红黑树的实现源码(第二次修订版) [转自网络]

我曾经写过两个两个红黑树的实现, 分别在:
http://www.cppblog.com/converse/archive/2006/10/07/13413.html
http://www.cppblog.com/converse/archive/2007/11/28/37430.html

最近因为要给ccache加入红黑树的支持, 找出来曾经实现的代码作为参考, 这才发现原来的实现都是有问题的,也怪我的测试用例写的不好, 仅仅对插入操作进行了测试, 我向所有因为阅读了这份代码而造成困惑的朋友表示道歉.

这次重新实现, 所有的代码推倒重新编写, 参考了linux内核中红黑树的实现算法, 并且对测试用例进行了加强,希望这是最后一个对红黑树算法的修订版本.

/*-----------------------------------------------------------
    RB-Tree的插入和删除操作的实现算法
    参考资料:
    1) <<Introduction to algorithm>>
    2) http://lxr.linux.no/linux/lib/rbtree.c

    作者：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)空节点是黑色的（红黑树中，根节点的parent以及所有叶节点lchild、rchild都不指向NULL，而是指向一个定义好的空节点）。 
    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 <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;
}