[数据结构]红黑树的实现源码

[数据结构]红黑树的实现源码

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;
}