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于2007.11.28：这份代码是有问题的，修正的在这里： http://www.cppblog.com/converse/archive/2007/11/28/37430.html半年之前写的一个红黑树的实现算法了,当时有点忙没有写相应的文档,一下子几乎全都忘记了,作一个记录,改天有空了来补充说明文档.
  /**//*-----------------------------------------------------------
 RB-Tree的插入和删除操作的实现算法
参考资料:
1) <<Introduction to algorithm>>
2) <<STL源码剖析>>
3) sgi-stl中stl_tree.h中的实现算法
4) http://epaperpress.com/sortsearch/index.html
5) http://www.ececs.uc.edu/~franco/C321/html/RedBlack/redblack.html
作者：李创 (http://www.cppblog.com/converse/)
您可以自由的传播，修改这份代码，转载处请注明原作者
红黑树的几个性质:
1) 每个结点只有红和黑两种颜色
2) 根结点是黑色的
3) 每个叶子结点(空结点被认为是叶子结点)是黑色的
4) 如果一个结点是红色的,那么它的左右两个子结点的颜色是黑色的
5) 对于每个结点而言,从这个结点到叶子结点的任何路径上的黑色结点
的数目相同
 -------------------------------------------------------------*/
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
typedef int KEY;
enum NODECOLOR
 {
BLACK = 0,
RED = 1
};
typedef struct RBTree
{
struct RBTree *parent;
struct RBTree *left, *right;
KEY key;
NODECOLOR color;
}RBTree, *PRBTree;
PRBTree RB_InsertNode(PRBTree root, KEY key);
PRBTree RB_InsertNode_Fixup(PRBTree root, PRBTree z);
PRBTree RB_DeleteNode(PRBTree root, KEY key);
PRBTree RB_DeleteNode_Fixup(PRBTree root, PRBTree z);
PRBTree Find_Node(PRBTree root, KEY key);
void Left_Rotate(PRBTree A, PRBTree& root);
void Right_Rotate(PRBTree A, PRBTree& root);
void Mid_Visit(PRBTree T);
void Mid_DeleteTree(PRBTree T);
void Print_Node(PRBTree node);
/**//*-----------------------------------------------------------
| A B
| / \ ==> / \
| a B A y
| / \ / \
| b y a b
-----------------------------------------------------------*/
void Left_Rotate(PRBTree A, PRBTree& root)
{
PRBTree B;
B = A->right;
if (NULL == B)
return;
A->right = B->left;
if (NULL != B->left)
B->left->parent = A;
B->parent = A->parent;
// 这样三个判断连在一起避免了A->parent = NULL的情况
if (A == root)
  {
root = B;
 }
else if (A == A->parent->left)
{
A->parent->left = B;
}
else
{
A->parent->right = B;
}
B->left = A;
A->parent = B;
}
/**//*-----------------------------------------------------------
| A B
| / \ / \
| B y ==> a A
| / \ / \
|a b b y
-----------------------------------------------------------*/
void Right_Rotate(PRBTree A, PRBTree& root)
{
PRBTree B;
B = A->left;
if (NULL == B)
return;
A->left = B->right;
if (NULL != B->right)
B->right->parent = A;
B->parent = A->parent;
// 这样三个判断连在一起避免了A->parent = NULL的情况
if (A == root)
{
root = B;
}
else if (A == A->parent->left)
{
A->parent->left = B;
}
else
{
A->parent->right = B;
}
A->parent = B;
B->right = A;
}
/**//*-----------------------------------------------------------
| 函数作用:查找key值对应的结点指针
| 输入参数:根节点root,待查找关键值key
| 返回参数:如果找到返回结点指针,否则返回NULL
-------------------------------------------------------------*/
PRBTree Find_Node(PRBTree root, KEY key)
{
PRBTree x;
// 找到key所在的node
x = root;
do
{
if (key == x->key)
break;
if (key < x->key)
{
if (NULL != x->left)
x = x->left;
else
break;
}
else
{
if (NULL != x->right)
x = x->right;
else
break;
}
} while (NULL != x);
return x;
}
/**//*-----------------------------------------------------------
| 函数作用:在树中插入key值
| 输入参数:根节点root,待插入结点的关键值key
| 返回参数:根节点root
-------------------------------------------------------------*/
PRBTree RB_InsertNode(PRBTree root, KEY key)
{
PRBTree x, y;
PRBTree z;
if (NULL == (z = (PRBTree)malloc(sizeof(RBTree))))
{
printf("Memory alloc error\n");
return NULL;
}
z->key = key;
// 得到z的父节点
x = root, y = NULL;
while (NULL != x)
{
y = x;
if (z->key < x->key)
{
if (NULL != x->left)
{
x = x->left;
}
else
{
break;
}
}
else
{
if (NULL != x->right)
{
x = x->right;
}
else
{
break;
}
}
}
// 把z放到合适的位置
z->parent = y;
if (NULL == y)
{
root = z;
}
else
{
if (z->key < y->key)
y->left = z;
else
y->right = z;
}
// 设置z的左右子树为空并且颜色是red，注意新插入的节点颜色都是red
z->left = z->right = NULL;
z->color = RED;
// 对红黑树进行修正
return RB_InsertNode_Fixup(root, z);
}
/**//*-----------------------------------------------------------
| 函数作用:对插入key值之后的树进行修正
| 输入参数:根节点root,插入的结点z
| 返回参数:根节点root
-------------------------------------------------------------*/
PRBTree RB_InsertNode_Fixup(PRBTree root, PRBTree z)
{
PRBTree y;
while (root != z && RED == z->parent->color) // 当z不是根同时父节点的颜色是red
{
if (z->parent == z->parent->parent->left) // 父节点是祖父节点的左子树
{
y = z->parent->parent->right; // y为z的伯父节点
if (NULL != y && RED == y->color) // 伯父节点存在且颜色是red
{
z->parent->color = BLACK; // 更改z的父节点颜色是B
y->color = BLACK; // 更改z的伯父节点颜色是B
z->parent->parent->color = RED; // 更改z的祖父节点颜色是B
z = z->parent->parent; // 更新z为它的祖父节点
}
else // 无伯父节点或者伯父节点颜色是b
{
if (z == z->parent->right) // 如果新节点是父节点的右子树
{
z = z->parent;
Left_Rotate(z, root);
}
z->parent->color = BLACK; // 改变父节点颜色是B
z->parent->parent->color = RED; // 改变祖父节点颜色是R
Right_Rotate(z->parent->parent, root);
}
}
else // 父节点为祖父节点的右子树
{
y = z->parent->parent->left; // y为z的伯父节点
if (NULL != y && RED == y->color) // 如果y的颜色是red
{
z->parent->color = BLACK; // 更改父节点的颜色为B
y->color = BLACK; // 更改伯父节点的颜色是B
z->parent->parent->color = RED; // 更改祖父节点颜色是R
z = z->parent->parent; // 更改z指向祖父节点
}
else // y不存在或者颜色是B
{
if (z == z->parent->left) // 如果是父节点的左子树
{
z = z->parent;
Right_Rotate(z, root);
}
z->parent->color = BLACK; // 改变父节点的颜色是B
z->parent->parent->color = RED; // 改变祖父节点的颜色是RED
Left_Rotate(z->parent->parent, root);
}
}
} // while(RED == z->parent->color)
// 根节点的颜色始终都是B
root->color = BLACK;
return root;
}
/**//*-----------------------------------------------------------
| 函数作用:在树中删除key值
| 输入参数:根节点root,待插入结点的关键值key
| 返回参数:根节点root
-------------------------------------------------------------*/
PRBTree RB_DeleteNode(PRBTree root, KEY key)
{
PRBTree x, y, z, x_parent;
z = Find_Node(root, key);
if (NULL == z)
return root;
// 当z有一个空子树的时候,y == z
// 否则,y是大于z最小的结点
if (NULL == z->left || NULL == z->right)
y = z;
else
{
y = z->right;
while (NULL != y->left)
y = y->left;
}
// x是y的子树,可能为NULL
if (NULL != y->left)
x = y->left;
else
x = y->right;
// 设定x的位置取代y
if (NULL != x)
x->parent = y->parent;
if (NULL == y->parent)
root = x;
else if (y == y->parent->left)
y->parent->left = x;
else
y->parent->right = x;
// 把y的key拷贝到z中,这样y就是待删除的结点了
if (y != z)
{
z->key = y->key;
}
// 如果y的颜色值是B,那么要对树进行修正
if (BLACK == y->color && NULL != x)
RB_DeleteNode_Fixup(root, x);
free(y);
return root;
}
/**//*-----------------------------------------------------------
| 函数作用:对删除key值之后的树进行修正
| 输入参数:根节点root,删除的结点的子结点x
| 返回参数:根节点root
-------------------------------------------------------------*/
PRBTree RB_DeleteNode_Fixup(PRBTree root, PRBTree x)
{
PRBTree w;
while (x != root && BLACK == x->color)
{
if (x == x->parent->left) // 如果x是左子树
{
w = x->parent->right; // w是x的兄弟结点
if (NULL == w)
continue;
if (RED == w->color) // 如果w的颜色是红色
{
w->color = BLACK;
x->parent->color = RED;
Left_Rotate(x->parent, root);
w = x->parent->right;
}
if (NULL != w->left && BLACK == w->left->color &&
NULL != w->right && BLACK == w->right->color)
{
w->color = RED;
x = x->parent;
}
else
{
if (NULL != w->right && BLACK == w->right->color)
{
w->left->color = BLACK;
w->color = RED;
Right_Rotate(w, root);
w = x->parent->right;
}
w->color = x->parent->color;
x->parent->color = BLACK;
w->right->color = BLACK;
Left_Rotate(x->parent, root);
x = root;
}
}
else
{
w = x->parent->left;
if (NULL == w)
continue;
if (RED == w->color)
{
w->color = BLACK;
x->parent->color = RED;
Left_Rotate(x->parent, root);
w = x->parent->left;
}
if (NULL != w->left && BLACK == w->left->color &&
NULL != w->right && BLACK == w->right->color)
{
w->color = RED;
x = x->parent;
}
else
{
if (NULL != w->left && BLACK == w->left->color)
{
w->right->color = BLACK;
w->color = RED;
Left_Rotate(w, root);
w = x->parent->left;
}
w->color = x->parent->color;
x->parent->color = BLACK;
w->left->color = BLACK;
Right_Rotate(x->parent, root);
x = root;
}
}
}
x->color = BLACK;
return root;
}
void Print_Node(PRBTree node)
{
char* color[] = {"BLACK", "RED"};
printf("Key = %d,\tcolor = %s", node->key, color[node->color]);
if (NULL != node->parent)
printf(",\tparent = %d", node->parent->key);
if (NULL != node->left)
printf(",\tleft = %d", node->left->key);
if (NULL != node->right)
printf(",\tright = %d", node->right->key);
printf("\n");
}
// 中序遍历树
void Mid_Visit(PRBTree T)
{
if (NULL != T)
{
if (NULL != T->left)
Mid_Visit(T->left);
Print_Node(T);
if (NULL != T->right)
Mid_Visit(T->right);
}
}
// 中序删除树的各个节点
void Mid_DeleteTree(PRBTree T)
{
if (NULL != T)
{
if (NULL != T->left)
Mid_DeleteTree(T->left);
PRBTree temp = T->right;
free(T);
T = NULL;
if (NULL != temp)
Mid_DeleteTree(temp);
}
}
void Create_New_Array(int array[], int length)
{
for (int i = 0; i < length; i++)
{
array[i] = rand() % 256;
}
}
int main(int argc, char *argv[])
{
//int array[10] = {80, 116, 81, 205, 82, 68, 151, 20, 109, 100};
int array[10];
srand(time(NULL));
Create_New_Array(array, 10);
PRBTree root = NULL;
int i;
for (i = 0; i < 10; i++)
{
root = RB_InsertNode(root, array[i]);
}
Mid_Visit(root);
// 随机删除一个结点
int index = rand() % 10;
printf("delete node %d\n", array[index]);
root = RB_DeleteNode(root, array[index]);
Mid_Visit(root);
// 删除整颗树
Mid_DeleteTree(root);
return 0;
}
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