avl.c

   1 /*
   2  * Copyright (C) 2010 Joseph Adams <joeyadams3.14159@gmail.com>
   3  *
   4  * Permission is hereby granted, free of charge, to any person obtaining a copy
   5  * of this software and associated documentation files (the "Software"), to deal
   6  * in the Software without restriction, including without limitation the rights
   7  * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
   8  * copies of the Software, and to permit persons to whom the Software is
   9  * furnished to do so, subject to the following conditions:
  10  *
  11  * The above copyright notice and this permission notice shall be included in
  12  * all copies or substantial portions of the Software.
  13  *
  14  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  15  * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  16  * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  17  * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  18  * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  19  * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
  20  * THE SOFTWARE.
  21  */
  22
  23 #include <assert.h>
  24 #include <stdlib.h>
  25
  26 #include "smatch.h"
  27 #include "smatch_slist.h"
  28
  29 static AvlNode *mkNode(const struct sm_state *sm, const void *value);
  30 static void freeNode(AvlNode *node);
  31
  32 static AvlNode *lookup(const AVL *avl, AvlNode *node, const struct sm_state *sm);
  33
  34 static bool insert_sm(AVL *avl, AvlNode **p, const struct sm_state *sm, const void *value);
  35 static bool remove_sm(AVL *avl, AvlNode **p, const struct sm_state *sm, AvlNode **ret);
  36 static bool removeExtremum(AvlNode **p, int side, AvlNode **ret);
  37
  38 static int sway(AvlNode **p, int sway);
  39 static void balance(AvlNode **p, int side);
  40
  41 static bool checkBalances(AvlNode *node, int *height);
  42 static bool checkOrder(AVL *avl);
  43 static size_t countNode(AvlNode *node);
  44
  45 /*
  46  * Utility macros for converting between
  47  * "balance" values (-1 or 1) and "side" values (0 or 1).
  48  *
  49  * bal(0)   == -1
  50  * bal(1)   == +1
  51  * side(-1) == 0
  52  * side(+1) == 1
  53  */
  54 #define bal(side) ((side) == 0 ? -1 : 1)
  55 #define side(bal) ((bal)  == 1 ?  1 : 0)
  56
  57 static int sign(int cmp)
  58 {
  59         if (cmp < 0)
  60                 return -1;
  61         if (cmp == 0)
  62                 return 0;
  63         return 1;
  64 }
  65
  66 AVL *avl_new(void)
  67 {
  68         AVL *avl = malloc(sizeof(*avl));
  69
  70         assert(avl != NULL);
  71
  72         avl->root = NULL;
  73         avl->count = 0;
  74         return avl;
  75 }
  76
  77 void avl_free(AVL *avl)
  78 {
  79         freeNode(avl->root);
  80         free(avl);
  81 }
  82
  83 void *avl_lookup(const AVL *avl, const struct sm_state *sm)
  84 {
  85         AvlNode *found = lookup(avl, avl->root, sm);
  86         return found ? (void*) found->value : NULL;
  87 }
  88
  89 AvlNode *avl_lookup_node(const AVL *avl, const struct sm_state *sm)
  90 {
  91         return lookup(avl, avl->root, sm);
  92 }
  93
  94 size_t avl_count(const AVL *avl)
  95 {
  96         return avl->count;
  97 }
  98
  99 bool avl_insert(AVL *avl, const struct sm_state *sm, const void *value)
 100 {
 101         size_t old_count = avl->count;
 102         insert_sm(avl, &avl->root, sm, value);
 103         return avl->count != old_count;
 104 }
 105
 106 bool avl_remove(AVL *avl, const struct sm_state *sm)
 107 {
 108         AvlNode *node = NULL;
 109
 110         remove_sm(avl, &avl->root, sm, &node);
 111
 112         if (node == NULL) {
 113                 return false;
 114         } else {
 115                 free(node);
 116                 return true;
 117         }
 118 }
 119
 120 static AvlNode *mkNode(const struct sm_state *sm, const void *value)
 121 {
 122         AvlNode *node = malloc(sizeof(*node));
 123
 124         assert(node != NULL);
 125
 126         node->sm = sm;
 127         node->value = value;
 128         node->lr[0] = NULL;
 129         node->lr[1] = NULL;
 130         node->balance = 0;
 131         return node;
 132 }
 133
 134 static void freeNode(AvlNode *node)
 135 {
 136         if (node) {
 137                 freeNode(node->lr[0]);
 138                 freeNode(node->lr[1]);
 139                 free(node);
 140         }
 141 }
 142
 143 static AvlNode *lookup(const AVL *avl, AvlNode *node, const struct sm_state *sm)
 144 {
 145         int cmp;
 146
 147         if (node == NULL)
 148                 return NULL;
 149
 150         cmp = cmp_tracker(sm, node->sm);
 151
 152         if (cmp < 0)
 153                 return lookup(avl, node->lr[0], sm);
 154         if (cmp > 0)
 155                 return lookup(avl, node->lr[1], sm);
 156         return node;
 157 }
 158
 159 /*
 160  * Insert a sm/value into a subtree, rebalancing if necessary.
 161  *
 162  * Return true if the subtree's height increased.
 163  */
 164 static bool insert_sm(AVL *avl, AvlNode **p, const struct sm_state *sm, const void *value)
 165 {
 166         if (*p == NULL) {
 167                 *p = mkNode(sm, value);
 168                 avl->count++;
 169                 return true;
 170         } else {
 171                 AvlNode *node = *p;
 172                 int      cmp  = sign(cmp_tracker(sm, node->sm));
 173
 174                 if (cmp == 0) {
 175                         node->sm = sm;
 176                         node->value = value;
 177                         return false;
 178                 }
 179
 180                 if (!insert_sm(avl, &node->lr[side(cmp)], sm, value))
 181                         return false;
 182
 183                 /* If tree's balance became -1 or 1, it means the tree's height grew due to insertion. */
 184                 return sway(p, cmp) != 0;
 185         }
 186 }
 187
 188 /*
 189  * Remove the node matching the given sm.
 190  * If present, return the removed node through *ret .
 191  * The returned node's lr and balance are meaningless.
 192  *
 193  * Return true if the subtree's height decreased.
 194  */
 195 static bool remove_sm(AVL *avl, AvlNode **p, const struct sm_state *sm, AvlNode **ret)
 196 {
 197         if (*p == NULL) {
 198                 return false;
 199         } else {
 200                 AvlNode *node = *p;
 201                 int      cmp  = sign(cmp_tracker(sm, node->sm));
 202
 203                 if (cmp == 0) {
 204                         *ret = node;
 205                         avl->count--;
 206
 207                         if (node->lr[0] != NULL && node->lr[1] != NULL) {
 208                                 AvlNode *replacement;
 209                                 int      side;
 210                                 bool     shrunk;
 211
 212                                 /* Pick a subtree to pull the replacement from such that
 213                                  * this node doesn't have to be rebalanced. */
 214                                 side = node->balance <= 0 ? 0 : 1;
 215
 216                                 shrunk = removeExtremum(&node->lr[side], 1 - side, &replacement);
 217
 218                                 replacement->lr[0]   = node->lr[0];
 219                                 replacement->lr[1]   = node->lr[1];
 220                                 replacement->balance = node->balance;
 221                                 *p = replacement;
 222
 223                                 if (!shrunk)
 224                                         return false;
 225
 226                                 replacement->balance -= bal(side);
 227
 228                                 /* If tree's balance became 0, it means the tree's height shrank due to removal. */
 229                                 return replacement->balance == 0;
 230                         }
 231
 232                         if (node->lr[0] != NULL)
 233                                 *p = node->lr[0];
 234                         else
 235                                 *p = node->lr[1];
 236
 237                         return true;
 238
 239                 } else {
 240                         if (!remove_sm(avl, &node->lr[side(cmp)], sm, ret))
 241                                 return false;
 242
 243                         /* If tree's balance became 0, it means the tree's height shrank due to removal. */
 244                         return sway(p, -cmp) == 0;
 245                 }
 246         }
 247 }
 248
 249 /*
 250  * Remove either the left-most (if side == 0) or right-most (if side == 1)
 251  * node in a subtree, returning the removed node through *ret .
 252  * The returned node's lr and balance are meaningless.
 253  *
 254  * The subtree must not be empty (i.e. *p must not be NULL).
 255  *
 256  * Return true if the subtree's height decreased.
 257  */
 258 static bool removeExtremum(AvlNode **p, int side, AvlNode **ret)
 259 {
 260         AvlNode *node = *p;
 261
 262         if (node->lr[side] == NULL) {
 263                 *ret = node;
 264                 *p = node->lr[1 - side];
 265                 return true;
 266         }
 267
 268         if (!removeExtremum(&node->lr[side], side, ret))
 269                 return false;
 270
 271         /* If tree's balance became 0, it means the tree's height shrank due to removal. */
 272         return sway(p, -bal(side)) == 0;
 273 }
 274
 275 /*
 276  * Rebalance a node if necessary.  Think of this function
 277  * as a higher-level interface to balance().
 278  *
 279  * sway must be either -1 or 1, and indicates what was added to
 280  * the balance of this node by a prior operation.
 281  *
 282  * Return the new balance of the subtree.
 283  */
 284 static int sway(AvlNode **p, int sway)
 285 {
 286         if ((*p)->balance != sway)
 287                 (*p)->balance += sway;
 288         else
 289                 balance(p, side(sway));
 290
 291         return (*p)->balance;
 292 }
 293
 294 /*
 295  * Perform tree rotations on an unbalanced node.
 296  *
 297  * side == 0 means the node's balance is -2 .
 298  * side == 1 means the node's balance is +2 .
 299  */
 300 static void balance(AvlNode **p, int side)
 301 {
 302         AvlNode  *node  = *p,
 303                  *child = node->lr[side];
 304         int opposite    = 1 - side;
 305         int bal         = bal(side);
 306
 307         if (child->balance != -bal) {
 308                 /* Left-left (side == 0) or right-right (side == 1) */
 309                 node->lr[side]      = child->lr[opposite];
 310                 child->lr[opposite] = node;
 311                 *p = child;
 312
 313                 child->balance -= bal;
 314                 node->balance = -child->balance;
 315
 316         } else {
 317                 /* Left-right (side == 0) or right-left (side == 1) */
 318                 AvlNode *grandchild = child->lr[opposite];
 319
 320                 node->lr[side]           = grandchild->lr[opposite];
 321                 child->lr[opposite]      = grandchild->lr[side];
 322                 grandchild->lr[side]     = child;
 323                 grandchild->lr[opposite] = node;
 324                 *p = grandchild;
 325
 326                 node->balance       = 0;
 327                 child->balance      = 0;
 328
 329                 if (grandchild->balance == bal)
 330                         node->balance  = -bal;
 331                 else if (grandchild->balance == -bal)
 332                         child->balance = bal;
 333
 334                 grandchild->balance = 0;
 335         }
 336 }
 337
 338
 339 /************************* avl_check_invariants() *************************/
 340
 341 bool avl_check_invariants(AVL *avl)
 342 {
 343         int    dummy;
 344
 345         return checkBalances(avl->root, &dummy)
 346             && checkOrder(avl)
 347             && countNode(avl->root) == avl->count;
 348 }
 349
 350 static bool checkBalances(AvlNode *node, int *height)
 351 {
 352         if (node) {
 353                 int h0, h1;
 354
 355                 if (!checkBalances(node->lr[0], &h0))
 356                         return false;
 357                 if (!checkBalances(node->lr[1], &h1))
 358                         return false;
 359
 360                 if (node->balance != h1 - h0 || node->balance < -1 || node->balance > 1)
 361                         return false;
 362
 363                 *height = (h0 > h1 ? h0 : h1) + 1;
 364                 return true;
 365         } else {
 366                 *height = 0;
 367                 return true;
 368         }
 369 }
 370
 371 static bool checkOrder(AVL *avl)
 372 {
 373         AvlIter     i;
 374         const void *last     = NULL;
 375         bool        last_set = false;
 376
 377         avl_foreach(i, avl) {
 378                 if (last_set && cmp_tracker(last, i.sm) >= 0)
 379                         return false;
 380                 last     = i.sm;
 381                 last_set = true;
 382         }
 383
 384         return true;
 385 }
 386
 387 static size_t countNode(AvlNode *node)
 388 {
 389         if (node)
 390                 return 1 + countNode(node->lr[0]) + countNode(node->lr[1]);
 391         else
 392                 return 0;
 393 }
 394
 395
 396 /************************* Traversal *************************/
 397
 398 void avl_iter_begin(AvlIter *iter, AVL *avl, AvlDirection dir)
 399 {
 400         AvlNode *node = avl->root;
 401
 402         iter->stack_index = 0;
 403         iter->direction   = dir;
 404
 405         if (node == NULL) {
 406                 iter->sm      = NULL;
 407                 iter->value    = NULL;
 408                 iter->node     = NULL;
 409                 return;
 410         }
 411
 412         while (node->lr[dir] != NULL) {
 413                 iter->stack[iter->stack_index++] = node;
 414                 node = node->lr[dir];
 415         }
 416
 417         iter->sm   = (void*) node->sm;
 418         iter->value = (void*) node->value;
 419         iter->node  = node;
 420 }
 421
 422 void avl_iter_next(AvlIter *iter)
 423 {
 424         AvlNode     *node = iter->node;
 425         AvlDirection dir  = iter->direction;
 426
 427         if (node == NULL)
 428                 return;
 429
 430         node = node->lr[1 - dir];
 431         if (node != NULL) {
 432                 while (node->lr[dir] != NULL) {
 433                         iter->stack[iter->stack_index++] = node;
 434                         node = node->lr[dir];
 435                 }
 436         } else if (iter->stack_index > 0) {
 437                 node = iter->stack[--iter->stack_index];
 438         } else {
 439                 iter->sm      = NULL;
 440                 iter->value    = NULL;
 441                 iter->node     = NULL;
 442                 return;
 443         }
 444
 445         iter->node  = node;
 446         iter->sm   = (void*) node->sm;
 447         iter->value = (void*) node->value;
 448 }