/* libavl - library for manipulation of binary trees. Copyright (C) 1998-2002, 2004 Free Software Foundation, Inc. This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program 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 General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. The author may be contacted at on the Internet, or write to Ben Pfaff, Stanford University, Computer Science Dept., 353 Serra Mall, Stanford CA 94305, USA. */ #include #include #include #include #include "avl.h" /* Creates and returns a new table with comparison function |compare| using parameter |param| and memory allocator |allocator|. Returns |NULL| if memory allocation failed. */ struct avl_table * avl_create (avl_comparison_func *compare, void *param, struct libavl_allocator *allocator) { struct avl_table *tree; assert (compare != NULL); if (allocator == NULL) allocator = &avl_allocator_default; tree = allocator->libavl_malloc (allocator, sizeof *tree); if (tree == NULL) return NULL; tree->avl_root = NULL; tree->avl_compare = compare; tree->avl_param = param; tree->avl_alloc = allocator; tree->avl_count = 0; tree->avl_generation = 0; return tree; } /* Search |tree| for an item matching |item|, and return it if found. Otherwise return |NULL|. */ void * avl_find (const struct avl_table *tree, const void *item) { const struct avl_node *p; assert (tree != NULL && item != NULL); for (p = tree->avl_root; p != NULL; ) { int cmp = tree->avl_compare (item, p->avl_data, tree->avl_param); if (cmp < 0) p = p->avl_link[0]; else if (cmp > 0) p = p->avl_link[1]; else /* |cmp == 0| */ return p->avl_data; } return NULL; } /* Inserts |item| into |tree| and returns a pointer to |item|'s address. If a duplicate item is found in the tree, returns a pointer to the duplicate without inserting |item|. Returns |NULL| in case of memory allocation failure. */ void ** avl_probe (struct avl_table *tree, void *item) { struct avl_node *y, *z; /* Top node to update balance factor, and parent. */ struct avl_node *p, *q; /* Iterator, and parent. */ struct avl_node *n; /* Newly inserted node. */ struct avl_node *w; /* New root of rebalanced subtree. */ int dir; /* Direction to descend. */ unsigned char da[AVL_MAX_HEIGHT]; /* Cached comparison results. */ int k = 0; /* Number of cached results. */ assert (tree != NULL && item != NULL); z = (struct avl_node *) &tree->avl_root; y = tree->avl_root; dir = 0; for (q = z, p = y; p != NULL; q = p, p = p->avl_link[dir]) { int cmp = tree->avl_compare (item, p->avl_data, tree->avl_param); if (cmp == 0) return &p->avl_data; if (p->avl_balance != 0) z = q, y = p, k = 0; da[k++] = dir = cmp > 0; } n = q->avl_link[dir] = tree->avl_alloc->libavl_malloc (tree->avl_alloc, sizeof *n); if (n == NULL) return NULL; tree->avl_count++; n->avl_data = item; n->avl_link[0] = n->avl_link[1] = NULL; n->avl_balance = 0; if (y == NULL) return &n->avl_data; for (p = y, k = 0; p != n; p = p->avl_link[da[k]], k++) if (da[k] == 0) p->avl_balance--; else p->avl_balance++; if (y->avl_balance == -2) { struct avl_node *x = y->avl_link[0]; if (x->avl_balance == -1) { w = x; y->avl_link[0] = x->avl_link[1]; x->avl_link[1] = y; x->avl_balance = y->avl_balance = 0; } else { assert (x->avl_balance == +1); w = x->avl_link[1]; x->avl_link[1] = w->avl_link[0]; w->avl_link[0] = x; y->avl_link[0] = w->avl_link[1]; w->avl_link[1] = y; if (w->avl_balance == -1) x->avl_balance = 0, y->avl_balance = +1; else if (w->avl_balance == 0) x->avl_balance = y->avl_balance = 0; else /* |w->avl_balance == +1| */ x->avl_balance = -1, y->avl_balance = 0; w->avl_balance = 0; } } else if (y->avl_balance == +2) { struct avl_node *x = y->avl_link[1]; if (x->avl_balance == +1) { w = x; y->avl_link[1] = x->avl_link[0]; x->avl_link[0] = y; x->avl_balance = y->avl_balance = 0; } else { assert (x->avl_balance == -1); w = x->avl_link[0]; x->avl_link[0] = w->avl_link[1]; w->avl_link[1] = x; y->avl_link[1] = w->avl_link[0]; w->avl_link[0] = y; if (w->avl_balance == +1) x->avl_balance = 0, y->avl_balance = -1; else if (w->avl_balance == 0) x->avl_balance = y->avl_balance = 0; else /* |w->avl_balance == -1| */ x->avl_balance = +1, y->avl_balance = 0; w->avl_balance = 0; } } else return &n->avl_data; z->avl_link[y != z->avl_link[0]] = w; tree->avl_generation++; return &n->avl_data; } /* Inserts |item| into |table|. Returns |NULL| if |item| was successfully inserted or if a memory allocation error occurred. Otherwise, returns the duplicate item. */ void * avl_insert (struct avl_table *table, void *item) { void **p = avl_probe (table, item); return p == NULL || *p == item ? NULL : *p; } /* Inserts |item| into |table|, replacing any duplicate item. Returns |NULL| if |item| was inserted without replacing a duplicate, or if a memory allocation error occurred. Otherwise, returns the item that was replaced. */ void * avl_replace (struct avl_table *table, void *item) { void **p = avl_probe (table, item); if (p == NULL || *p == item) return NULL; else { void *r = *p; *p = item; return r; } } /* Deletes from |tree| and returns an item matching |item|. Returns a null pointer if no matching item found. */ void * avl_delete (struct avl_table *tree, const void *item) { /* Stack of nodes. */ struct avl_node *pa[AVL_MAX_HEIGHT]; /* Nodes. */ unsigned char da[AVL_MAX_HEIGHT]; /* |avl_link[]| indexes. */ int k; /* Stack pointer. */ struct avl_node *p; /* Traverses tree to find node to delete. */ int cmp; /* Result of comparison between |item| and |p|. */ assert (tree != NULL && item != NULL); k = 0; p = (struct avl_node *) &tree->avl_root; for (cmp = -1; cmp != 0; cmp = tree->avl_compare (item, p->avl_data, tree->avl_param)) { int dir = cmp > 0; pa[k] = p; da[k++] = dir; p = p->avl_link[dir]; if (p == NULL) return NULL; } item = p->avl_data; if (p->avl_link[1] == NULL) pa[k - 1]->avl_link[da[k - 1]] = p->avl_link[0]; else { struct avl_node *r = p->avl_link[1]; if (r->avl_link[0] == NULL) { r->avl_link[0] = p->avl_link[0]; r->avl_balance = p->avl_balance; pa[k - 1]->avl_link[da[k - 1]] = r; da[k] = 1; pa[k++] = r; } else { struct avl_node *s; int j = k++; for (;;) { da[k] = 0; pa[k++] = r; s = r->avl_link[0]; if (s->avl_link[0] == NULL) break; r = s; } s->avl_link[0] = p->avl_link[0]; r->avl_link[0] = s->avl_link[1]; s->avl_link[1] = p->avl_link[1]; s->avl_balance = p->avl_balance; pa[j - 1]->avl_link[da[j - 1]] = s; da[j] = 1; pa[j] = s; } } tree->avl_alloc->libavl_free (tree->avl_alloc, p); assert (k > 0); while (--k > 0) { struct avl_node *y = pa[k]; if (da[k] == 0) { y->avl_balance++; if (y->avl_balance == +1) break; else if (y->avl_balance == +2) { struct avl_node *x = y->avl_link[1]; if (x->avl_balance == -1) { struct avl_node *w; assert (x->avl_balance == -1); w = x->avl_link[0]; x->avl_link[0] = w->avl_link[1]; w->avl_link[1] = x; y->avl_link[1] = w->avl_link[0]; w->avl_link[0] = y; if (w->avl_balance == +1) x->avl_balance = 0, y->avl_balance = -1; else if (w->avl_balance == 0) x->avl_balance = y->avl_balance = 0; else /* |w->avl_balance == -1| */ x->avl_balance = +1, y->avl_balance = 0; w->avl_balance = 0; pa[k - 1]->avl_link[da[k - 1]] = w; } else { y->avl_link[1] = x->avl_link[0]; x->avl_link[0] = y; pa[k - 1]->avl_link[da[k - 1]] = x; if (x->avl_balance == 0) { x->avl_balance = -1; y->avl_balance = +1; break; } else x->avl_balance = y->avl_balance = 0; } } } else { y->avl_balance--; if (y->avl_balance == -1) break; else if (y->avl_balance == -2) { struct avl_node *x = y->avl_link[0]; if (x->avl_balance == +1) { struct avl_node *w; assert (x->avl_balance == +1); w = x->avl_link[1]; x->avl_link[1] = w->avl_link[0]; w->avl_link[0] = x; y->avl_link[0] = w->avl_link[1]; w->avl_link[1] = y; if (w->avl_balance == -1) x->avl_balance = 0, y->avl_balance = +1; else if (w->avl_balance == 0) x->avl_balance = y->avl_balance = 0; else /* |w->avl_balance == +1| */ x->avl_balance = -1, y->avl_balance = 0; w->avl_balance = 0; pa[k - 1]->avl_link[da[k - 1]] = w; } else { y->avl_link[0] = x->avl_link[1]; x->avl_link[1] = y; pa[k - 1]->avl_link[da[k - 1]] = x; if (x->avl_balance == 0) { x->avl_balance = +1; y->avl_balance = -1; break; } else x->avl_balance = y->avl_balance = 0; } } } } tree->avl_count--; tree->avl_generation++; return (void *) item; } /* Refreshes the stack of parent pointers in |trav| and updates its generation number. */ static void trav_refresh (struct avl_traverser *trav) { assert (trav != NULL); trav->avl_generation = trav->avl_table->avl_generation; if (trav->avl_node != NULL) { avl_comparison_func *cmp = trav->avl_table->avl_compare; void *param = trav->avl_table->avl_param; struct avl_node *node = trav->avl_node; struct avl_node *i; trav->avl_height = 0; for (i = trav->avl_table->avl_root; i != node; ) { assert (trav->avl_height < AVL_MAX_HEIGHT); assert (i != NULL); trav->avl_stack[trav->avl_height++] = i; i = i->avl_link[cmp (node->avl_data, i->avl_data, param) > 0]; } } } /* Initializes |trav| for use with |tree| and selects the null node. */ void avl_t_init (struct avl_traverser *trav, struct avl_table *tree) { trav->avl_table = tree; trav->avl_node = NULL; trav->avl_height = 0; trav->avl_generation = tree->avl_generation; } /* Initializes |trav| for |tree| and selects and returns a pointer to its least-valued item. Returns |NULL| if |tree| contains no nodes. */ void * avl_t_first (struct avl_traverser *trav, struct avl_table *tree) { struct avl_node *x; assert (tree != NULL && trav != NULL); trav->avl_table = tree; trav->avl_height = 0; trav->avl_generation = tree->avl_generation; x = tree->avl_root; if (x != NULL) while (x->avl_link[0] != NULL) { assert (trav->avl_height < AVL_MAX_HEIGHT); trav->avl_stack[trav->avl_height++] = x; x = x->avl_link[0]; } trav->avl_node = x; return x != NULL ? x->avl_data : NULL; } /* Initializes |trav| for |tree| and selects and returns a pointer to its greatest-valued item. Returns |NULL| if |tree| contains no nodes. */ void * avl_t_last (struct avl_traverser *trav, struct avl_table *tree) { struct avl_node *x; assert (tree != NULL && trav != NULL); trav->avl_table = tree; trav->avl_height = 0; trav->avl_generation = tree->avl_generation; x = tree->avl_root; if (x != NULL) while (x->avl_link[1] != NULL) { assert (trav->avl_height < AVL_MAX_HEIGHT); trav->avl_stack[trav->avl_height++] = x; x = x->avl_link[1]; } trav->avl_node = x; return x != NULL ? x->avl_data : NULL; } /* Searches for |item| in |tree|. If found, initializes |trav| to the item found and returns the item as well. If there is no matching item, initializes |trav| to the null item and returns |NULL|. */ void * avl_t_find (struct avl_traverser *trav, struct avl_table *tree, void *item) { struct avl_node *p, *q; assert (trav != NULL && tree != NULL && item != NULL); trav->avl_table = tree; trav->avl_height = 0; trav->avl_generation = tree->avl_generation; for (p = tree->avl_root; p != NULL; p = q) { int cmp = tree->avl_compare (item, p->avl_data, tree->avl_param); if (cmp < 0) q = p->avl_link[0]; else if (cmp > 0) q = p->avl_link[1]; else /* |cmp == 0| */ { trav->avl_node = p; return p->avl_data; } assert (trav->avl_height < AVL_MAX_HEIGHT); trav->avl_stack[trav->avl_height++] = p; } trav->avl_height = 0; trav->avl_node = NULL; return NULL; } /* Attempts to insert |item| into |tree|. If |item| is inserted successfully, it is returned and |trav| is initialized to its location. If a duplicate is found, it is returned and |trav| is initialized to its location. No replacement of the item occurs. If a memory allocation failure occurs, |NULL| is returned and |trav| is initialized to the null item. */ void * avl_t_insert (struct avl_traverser *trav, struct avl_table *tree, void *item) { void **p; assert (trav != NULL && tree != NULL && item != NULL); p = avl_probe (tree, item); if (p != NULL) { trav->avl_table = tree; trav->avl_node = ((struct avl_node *) ((char *) p - offsetof (struct avl_node, avl_data))); trav->avl_generation = tree->avl_generation - 1; return *p; } else { avl_t_init (trav, tree); return NULL; } } /* Initializes |trav| to have the same current node as |src|. */ void * avl_t_copy (struct avl_traverser *trav, const struct avl_traverser *src) { assert (trav != NULL && src != NULL); if (trav != src) { trav->avl_table = src->avl_table; trav->avl_node = src->avl_node; trav->avl_generation = src->avl_generation; if (trav->avl_generation == trav->avl_table->avl_generation) { trav->avl_height = src->avl_height; memcpy (trav->avl_stack, (const void *) src->avl_stack, sizeof *trav->avl_stack * trav->avl_height); } } return trav->avl_node != NULL ? trav->avl_node->avl_data : NULL; } /* Returns the next data item in inorder within the tree being traversed with |trav|, or if there are no more data items returns |NULL|. */ void * avl_t_next (struct avl_traverser *trav) { struct avl_node *x; assert (trav != NULL); if (trav->avl_generation != trav->avl_table->avl_generation) trav_refresh (trav); x = trav->avl_node; if (x == NULL) { return avl_t_first (trav, trav->avl_table); } else if (x->avl_link[1] != NULL) { assert (trav->avl_height < AVL_MAX_HEIGHT); trav->avl_stack[trav->avl_height++] = x; x = x->avl_link[1]; while (x->avl_link[0] != NULL) { assert (trav->avl_height < AVL_MAX_HEIGHT); trav->avl_stack[trav->avl_height++] = x; x = x->avl_link[0]; } } else { struct avl_node *y; do { if (trav->avl_height == 0) { trav->avl_node = NULL; return NULL; } y = x; x = trav->avl_stack[--trav->avl_height]; } while (y == x->avl_link[1]); } trav->avl_node = x; return x->avl_data; } /* Returns the previous data item in inorder within the tree being traversed with |trav|, or if there are no more data items returns |NULL|. */ void * avl_t_prev (struct avl_traverser *trav) { struct avl_node *x; assert (trav != NULL); if (trav->avl_generation != trav->avl_table->avl_generation) trav_refresh (trav); x = trav->avl_node; if (x == NULL) { return avl_t_last (trav, trav->avl_table); } else if (x->avl_link[0] != NULL) { assert (trav->avl_height < AVL_MAX_HEIGHT); trav->avl_stack[trav->avl_height++] = x; x = x->avl_link[0]; while (x->avl_link[1] != NULL) { assert (trav->avl_height < AVL_MAX_HEIGHT); trav->avl_stack[trav->avl_height++] = x; x = x->avl_link[1]; } } else { struct avl_node *y; do { if (trav->avl_height == 0) { trav->avl_node = NULL; return NULL; } y = x; x = trav->avl_stack[--trav->avl_height]; } while (y == x->avl_link[0]); } trav->avl_node = x; return x->avl_data; } /* Returns |trav|'s current item. */ void * avl_t_cur (struct avl_traverser *trav) { assert (trav != NULL); return trav->avl_node != NULL ? trav->avl_node->avl_data : NULL; } /* Replaces the current item in |trav| by |new| and returns the item replaced. |trav| must not have the null item selected. The new item must not upset the ordering of the tree. */ void * avl_t_replace (struct avl_traverser *trav, void *new) { void *old; assert (trav != NULL && trav->avl_node != NULL && new != NULL); old = trav->avl_node->avl_data; trav->avl_node->avl_data = new; return old; } /* Destroys |new| with |avl_destroy (new, destroy)|, first setting right links of nodes in |stack| within |new| to null pointers to avoid touching uninitialized data. */ static void copy_error_recovery (struct avl_node **stack, int height, struct avl_table *new, avl_item_func *destroy) { assert (stack != NULL && height >= 0 && new != NULL); for (; height > 2; height -= 2) stack[height - 1]->avl_link[1] = NULL; avl_destroy (new, destroy); } /* Copies |org| to a newly created tree, which is returned. If |copy != NULL|, each data item in |org| is first passed to |copy|, and the return values are inserted into the tree, with |NULL| return values taken as indications of failure. On failure, destroys the partially created new tree, applying |destroy|, if non-null, to each item in the new tree so far, and returns |NULL|. If |allocator != NULL|, it is used for allocation in the new tree. Otherwise, the same allocator used for |org| is used. */ struct avl_table * avl_copy (const struct avl_table *org, avl_copy_func *copy, avl_item_func *destroy, struct libavl_allocator *allocator) { struct avl_node *stack[2 * (AVL_MAX_HEIGHT + 1)]; int height = 0; struct avl_table *new; const struct avl_node *x; struct avl_node *y; assert (org != NULL); new = avl_create (org->avl_compare, org->avl_param, allocator != NULL ? allocator : org->avl_alloc); if (new == NULL) return NULL; new->avl_count = org->avl_count; if (new->avl_count == 0) return new; x = (const struct avl_node *) &org->avl_root; y = (struct avl_node *) &new->avl_root; for (;;) { while (x->avl_link[0] != NULL) { assert (height < 2 * (AVL_MAX_HEIGHT + 1)); y->avl_link[0] = new->avl_alloc->libavl_malloc (new->avl_alloc, sizeof *y->avl_link[0]); if (y->avl_link[0] == NULL) { if (y != (struct avl_node *) &new->avl_root) { y->avl_data = NULL; y->avl_link[1] = NULL; } copy_error_recovery (stack, height, new, destroy); return NULL; } stack[height++] = (struct avl_node *) x; stack[height++] = y; x = x->avl_link[0]; y = y->avl_link[0]; } y->avl_link[0] = NULL; for (;;) { y->avl_balance = x->avl_balance; if (copy == NULL) y->avl_data = x->avl_data; else { y->avl_data = copy (x->avl_data, org->avl_param); if (y->avl_data == NULL) { y->avl_link[1] = NULL; copy_error_recovery (stack, height, new, destroy); return NULL; } } if (x->avl_link[1] != NULL) { y->avl_link[1] = new->avl_alloc->libavl_malloc (new->avl_alloc, sizeof *y->avl_link[1]); if (y->avl_link[1] == NULL) { copy_error_recovery (stack, height, new, destroy); return NULL; } x = x->avl_link[1]; y = y->avl_link[1]; break; } else y->avl_link[1] = NULL; if (height <= 2) return new; y = stack[--height]; x = stack[--height]; } } } /* Frees storage allocated for |tree|. If |destroy != NULL|, applies it to each data item in inorder. */ void avl_destroy (struct avl_table *tree, avl_item_func *destroy) { struct avl_node *p, *q; assert (tree != NULL); for (p = tree->avl_root; p != NULL; p = q) if (p->avl_link[0] == NULL) { q = p->avl_link[1]; if (destroy != NULL && p->avl_data != NULL) destroy (p->avl_data, tree->avl_param); tree->avl_alloc->libavl_free (tree->avl_alloc, p); } else { q = p->avl_link[0]; p->avl_link[0] = q->avl_link[1]; q->avl_link[1] = p; } tree->avl_alloc->libavl_free (tree->avl_alloc, tree); } /* Allocates |size| bytes of space using |malloc()|. Returns a null pointer if allocation fails. */ void * avl_malloc (struct libavl_allocator *allocator, size_t size) { assert (allocator != NULL && size > 0); return malloc (size); } /* Frees |block|. */ void avl_free (struct libavl_allocator *allocator, void *block) { assert (allocator != NULL && block != NULL); free (block); } /* Default memory allocator that uses |malloc()| and |free()|. */ struct libavl_allocator avl_allocator_default = { avl_malloc, avl_free }; #undef NDEBUG #include /* Asserts that |avl_insert()| succeeds at inserting |item| into |table|. */ void (avl_assert_insert) (struct avl_table *table, void *item) { void **p = avl_probe (table, item); assert (p != NULL && *p == item); } /* Asserts that |avl_delete()| really removes |item| from |table|, and returns the removed item. */ void * (avl_assert_delete) (struct avl_table *table, void *item) { void *p = avl_delete (table, item); assert (p != NULL); return p; }