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/*
* Copyright (C) 2010 Joseph Adams <joeyadams3.14159@gmail.com>
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
#include "avl.h"
#include <assert.h>
#include <stdlib.h>
static AvlNode *mkNode(const void *key, const void *value);
static void freeNode(AvlNode *node);
static AvlNode *lookup(const AVL *avl, AvlNode *node, const void *key);
static bool insert(AVL *avl, AvlNode **p, const void *key, const void *value);
static bool remove(AVL *avl, AvlNode **p, const void *key, AvlNode **ret);
static bool removeExtremum(AvlNode **p, int side, AvlNode **ret);
static int sway(AvlNode **p, int sway);
static void balance(AvlNode **p, int side);
static bool checkBalances(AvlNode *node, int *height);
static bool checkOrder(AVL *avl);
static size_t countNode(AvlNode *node);
/*
* Utility macros for converting between
* "balance" values (-1 or 1) and "side" values (0 or 1).
*
* bal(0) == -1
* bal(1) == +1
* side(-1) == 0
* side(+1) == 1
*/
#define bal(side) ((side) == 0 ? -1 : 1)
#define side(bal) ((bal) == 1 ? 1 : 0)
static int sign(int cmp)
{
if (cmp < 0)
return -1;
if (cmp == 0)
return 0;
return 1;
}
AVL *avl_new(total_order_noctx_cb compare)
{
AVL *avl = malloc(sizeof(*avl));
assert(avl != NULL);
avl->compare = compare;
avl->root = NULL;
avl->count = 0;
return avl;
}
void avl_free(AVL *avl)
{
freeNode(avl->root);
free(avl);
}
void *avl_lookup(const AVL *avl, const void *key)
{
AvlNode *found = lookup(avl, avl->root, key);
return found ? (void*) found->value : NULL;
}
AvlNode *avl_lookup_node(const AVL *avl, const void *key)
{
return lookup(avl, avl->root, key);
}
size_t avl_count(const AVL *avl)
{
return avl->count;
}
bool avl_insert(AVL *avl, const void *key, const void *value)
{
size_t old_count = avl->count;
insert(avl, &avl->root, key, value);
return avl->count != old_count;
}
bool avl_remove(AVL *avl, const void *key)
{
AvlNode *node = NULL;
remove(avl, &avl->root, key, &node);
if (node == NULL) {
return false;
} else {
free(node);
return true;
}
}
static AvlNode *mkNode(const void *key, const void *value)
{
AvlNode *node = malloc(sizeof(*node));
assert(node != NULL);
node->key = key;
node->value = value;
node->lr[0] = NULL;
node->lr[1] = NULL;
node->balance = 0;
return node;
}
static void freeNode(AvlNode *node)
{
if (node) {
freeNode(node->lr[0]);
freeNode(node->lr[1]);
free(node);
}
}
static AvlNode *lookup(const AVL *avl, AvlNode *node, const void *key)
{
int cmp;
if (node == NULL)
return NULL;
cmp = avl->compare(key, node->key);
if (cmp < 0)
return lookup(avl, node->lr[0], key);
if (cmp > 0)
return lookup(avl, node->lr[1], key);
return node;
}
/*
* Insert a key/value into a subtree, rebalancing if necessary.
*
* Return true if the subtree's height increased.
*/
static bool insert(AVL *avl, AvlNode **p, const void *key, const void *value)
{
if (*p == NULL) {
*p = mkNode(key, value);
avl->count++;
return true;
} else {
AvlNode *node = *p;
int cmp = sign(avl->compare(key, node->key));
if (cmp == 0) {
node->key = key;
node->value = value;
return false;
}
if (!insert(avl, &node->lr[side(cmp)], key, value))
return false;
/* If tree's balance became -1 or 1, it means the tree's height grew due to insertion. */
return sway(p, cmp) != 0;
}
}
/*
* Remove the node matching the given key.
* If present, return the removed node through *ret .
* The returned node's lr and balance are meaningless.
*
* Return true if the subtree's height decreased.
*/
static bool remove(AVL *avl, AvlNode **p, const void *key, AvlNode **ret)
{
if (*p == NULL) {
return false;
} else {
AvlNode *node = *p;
int cmp = sign(avl->compare(key, node->key));
if (cmp == 0) {
*ret = node;
avl->count--;
if (node->lr[0] != NULL && node->lr[1] != NULL) {
AvlNode *replacement;
int side;
bool shrunk;
/* Pick a subtree to pull the replacement from such that
* this node doesn't have to be rebalanced. */
side = node->balance <= 0 ? 0 : 1;
shrunk = removeExtremum(&node->lr[side], 1 - side, &replacement);
replacement->lr[0] = node->lr[0];
replacement->lr[1] = node->lr[1];
replacement->balance = node->balance;
*p = replacement;
if (!shrunk)
return false;
replacement->balance -= bal(side);
/* If tree's balance became 0, it means the tree's height shrank due to removal. */
return replacement->balance == 0;
}
if (node->lr[0] != NULL)
*p = node->lr[0];
else
*p = node->lr[1];
return true;
} else {
if (!remove(avl, &node->lr[side(cmp)], key, ret))
return false;
/* If tree's balance became 0, it means the tree's height shrank due to removal. */
return sway(p, -cmp) == 0;
}
}
}
/*
* Remove either the left-most (if side == 0) or right-most (if side == 1)
* node in a subtree, returning the removed node through *ret .
* The returned node's lr and balance are meaningless.
*
* The subtree must not be empty (i.e. *p must not be NULL).
*
* Return true if the subtree's height decreased.
*/
static bool removeExtremum(AvlNode **p, int side, AvlNode **ret)
{
AvlNode *node = *p;
if (node->lr[side] == NULL) {
*ret = node;
*p = node->lr[1 - side];
return true;
}
if (!removeExtremum(&node->lr[side], side, ret))
return false;
/* If tree's balance became 0, it means the tree's height shrank due to removal. */
return sway(p, -bal(side)) == 0;
}
/*
* Rebalance a node if necessary. Think of this function
* as a higher-level interface to balance().
*
* sway must be either -1 or 1, and indicates what was added to
* the balance of this node by a prior operation.
*
* Return the new balance of the subtree.
*/
static int sway(AvlNode **p, int sway)
{
if ((*p)->balance != sway)
(*p)->balance += sway;
else
balance(p, side(sway));
return (*p)->balance;
}
/*
* Perform tree rotations on an unbalanced node.
*
* side == 0 means the node's balance is -2 .
* side == 1 means the node's balance is +2 .
*/
static void balance(AvlNode **p, int side)
{
AvlNode *node = *p,
*child = node->lr[side];
int opposite = 1 - side;
int bal = bal(side);
if (child->balance != -bal) {
/* Left-left (side == 0) or right-right (side == 1) */
node->lr[side] = child->lr[opposite];
child->lr[opposite] = node;
*p = child;
child->balance -= bal;
node->balance = -child->balance;
} else {
/* Left-right (side == 0) or right-left (side == 1) */
AvlNode *grandchild = child->lr[opposite];
node->lr[side] = grandchild->lr[opposite];
child->lr[opposite] = grandchild->lr[side];
grandchild->lr[side] = child;
grandchild->lr[opposite] = node;
*p = grandchild;
node->balance = 0;
child->balance = 0;
if (grandchild->balance == bal)
node->balance = -bal;
else if (grandchild->balance == -bal)
child->balance = bal;
grandchild->balance = 0;
}
}
/************************* avl_check_invariants() *************************/
bool avl_check_invariants(AVL *avl)
{
int dummy;
return checkBalances(avl->root, &dummy)
&& checkOrder(avl)
&& countNode(avl->root) == avl->count;
}
static bool checkBalances(AvlNode *node, int *height)
{
if (node) {
int h0, h1;
if (!checkBalances(node->lr[0], &h0))
return false;
if (!checkBalances(node->lr[1], &h1))
return false;
if (node->balance != h1 - h0 || node->balance < -1 || node->balance > 1)
return false;
*height = (h0 > h1 ? h0 : h1) + 1;
return true;
} else {
*height = 0;
return true;
}
}
static bool checkOrder(AVL *avl)
{
AvlIter i;
const void *last = NULL;
bool last_set = false;
avl_foreach(i, avl) {
if (last_set && avl->compare(last, i.key) >= 0)
return false;
last = i.key;
last_set = true;
}
return true;
}
static size_t countNode(AvlNode *node)
{
if (node)
return 1 + countNode(node->lr[0]) + countNode(node->lr[1]);
else
return 0;
}
/************************* Traversal *************************/
void avl_iter_begin(AvlIter *iter, AVL *avl, AvlDirection dir)
{
AvlNode *node = avl->root;
iter->stack_index = 0;
iter->direction = dir;
if (node == NULL) {
iter->key = NULL;
iter->value = NULL;
iter->node = NULL;
return;
}
while (node->lr[dir] != NULL) {
iter->stack[iter->stack_index++] = node;
node = node->lr[dir];
}
iter->key = (void*) node->key;
iter->value = (void*) node->value;
iter->node = node;
}
void avl_iter_next(AvlIter *iter)
{
AvlNode *node = iter->node;
AvlDirection dir = iter->direction;
if (node == NULL)
return;
node = node->lr[1 - dir];
if (node != NULL) {
while (node->lr[dir] != NULL) {
iter->stack[iter->stack_index++] = node;
node = node->lr[dir];
}
} else if (iter->stack_index > 0) {
node = iter->stack[--iter->stack_index];
} else {
iter->key = NULL;
iter->value = NULL;
iter->node = NULL;
return;
}
iter->node = node;
iter->key = (void*) node->key;
iter->value = (void*) node->value;
}