我曾經寫過兩個兩個紅黑樹的實現, 分別在:
http://m.shnenglu.com/converse/archive/2006/10/07/13413.html
http://m.shnenglu.com/converse/archive/2007/11/28/37430.html
最近因為要給ccache加入紅黑樹的支持, 找出來曾經實現的代碼作為參考, 這才發現原來的實現都是有問題的,也怪我的測試用例寫的不好, 僅僅對插入操作進行了測試, 我向所有因為閱讀了這份代碼而造成困惑的朋友表示道歉.
這次重新實現, 所有的代碼推倒重新編寫, 參考了linux內核中紅黑樹的實現算法, 并且對測試用例進行了加強,希望這是最后一個對紅黑樹算法的修訂版本.
/*-----------------------------------------------------------
RB-Tree的插入和刪除操作的實現算法
參考資料:
1) <<Introduction to algorithm>>
2) http://lxr.linux.no/linux/lib/rbtree.c
作者：http://m.shnenglu.com/converse/
您可以自由的傳播，修改這份代碼，轉載處請注明原作者
紅黑樹的幾個性質:
1) 每個結點只有紅和黑兩種顏色
2) 根結點是黑色的
3)空節點是黑色的（紅黑樹中，根節點的parent以及所有葉節點lchild、rchild都不指向NULL，而是指向一個定義好的空節點）。
4) 如果一個結點是紅色的,那么它的左右兩個子結點的顏色是黑色的
5) 對于每個結點而言,從這個結點到葉子結點的任何路徑上的黑色結點
的數目相同
-------------------------------------------------------------*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
typedef int key_t;
typedef int data_t;
typedef enum color_t
{
RED = 0,
BLACK = 1
}color_t;
typedef struct rb_node_t
{
struct rb_node_t *left, *right, *parent;
key_t key;
data_t data;
color_t color;
}rb_node_t;
/* forward declaration */
rb_node_t* rb_insert(key_t key, data_t data, rb_node_t* root);
rb_node_t* rb_search(key_t key, rb_node_t* root);
rb_node_t* rb_erase(key_t key, rb_node_t* root);
int main()
{
int i, count = 900000;
key_t key;
rb_node_t* root = NULL, *node = NULL;
srand(time(NULL));
for (i = 1; i < count; ++i)
{
key = rand() % count;
if ((root = rb_insert(key, i, root)))
{
printf("[i = %d] insert key %d success!\n", i, key);
}
else
{
printf("[i = %d] insert key %d error!\n", i, key);
exit(-1);
}
if ((node = rb_search(key, root)))
{
printf("[i = %d] search key %d success!\n", i, key);
}
else
{
printf("[i = %d] search key %d error!\n", i, key);
exit(-1);
}
if (!(i % 10))
{
if ((root = rb_erase(key, root)))
{
printf("[i = %d] erase key %d success\n", i, key);
}
else
{
printf("[i = %d] erase key %d error\n", i, key);
}
}
}
return 0;
}
static rb_node_t* rb_new_node(key_t key, data_t data)
{
rb_node_t *node = (rb_node_t*)malloc(sizeof(struct rb_node_t));
if (!node)
{
printf("malloc error!\n");
exit(-1);
}
node->key = key, node->data = data;
return node;
}
/*-----------------------------------------------------------
| node right
| / \ ==> / \
| a right node y
| / \ / \
| b y a b
-----------------------------------------------------------*/
static rb_node_t* rb_rotate_left(rb_node_t* node, rb_node_t* root)
{
rb_node_t* right = node->right;
if ((node->right = right->left))
{
right->left->parent = node;
}
right->left = node;
if ((right->parent = node->parent))
{
if (node == node->parent->right)
{
node->parent->right = right;
}
else
{
node->parent->left = right;
}
}
else
{
root = right;
}
node->parent = right;
return root;
}
/*-----------------------------------------------------------
| node left
| / \ / \
| left y ==> a node
| / \ / \
| a b b y
-----------------------------------------------------------*/
static rb_node_t* rb_rotate_right(rb_node_t* node, rb_node_t* root)
{
rb_node_t* left = node->left;
if ((node->left = left->right))
{
left->right->parent = node;
}
left->right = node;
if ((left->parent = node->parent))
{
if (node == node->parent->right)
{
node->parent->right = left;
}
else
{
node->parent->left = left;
}
}
else
{
root = left;
}
node->parent = left;
return root;
}
static rb_node_t* rb_insert_rebalance(rb_node_t *node, rb_node_t *root)
{
rb_node_t *parent, *gparent, *uncle, *tmp;
while ((parent = node->parent) && parent->color == RED)
{
gparent = parent->parent;
if (parent == gparent->left)
{
uncle = gparent->right;
if (uncle && uncle->color == RED)
{
uncle->color = BLACK;
parent->color = BLACK;
gparent->color = RED;
node = gparent;
}
else
{
if (parent->right == node)
{
root = rb_rotate_left(parent, root);
tmp = parent;
parent = node;
node = tmp;
}
parent->color = BLACK;
gparent->color = RED;
root = rb_rotate_right(gparent, root);
}
}
else
{
uncle = gparent->left;
if (uncle && uncle->color == RED)
{
uncle->color = BLACK;
parent->color = BLACK;
gparent->color = RED;
node = gparent;
}
else
{
if (parent->left == node)
{
root = rb_rotate_right(parent, root);
tmp = parent;
parent = node;
node = tmp;
}
parent->color = BLACK;
gparent->color = RED;
root = rb_rotate_left(gparent, root);
}
}
}
root->color = BLACK;
return root;
}
static rb_node_t* rb_erase_rebalance(rb_node_t *node, rb_node_t *parent, rb_node_t *root)
{
rb_node_t *other, *o_left, *o_right;
while ((!node || node->color == BLACK) && node != root)
{
if (parent->left == node)
{
other = parent->right;
if (other->color == RED)
{
other->color = BLACK;
parent->color = RED;
root = rb_rotate_left(parent, root);
other = parent->right;
}
if ((!other->left || other->left->color == BLACK) &&
(!other->right || other->right->color == BLACK))
{
other->color = RED;
node = parent;
parent = node->parent;
}
else
{
if (!other->right || other->right->color == BLACK)
{
if ((o_left = other->left))
{
o_left->color = BLACK;
}
other->color = RED;
root = rb_rotate_right(other, root);
other = parent->right;
}
other->color = parent->color;
parent->color = BLACK;
if (other->right)
{
other->right->color = BLACK;
}
root = rb_rotate_left(parent, root);
node = root;
break;
}
}
else
{
other = parent->left;
if (other->color == RED)
{
other->color = BLACK;
parent->color = RED;
root = rb_rotate_right(parent, root);
other = parent->left;
}
if ((!other->left || other->left->color == BLACK) &&
(!other->right || other->right->color == BLACK))
{
other->color = RED;
node = parent;
parent = node->parent;
}
else
{
if (!other->left || other->left->color == BLACK)
{
if ((o_right = other->right))
{
o_right->color = BLACK;
}
other->color = RED;
root = rb_rotate_left(other, root);
other = parent->left;
}
other->color = parent->color;
parent->color = BLACK;
if (other->left)
{
other->left->color = BLACK;
}
root = rb_rotate_right(parent, root);
node = root;
break;
}
}
}
if (node)
{
node->color = BLACK;
}
return root;
}
static rb_node_t* rb_search_auxiliary(key_t key, rb_node_t* root, rb_node_t** save)
{
rb_node_t *node = root, *parent = NULL;
int ret;
while (node)
{
parent = node;
ret = node->key - key;
if (0 < ret)
{
node = node->left;
}
else if (0 > ret)
{
node = node->right;
}
else
{
return node;
}
}
if (save)
{
*save = parent;
}
return NULL;
}
rb_node_t* rb_insert(key_t key, data_t data, rb_node_t* root)
{
rb_node_t *parent = NULL, *node;
parent = NULL;
if ((node = rb_search_auxiliary(key, root, &parent)))
{
return root;
}
node = rb_new_node(key, data);
node->parent = parent;
node->left = node->right = NULL;
node->color = RED;
if (parent)
{
if (parent->key > key)
{
parent->left = node;
}
else
{
parent->right = node;
}
}
else
{
root = node;
}
return rb_insert_rebalance(node, root);
}
rb_node_t* rb_search(key_t key, rb_node_t* root)
{
return rb_search_auxiliary(key, root, NULL);
}
rb_node_t* rb_erase(key_t key, rb_node_t *root)
{
rb_node_t *child, *parent, *old, *left, *node;
color_t color;
if (!(node = rb_search_auxiliary(key, root, NULL)))
{
printf("key %d is not exist!\n");
return root;
}
old = node;
if (node->left && node->right)
{
node = node->right;
while ((left = node->left) != NULL)
{
node = left;
}
child = node->right;
parent = node->parent;
color = node->color;
if (child)
{
child->parent = parent;
}
if (parent)
{
if (parent->left == node)
{
parent->left = child;
}
else
{
parent->right = child;
}
}
else
{
root = child;
}
if (node->parent == old)
{
parent = node;
}
node->parent = old->parent;
node->color = old->color;
node->right = old->right;
node->left = old->left;
if (old->parent)
{
if (old->parent->left == old)
{
old->parent->left = node;
}
else
{
old->parent->right = node;
}
}
else
{
root = node;
}
old->left->parent = node;
if (old->right)
{
old->right->parent = node;
}
}
else
{
if (!node->left)
{
child = node->right;
}
else if (!node->right)
{
child = node->left;
}
parent = node->parent;
color = node->color;
if (child)
{
child->parent = parent;
}
if (parent)
{
if (parent->left == node)
{
parent->left = child;
}
else
{
parent->right = child;
}
}
else
{
root = child;
}
}
free(old);
if (color == BLACK)
{
root = rb_erase_rebalance(child, parent, root);
}
return root;
}