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/* Copyright (c) 2008 Derrick Coetzee
* http://en.literateprograms.org/Red-black_tree_(C)?oldid=7982
*
* 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 "rbtree.h"
#include <assert.h>
#ifndef NULL
# define NULL ((void*)0)
#endif
typedef rbtree_node node;
typedef enum rbtree_node_color color;
static node grandparent(node n);
static node sibling(node n);
static node uncle(node n);
static void verify_properties(rbtree t);
static void verify_property_1(node root);
/* static void verify_property_2(node root); */
static color node_color(node n);
static void verify_property_4(node root);
/* static void verify_property_5(node root); */
static void verify_property_5_helper(node n, int black_count, int* black_count_path);
static node lookup_node(rbtree t, void* key);
static void rotate_left(rbtree t, node n);
static void rotate_right(rbtree t, node n);
static void replace_node(rbtree t, node oldn, node newn);
static void insert_case1(rbtree t, node n);
static void insert_case2(rbtree t, node n);
static void insert_case3(rbtree t, node n);
static void insert_case4(rbtree t, node n);
static void insert_case5(rbtree t, node n);
static node maximum_node(node root);
static void delete_case1(rbtree t, node n);
static void delete_case2(rbtree t, node n);
static void delete_case3(rbtree t, node n);
static void delete_case4(rbtree t, node n);
static void delete_case5(rbtree t, node n);
static void delete_case6(rbtree t, node n);
node grandparent(node n) {
assert (n != NULL);
assert (n->parent != NULL); /* Not the root node */
assert (n->parent->parent != NULL); /* Not child of root */
return n->parent->parent;
}
node sibling(node n) {
assert (n != NULL);
assert (n->parent != NULL); /* Root node has no sibling */
if (n == n->parent->left)
return n->parent->right;
else
return n->parent->left;
}
node uncle(node n) {
assert (n != NULL);
assert (n->parent != NULL); /* Root node has no uncle */
assert (n->parent->parent != NULL); /* Children of root have no uncle */
return sibling(n->parent);
}
void verify_properties(rbtree t) {
#ifdef VERIFY_RBTREE
verify_property_1(t->root);
verify_property_2(t->root);
/* Property 3 is implicit */
verify_property_4(t->root);
verify_property_5(t->root);
#endif
}
void verify_property_1(node n) {
assert(node_color(n) == RED || node_color(n) == BLACK);
if (n == NULL) return;
verify_property_1(n->left);
verify_property_1(n->right);
}
/*
void verify_property_2(node root) {
assert(node_color(root) == BLACK);
}
*/
color node_color(node n) {
return n == NULL ? BLACK : n->color;
}
void verify_property_4(node n) {
if (node_color(n) == RED) {
assert (node_color(n->left) == BLACK);
assert (node_color(n->right) == BLACK);
assert (node_color(n->parent) == BLACK);
}
if (n == NULL) return;
verify_property_4(n->left);
verify_property_4(n->right);
}
/*
void verify_property_5(node root) {
int black_count_path = -1;
verify_property_5_helper(root, 0, &black_count_path);
}
*/
void verify_property_5_helper(node n, int black_count, int* path_black_count) {
if (node_color(n) == BLACK) {
black_count++;
}
if (n == NULL) {
if (*path_black_count == -1) {
*path_black_count = black_count;
} else {
assert (black_count == *path_black_count);
}
return;
}
verify_property_5_helper(n->left, black_count, path_black_count);
verify_property_5_helper(n->right, black_count, path_black_count);
}
void rbtree_init(rbtree t, rbtree_compare_func compare) {
t->root = NULL;
t->compare = compare;
verify_properties(t);
}
node lookup_node(rbtree t, void* key) {
node n = t->root;
while (n != NULL) {
int comp_result = t->compare(key, n->key);
if (comp_result == 0) {
return n;
} else if (comp_result < 0) {
n = n->left;
} else {
assert(comp_result > 0);
n = n->right;
}
}
return n;
}
void* rbtree_lookup(rbtree t, void* key) {
node n = lookup_node(t, key);
return n == NULL ? NULL : n->value;
}
void rotate_left(rbtree t, node n) {
node r = n->right;
replace_node(t, n, r);
n->right = r->left;
if (r->left != NULL) {
r->left->parent = n;
}
r->left = n;
n->parent = r;
}
void rotate_right(rbtree t, node n) {
node L = n->left;
replace_node(t, n, L);
n->left = L->right;
if (L->right != NULL) {
L->right->parent = n;
}
L->right = n;
n->parent = L;
}
void replace_node(rbtree t, node oldn, node newn) {
if (oldn->parent == NULL) {
t->root = newn;
} else {
if (oldn == oldn->parent->left)
oldn->parent->left = newn;
else
oldn->parent->right = newn;
}
if (newn != NULL) {
newn->parent = oldn->parent;
}
}
void rbtree_insert(rbtree t, rbtree_node inserted_node) {
inserted_node->color = RED;
inserted_node->left = NULL;
inserted_node->right = NULL;
inserted_node->parent = NULL;
if (t->root == NULL) {
t->root = inserted_node;
} else {
node n = t->root;
while (1) {
int comp_result = t->compare(inserted_node->key, n->key);
if (comp_result == 0) {
n->value = inserted_node->value;
return;
} else if (comp_result < 0) {
if (n->left == NULL) {
n->left = inserted_node;
break;
} else {
n = n->left;
}
} else {
assert (comp_result > 0);
if (n->right == NULL) {
n->right = inserted_node;
break;
} else {
n = n->right;
}
}
}
inserted_node->parent = n;
}
insert_case1(t, inserted_node);
verify_properties(t);
}
void insert_case1(rbtree t, node n) {
if (n->parent == NULL)
n->color = BLACK;
else
insert_case2(t, n);
}
void insert_case2(rbtree t, node n) {
if (node_color(n->parent) == BLACK)
return; /* Tree is still valid */
else
insert_case3(t, n);
}
void insert_case3(rbtree t, node n) {
if (node_color(uncle(n)) == RED) {
n->parent->color = BLACK;
uncle(n)->color = BLACK;
grandparent(n)->color = RED;
insert_case1(t, grandparent(n));
} else {
insert_case4(t, n);
}
}
void insert_case4(rbtree t, node n) {
if (n == n->parent->right && n->parent == grandparent(n)->left) {
rotate_left(t, n->parent);
n = n->left;
} else if (n == n->parent->left && n->parent == grandparent(n)->right) {
rotate_right(t, n->parent);
n = n->right;
}
insert_case5(t, n);
}
void insert_case5(rbtree t, node n) {
n->parent->color = BLACK;
grandparent(n)->color = RED;
if (n == n->parent->left && n->parent == grandparent(n)->left) {
rotate_right(t, grandparent(n));
} else {
assert (n == n->parent->right && n->parent == grandparent(n)->right);
rotate_left(t, grandparent(n));
}
}
rbtree_node rbtree_delete(rbtree t, void* key) {
node child;
node n = lookup_node(t, key);
if (n == NULL) return NULL; /* Key not found, do nothing */
if (n->left != NULL && n->right != NULL) {
/* Copy key/value from predecessor and then delete it instead */
node pred = maximum_node(n->left);
n->key = pred->key;
n->value = pred->value;
n = pred;
}
assert(n->left == NULL || n->right == NULL);
child = n->right == NULL ? n->left : n->right;
if (node_color(n) == BLACK) {
n->color = node_color(child);
delete_case1(t, n);
}
replace_node(t, n, child);
verify_properties(t);
return n;
}
static node maximum_node(node n) {
assert (n != NULL);
while (n->right != NULL) {
n = n->right;
}
return n;
}
void delete_case1(rbtree t, node n) {
if (n->parent == NULL)
return;
else
delete_case2(t, n);
}
void delete_case2(rbtree t, node n) {
if (node_color(sibling(n)) == RED) {
n->parent->color = RED;
sibling(n)->color = BLACK;
if (n == n->parent->left)
rotate_left(t, n->parent);
else
rotate_right(t, n->parent);
}
delete_case3(t, n);
}
void delete_case3(rbtree t, node n) {
if (node_color(n->parent) == BLACK &&
node_color(sibling(n)) == BLACK &&
node_color(sibling(n)->left) == BLACK &&
node_color(sibling(n)->right) == BLACK)
{
sibling(n)->color = RED;
delete_case1(t, n->parent);
}
else
delete_case4(t, n);
}
void delete_case4(rbtree t, node n) {
if (node_color(n->parent) == RED &&
node_color(sibling(n)) == BLACK &&
node_color(sibling(n)->left) == BLACK &&
node_color(sibling(n)->right) == BLACK)
{
sibling(n)->color = RED;
n->parent->color = BLACK;
}
else
delete_case5(t, n);
}
void delete_case5(rbtree t, node n) {
if (n == n->parent->left &&
node_color(sibling(n)) == BLACK &&
node_color(sibling(n)->left) == RED &&
node_color(sibling(n)->right) == BLACK)
{
sibling(n)->color = RED;
sibling(n)->left->color = BLACK;
rotate_right(t, sibling(n));
}
else if (n == n->parent->right &&
node_color(sibling(n)) == BLACK &&
node_color(sibling(n)->right) == RED &&
node_color(sibling(n)->left) == BLACK)
{
sibling(n)->color = RED;
sibling(n)->right->color = BLACK;
rotate_left(t, sibling(n));
}
delete_case6(t, n);
}
void delete_case6(rbtree t, node n) {
sibling(n)->color = node_color(n->parent);
n->parent->color = BLACK;
if (n == n->parent->left) {
assert (node_color(sibling(n)->right) == RED);
sibling(n)->right->color = BLACK;
rotate_left(t, n->parent);
}
else
{
assert (node_color(sibling(n)->left) == RED);
sibling(n)->left->color = BLACK;
rotate_right(t, n->parent);
}
}
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