avl.cpp

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/*****************************************************************************
 
    avl.c - Source code for the AVL-tree library.
 
    Copyright (C) 1998  Michael H. Buselli <cosine@cosine.org>
    Copyright (C) 2000-2002  Wessel Dankers <wsl@nl.linux.org>
 
    This library 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 2.1 of the License, or (at your option) any later version.
 
    This library 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 library; if not, write to the Free Software
    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307  USA
 
    Augmented AVL-tree. Original by Michael H. Buselli <cosine@cosine.org>.
 
    Modified by Wessel Dankers <wsl@nl.linux.org> to add a bunch of bloat to
    the sourcecode, change the interface and squash a few bugs.
    Mail him if you find new bugs.
 
*****************************************************************************/
 
#include <stdio.h>
#include <stdlib.h>
#include <errno.h>
#include "avl.h"
 
static void avl_rebalance(avl_tree_t *, avl_node_t *);
 
#ifdef AVL_COUNT
#define NODE_COUNT(n)  ((n) ? (n)->count : 0)
#define L_COUNT(n)     (NODE_COUNT((n)->left))
#define R_COUNT(n)     (NODE_COUNT((n)->right))
#define CALC_COUNT(n)  (L_COUNT(n) + R_COUNT(n) + 1)
#endif
 
#ifdef AVL_DEPTH
#define NODE_DEPTH(n)  ((n) ? (n)->depth : 0)
#define L_DEPTH(n)     (NODE_DEPTH((n)->left))
#define R_DEPTH(n)     (NODE_DEPTH((n)->right))
#define CALC_DEPTH(n)  ((L_DEPTH(n)>R_DEPTH(n)?L_DEPTH(n):R_DEPTH(n)) + 1)
#endif
 
#ifndef AVL_DEPTH
/* Also known as ffs() (from BSD) */
static int lg(unsigned int u) {
        int r = 1;
        if(!u) return 0;
        if(u & 0xffff0000) { u >>= 16; r += 16; }
        if(u & 0x0000ff00) { u >>= 8; r += 8; }
        if(u & 0x000000f0) { u >>= 4; r += 4; }
        if(u & 0x0000000c) { u >>= 2; r += 2; }
        if(u & 0x00000002) r++;
        return r;
}
#endif
 
static int avl_check_balance(avl_node_t *avlnode) {
#ifdef AVL_DEPTH
        int d;
        d = R_DEPTH(avlnode) - L_DEPTH(avlnode);
        return d<-1?-1:d>1?1:0;
#else
/*      int d;
 *      d = lg(R_COUNT(avlnode)) - lg(L_COUNT(avlnode));
 *      d = d<-1?-1:d>1?1:0;
 */
#ifdef AVL_COUNT
        int pl, r;
 
        pl = lg(L_COUNT(avlnode));
        r = R_COUNT(avlnode);
 
        if(r>>pl+1)
                return 1;
        if(pl<2 || r>>pl-2)
                return 0;
        return -1;
#else
#error No balancing possible.
#endif
#endif
}
 
#ifdef AVL_COUNT
unsigned int avl_count(const avl_tree_t *avltree) {
        return NODE_COUNT(avltree->top);
}
 
avl_node_t *avl_at(const avl_tree_t *avltree, unsigned int index) {
        avl_node_t *avlnode;
        unsigned int c;
 
        avlnode = avltree->top;
 
        while(avlnode) {
                c = L_COUNT(avlnode);
 
                if(index < c) {
                        avlnode = avlnode->left;
                } else if(index > c) {
                        avlnode = avlnode->right;
                        index -= c+1;
                } else {
                        return avlnode;
                }
        }
        return NULL;
}
 
unsigned int avl_index(const avl_node_t *avlnode) {
        avl_node_t *next;
        unsigned int c;
 
        c = L_COUNT(avlnode);
 
        while((next = avlnode->parent)) {
                if(avlnode == next->right)
                        c += L_COUNT(next) + 1;
                avlnode = next;
        }
 
        return c;
}
#endif
 
int avl_search_closest(const avl_tree_t *avltree, const void *item, avl_node_t **avlnode) {
        avl_node_t *node;
        avl_compare_t cmp;
        int c;
 
        if(!avlnode)
                avlnode = &node;
 
        node = avltree->top;
 
        if(!node)
                return *avlnode = NULL, 0;
 
        cmp = avltree->cmp;
 
        for(;;) {
                c = cmp(item, node->item);
 
                if(c < 0) {
                        if(node->left)
                                node = node->left;
                        else
                                return *avlnode = node, -1;
                } else if(c > 0) {
                        if(node->right)
                                node = node->right;
                        else
                                return *avlnode = node, 1;
                } else {
                        return *avlnode = node, 0;
                }
        }
}
 
/*
 * avl_search:
 * Return a pointer to a node with the given item in the tree.
 * If no such item is in the tree, then NULL is returned.
 */
avl_node_t *avl_search(const avl_tree_t *avltree, const void *item) {
        avl_node_t *node;
        return avl_search_closest(avltree, item, &node) ? NULL : node;
}
 
avl_tree_t *avl_init_tree(avl_tree_t *rc, avl_compare_t cmp, avl_freeitem_t freeitem) {
        if(rc) {
                rc->head = NULL;
                rc->tail = NULL;
                rc->top = NULL;
                rc->cmp = cmp;
                rc->freeitem = freeitem;
        }
        return rc;
}
 
avl_tree_t *avl_alloc_tree(avl_compare_t cmp, avl_freeitem_t freeitem) {
        return avl_init_tree((avl_tree_t*)malloc(sizeof(avl_tree_t)), cmp, freeitem);
}
 
void avl_clear_tree(avl_tree_t *avltree) {
        avltree->top = avltree->head = avltree->tail = NULL;
}
 
void avl_free_nodes(avl_tree_t *avltree) {
        avl_node_t *node, *next;
        avl_freeitem_t freeitem;
 
        freeitem = avltree->freeitem;
 
        for(node = avltree->head; node; node = next) {
                next = node->next;
                if(freeitem)
                        freeitem(node->item);
                free(node);
        }
        return avl_clear_tree(avltree);
}
 
/*
 * avl_free_tree:
 * Free all memory used by this tree.  If freeitem is not NULL, then
 * it is assumed to be a destructor for the items referenced in the avl_
 * tree, and they are deleted as well.
 */
void avl_free_tree(avl_tree_t *avltree) {
        avl_free_nodes(avltree);
        free(avltree);
}
 
static void avl_clear_node(avl_node_t *newnode) {
        newnode->left = newnode->right = NULL;
        #ifdef AVL_COUNT
        newnode->count = 1;
        #endif
        #ifdef AVL_DEPTH
        newnode->depth = 1;
        #endif
}
 
avl_node_t *avl_init_node(avl_node_t *newnode, void *item) {
        if(newnode) {
          avl_clear_node(newnode); 
          newnode->item = item;
        }
        return newnode;
}
 
avl_node_t *avl_insert_top(avl_tree_t *avltree, avl_node_t *newnode) {
        avl_clear_node(newnode);
        newnode->prev = newnode->next = newnode->parent = NULL;
        avltree->head = avltree->tail = avltree->top = newnode;
        return newnode;
}
 
avl_node_t *avl_insert_before(avl_tree_t *avltree, avl_node_t *node, avl_node_t *newnode) {
        if(!node)
                return avltree->tail
                        ? avl_insert_after(avltree, avltree->tail, newnode)
                        : avl_insert_top(avltree, newnode);
 
        if(node->left)
                return avl_insert_after(avltree, node->prev, newnode);
 
        avl_clear_node(newnode);
 
        newnode->next = node;
        newnode->parent = node;
 
        newnode->prev = node->prev;
        if(node->prev)
                node->prev->next = newnode;
        else
                avltree->head = newnode;
        node->prev = newnode;
 
        node->left = newnode;
        avl_rebalance(avltree, node);
        return newnode;
}
 
avl_node_t *avl_insert_after(avl_tree_t *avltree, avl_node_t *node, avl_node_t *newnode) {
        if(!node)
                return avltree->head
                        ? avl_insert_before(avltree, avltree->head, newnode)
                        : avl_insert_top(avltree, newnode);
 
        if(node->right)
                return avl_insert_before(avltree, node->next, newnode);
 
        avl_clear_node(newnode);
 
        newnode->prev = node;
        newnode->parent = node;
 
        newnode->next = node->next;
        if(node->next)
                node->next->prev = newnode;
        else
                avltree->tail = newnode;
        node->next = newnode;
 
        node->right = newnode;
        avl_rebalance(avltree, node);
        return newnode;
}
 
avl_node_t *avl_insert_node(avl_tree_t *avltree, avl_node_t *newnode) {
        avl_node_t *node;
 
        if(!avltree->top)
                return avl_insert_top(avltree, newnode);
 
        switch(avl_search_closest(avltree, newnode->item, &node)) {
                case -1:
                        return avl_insert_before(avltree, node, newnode);
                case 1:
                        return avl_insert_after(avltree, node, newnode);
        }
 
        return NULL;
}
 
/*
 * avl_insert:
 * Create a new node and insert an item there.
 * Returns the new node on success or NULL if no memory could be allocated.
 */
avl_node_t *avl_insert(avl_tree_t *avltree, void *item) {
        avl_node_t *newnode;
 
        newnode = avl_init_node((avl_node_t*)malloc(sizeof(avl_node_t)), item);
        if(newnode) {
                if(avl_insert_node(avltree, newnode))
                        return newnode;
                free(newnode);
                errno = EEXIST;
        }
        return NULL;
}
 
/*
 * avl_unlink_node:
 * Removes the given node.  Does not delete the item at that node.
 * The item of the node may be freed before calling avl_unlink_node.
 * (In other words, it is not referenced by this function.)
 */
void avl_unlink_node(avl_tree_t *avltree, avl_node_t *avlnode) {
        avl_node_t *parent;
        avl_node_t **superparent;
        avl_node_t *subst, *left, *right;
        avl_node_t *balnode;
 
        if(avlnode->prev)
                avlnode->prev->next = avlnode->next;
        else
                avltree->head = avlnode->next;
 
        if(avlnode->next)
                avlnode->next->prev = avlnode->prev;
        else
                avltree->tail = avlnode->prev;
 
        parent = avlnode->parent;
 
        superparent = parent
                ? avlnode == parent->left ? &parent->left : &parent->right
                : &avltree->top;
 
        left = avlnode->left;
        right = avlnode->right;
        if(!left) {
                *superparent = right;
                if(right)
                        right->parent = parent;
                balnode = parent;
        } else if(!right) {
                *superparent = left;
                left->parent = parent;
                balnode = parent;
        } else {
                subst = avlnode->prev;
                if(subst == left) {
                        balnode = subst;
                } else {
                        balnode = subst->parent;
                        balnode->right = subst->left;
                        if(balnode->right)
                                balnode->right->parent = balnode;
                        subst->left = left;
                        left->parent = subst;
                }
                subst->right = right;
                subst->parent = parent;
                right->parent = subst;
                *superparent = subst;
        }
 
        avl_rebalance(avltree, balnode);
}
 
void *avl_delete_node(avl_tree_t *avltree, avl_node_t *avlnode) {
        void *item = NULL;
        if(avlnode) {
                item = avlnode->item;
                avl_unlink_node(avltree, avlnode);
                if(avltree->freeitem)
                        avltree->freeitem(item);
                free(avlnode);
        }
        return item;
}
 
void *avl_delete(avl_tree_t *avltree, const void *item) {
        return avl_delete_node(avltree, avl_search(avltree, item));
}
 
avl_node_t *avl_fixup_node(avl_tree_t *avltree, avl_node_t *newnode) {
        avl_node_t *oldnode = NULL, *node;
 
        if(!avltree || !newnode)
                return NULL;
 
        node = newnode->prev;
        if(node) {
                oldnode = node->next;
                node->next = newnode;
        } else {
                avltree->head = newnode;
        }
 
        node = newnode->next;
        if(node) {
                oldnode = node->prev;
                node->prev = newnode;
        } else {
                avltree->tail = newnode;
        }
 
        node = newnode->parent;
        if(node) {
                if(node->left == oldnode)
                        node->left = newnode;
                else
                        node->right = newnode;
        } else {
                oldnode = avltree->top;
                avltree->top = newnode;
        }
 
        return oldnode;
}
 
/*
 * avl_rebalance:
 * Rebalances the tree if one side becomes too heavy.  This function
 * assumes that both subtrees are AVL-trees with consistant data.  The
 * function has the additional side effect of recalculating the count of
 * the tree at this node.  It should be noted that at the return of this
 * function, if a rebalance takes place, the top of this subtree is no
 * longer going to be the same node.
 */
void avl_rebalance(avl_tree_t *avltree, avl_node_t *avlnode) {
        avl_node_t *child;
        avl_node_t *gchild;
        avl_node_t *parent;
        avl_node_t **superparent;
 
        parent = avlnode;
 
        while(avlnode) {
                parent = avlnode->parent;
 
                superparent = parent
                        ? avlnode == parent->left ? &parent->left : &parent->right
                        : &avltree->top;
 
                switch(avl_check_balance(avlnode)) {
                case -1:
                        child = avlnode->left;
                        #ifdef AVL_DEPTH
                        if(L_DEPTH(child) >= R_DEPTH(child)) {
                        #else
                        #ifdef AVL_COUNT
                        if(L_COUNT(child) >= R_COUNT(child)) {
                        #else
                        #error No balancing possible.
                        #endif
                        #endif
                                avlnode->left = child->right;
                                if(avlnode->left)
                                        avlnode->left->parent = avlnode;
                                child->right = avlnode;
                                avlnode->parent = child;
                                *superparent = child;
                                child->parent = parent;
                                #ifdef AVL_COUNT
                                avlnode->count = CALC_COUNT(avlnode);
                                child->count = CALC_COUNT(child);
                                #endif
                                #ifdef AVL_DEPTH
                                avlnode->depth = CALC_DEPTH(avlnode);
                                child->depth = CALC_DEPTH(child);
                                #endif
                        } else {
                                gchild = child->right;
                                avlnode->left = gchild->right;
                                if(avlnode->left)
                                        avlnode->left->parent = avlnode;
                                child->right = gchild->left;
                                if(child->right)
                                        child->right->parent = child;
                                gchild->right = avlnode;
                                if(gchild->right)
                                        gchild->right->parent = gchild;
                                gchild->left = child;
                                if(gchild->left)
                                        gchild->left->parent = gchild;
                                *superparent = gchild;
                                gchild->parent = parent;
                                #ifdef AVL_COUNT
                                avlnode->count = CALC_COUNT(avlnode);
                                child->count = CALC_COUNT(child);
                                gchild->count = CALC_COUNT(gchild);
                                #endif
                                #ifdef AVL_DEPTH
                                avlnode->depth = CALC_DEPTH(avlnode);
                                child->depth = CALC_DEPTH(child);
                                gchild->depth = CALC_DEPTH(gchild);
                                #endif
                        }
                break;
                case 1:
                        child = avlnode->right;
                        #ifdef AVL_DEPTH
                        if(R_DEPTH(child) >= L_DEPTH(child)) {
                        #else
                        #ifdef AVL_COUNT
                        if(R_COUNT(child) >= L_COUNT(child)) {
                        #else
                        #error No balancing possible.
                        #endif
                        #endif
                                avlnode->right = child->left;
                                if(avlnode->right)
                                        avlnode->right->parent = avlnode;
                                child->left = avlnode;
                                avlnode->parent = child;
                                *superparent = child;
                                child->parent = parent;
                                #ifdef AVL_COUNT
                                avlnode->count = CALC_COUNT(avlnode);
                                child->count = CALC_COUNT(child);
                                #endif
                                #ifdef AVL_DEPTH
                                avlnode->depth = CALC_DEPTH(avlnode);
                                child->depth = CALC_DEPTH(child);
                                #endif
                        } else {
                                gchild = child->left;
                                avlnode->right = gchild->left;
                                if(avlnode->right)
                                        avlnode->right->parent = avlnode;
                                child->left = gchild->right;
                                if(child->left)
                                        child->left->parent = child;
                                gchild->left = avlnode;
                                if(gchild->left)
                                        gchild->left->parent = gchild;
                                gchild->right = child;
                                if(gchild->right)
                                        gchild->right->parent = gchild;
                                *superparent = gchild;
                                gchild->parent = parent;
                                #ifdef AVL_COUNT
                                avlnode->count = CALC_COUNT(avlnode);
                                child->count = CALC_COUNT(child);
                                gchild->count = CALC_COUNT(gchild);
                                #endif
                                #ifdef AVL_DEPTH
                                avlnode->depth = CALC_DEPTH(avlnode);
                                child->depth = CALC_DEPTH(child);
                                gchild->depth = CALC_DEPTH(gchild);
                                #endif
                        }
                break;
                default:
                        #ifdef AVL_COUNT
                        avlnode->count = CALC_COUNT(avlnode);
                        #endif
                        #ifdef AVL_DEPTH
                        avlnode->depth = CALC_DEPTH(avlnode);
                        #endif
                }
                avlnode = parent;
        }
}