " In this way you will cover all the corridors of the maze (until you get back
25 " to where you started from, if you do not stop).
26 "
27 " By examining a maze produced by the maze.c program you will see that
28 " each square of the maze is one character high and two characters wide.
29 " To go north or south, you move by a one character step, but to move east or
30 " west you move by a two character step. Also note that in any position
31 " there are four places where walls could be put - to the north, to the south,
32 " to the east and to the west.
33 " A wall exists to the north of you if the character to the north of
34 " you is a _ (otherwise it is a space).
35 " A wall exists to the east of you if the character to the east of you
36 " is a | (otherwise it is a .).
37 " A wall exists to the west of you if the character to the west of you
38 " is a | (otherwise it is a .).
39 " A wall exists to the south of you if the character where you are
40 " is a _ (otherwise it is a space).
41 "
42 " Note the difference for direction south, where we must examine the character
43 " where the cursor is rather than an adjacent cell.
44 "
45 " If you were implementing the above procedure is a normal computer language
46 " you could use a loop with if statements and continue statements,
47 " However, these constructs are not available in vi macros so I have used
48 " a state machine with 8 states. Each state signifies the direction you
49 " are going in and whether or not you have checked if there is a wall on
50 " your left.
51 "
52 " The transition from state to state and the actions taken on each transition
53 " are given in the state table below.
54 " The names of the states are N1, N2, S1, S2, E1, E2, W1, W2, where each letter
55 " stands for a direction of the compass, the number 1 indicates that the we
56 " have not yet checked to see if there is a wall on our left and the number 2
57 " indicates that we have checked and there is a wall on our left.
58 "
59 " For each state we must consider the existence or not of a wall in a
60 " particular direction. This direction is given in the following table.
61 "
62 " NextChar table:
63 " state direction vi commands
64 " N1 W hF
65 " N2 N kF
66 " S1 E lF
67 " S2 S F
68 " E1 N kF
69 " E2 E lF
70 " W1 S F
71 " W2 W hF
72 "
73 " where F is a macro which yanks the character under the cursor into
74 " the NextChar register (n).
75 "
76 " State table:
77 " In the 'vi commands' column is given the actions to carry out when in
78 " this state and the NextChar is as given. The commands k, j, ll, hh move
79 " the current position north, south, east and west respectively. The
80 " command mm is used as a no-op command.
81 " In the 'next state' column is given the new state of the machine after
82 " the action is carried out.
83 "
84 " current state NextChar vi commands next state
85 " N1 . hh W1
86 " N1 | mm N2
87 " N2 _ mm E1
88 " N2 space k N1
89 " S1 . ll E1
90 " S1 | mm S2
91 " S2 _ mm W1
92 " S2 space j S1
93 " E1 space k N1
94 " E1 _ mm E2
95 " E2 | mm S1
96 " E2 . ll E1
97 " W1 space j S1
98 " W1 _ mm W2
99 " W2 | mm N1
100 " W2 . hh W1
101 "
102 "
103 " Complaint about vi macros:
104 " It seems that you cannot have more than one 'undo-able' vi command
105 " in the one macro, so you have to make lots of little macros and
106 " put them together.
107 "
108 " I'll explain what I mean by an example. Edit a file and
109 " type ':map Q rXY'. This should map the Q key to 'replace the
110 " character under the cursor with X and yank the line'.
111 " But when I type Q, vi tells me 'Can't yank inside global/macro' and
112 " goes into ex mode. However if I type ':map Q rXT' and ':map T Y',
113 " everything is OK. I`m doing all this on a Sparcstation.
114 " If anyone reading this has an answer to this problem, the author would
115 " love to find out. Mail to gregm@otc.otca.oz.au.
116 "
117 " The macros:
118 " The macro to run the maze solver is 'g'. This simply calls two other
119 " macros: I, to initialise everything, and L, to loop forever running
120 " through the state table.
121 " Both of these macros are long sequences of calls to other macros. All
122 " of these other macros are quite simple and so to understand how this
123 " works, all you need to do is examine macros I and L and learn what they
124 " do (a simple sequence of vi actions) and how L loops (by calling U, which
125 " simply calls L again).
126 "
127 " Macro I sets up the state table and NextChar table at the end of the file.
128 " Macro L then searches these tables to find out what actions to perform and
129 " what state changes to make.
130 "
131 " The entries in the state table all begin with a key consisting of the
132 " letter 's', the current state and the NextChar. After this is the
133 " action to take in this state and after this is the next state to change to.
134 "
135 " The entries in the NextChar table begin with a key consisting of the
136 " letter 'n' and the current state. After this is the action to take to
137 " obtain NextChar - the character that must be examined to change state.
138 "
139 " One way to see what each part of the macros is doing is to type in the
140 " body of the macros I and L manually (instead of typing 'g') and see
141 " what happens at each step.
142 "
143 " Good luck.
144 "
145 " Registers used by the macros:
146 " s (State) - holds the state the machine is in
147 " c (Char) - holds the character under the current position
148 " m (Macro) - holds a vi command string to be executed later
149 " n (NextChar) - holds the character we must examine to change state
150 " r (Second Macro) - holds a second vi command string to be executed later
151 "
152 set remap
153 set nomagic
154 set noterse
155 set wrapscan
156 "
157 "================================================================
158 " g - go runs the whole show
159 " I - initialise
160 " L - then loop forever
161 map g IL
162 "
163 "================================================================
164 " I - initialise everything before running the loop
165 " G$?.^M - find the last . in the maze
166 " ^ - replace it with an X (the goal)
167 " GYKeDP - print the state table and next char table at the end of the file
168 " 0S - initialise the state of the machine to E1
169 " 2Gl - move to the top left cell of the maze
170 map I G$?.\r^GYKeDP0S2Gl
171 "
172 "================================================================
173 " L - the loop which is executed forever
174 " Q - save the current character in the Char register
175 " A - replace the current character with an 'O'
176 " ma - mark the current position with mark 'a'
177 " GNB - on bottom line, create a command to search the NextChar table
178 " for the current state
179 " 0M0E@m^M - yank the command into the Macro register and execute it
180 " wX - we have now found the entry in the table, now yank the
181 " following word into the Macro register
182 " `a@m - go back to the current position and execute the macro, this will
183 " yank the NextChar in register n
184 " GT$B$R - on bottom line, create a command to search the state table
185 " for the current state and NextChar
186 " 0M0E@m^M - yank the command into the Macro register and execute it
187 " 2WS - we have now found the entry in the table, now yank the
188 " next state into the State macro
189 " bX - and yank the action corresponding to this state table entry
190 " into the Macro register
191 " GVJ - on bottom line, create a command to restore the current character
192 " 0H - and save the command into the second Macro register
193 " `a@r - go back to the current position and exectute the macro to restore
194 " the current character
195 " @m - execute the action associated with this state
196 " U - and repeat
198 "
199 "================================================================
200 " U - no tail recursion allowed in vi macros so cheat and set U = L
201 map U L
202 "
203 "================================================================
204 " S - yank the next two characters into the State register
205 map S "sy2l
206 "
207 "================================================================
208 " Q - save the current character in the Char register
209 map Q "cyl
210 "
211 "================================================================
212 " A - replace the current character with an 'O'
213 map A rO
214 "
215 "================================================================
216 " N - replace this line with the string 'n'
217 map N C/n\e
218 "
219 "================================================================
220 " B - put the current state
221 map B "sp
222 "
223 "================================================================
224 " M - yank this line into the Macro register
225 map M "my$
226 "
227 "================================================================
228 " E - delete to the end of the line
229 map E d$
230 "
231 "================================================================
232 " X - yank this word into the Macro register
233 map X "myt
234 "
235 "================================================================
236 " T - replace this line with the string 's'
237 map T C/s\e
238 "
239 "================================================================
240 " R - put NextChar
241 map R "np
242 "
243 "================================================================
244 " V - add the letter 'r' (the replace vi command)
245 map V ar\e
246 "
247 "================================================================
248 " J - restore the current character
249 map J "cp
250 "
251 "================================================================
252 " H - yank this line into the second Macro register
253 map H "ry$
254 "
255 "================================================================
256 " F - yank NextChar (this macro is called from the Macro register)
257 map F "nyl
258 "
259 "================================================================
260 " ^ - replace the current character with an 'X'
261 map ^ rX
262 "
263 "================================================================
264 " YKeDP - create the state table, NextChar table and initial state
265 " Note that you have to escape the bar character, since it is special to
266 " the map command (it indicates a new line).