二叉搜索树-《算法导论》学习笔记十一

二叉搜索树是以一颗二叉树来组织的，每个节点除数据外，还包括三个分别指向父结点、左孩子、右孩子的指针，二叉搜索树有个特性：某个结点root的左子树的某个节点x的关键值小于等于root结点右子树某个结点y的关键值。

二叉搜索树有几个操作：
1、查找
查找与给定关键值相等的结点
2、遍历
前序、中序、后序遍历输出
3、从某结点出发，寻找子树中最小关键值的结点
4、从某结点出发，寻找子树中最大关键值的结点
5、以某种遍历方式的次数，寻找某结点的前驱结点和后继结点
例如中序遍历的顺序为123456，则4结点的前驱为3，后继为5
6、插入结点
7、删除结点
删除某个结点后，要把它的后继结点补在删除的位置上，要注意：

• 如果结点没有孩子结点，那么只是简单地将它删除，并删改它的父结点的孩子指针指向它
• 如果结点只有一个孩子，那么将它孩子提升到它的位置，并修改它的父结点的孩子指针指向它

• 如果节点有两个孩子，那么寻找它的后继（按中序遍历来说一定在右子树），并让后继占据它的位置，后继（按中序遍历来说一定没有左子树）的子树提升到后继的位置

  情况如上，具体删除时如何替换，又有不同情况：

• 如果结点只有左或孩子，用孩子替换结点

• 如果结点有左右两个孩子，那么要查找结点的后继：(1)、如果后继是结点的右孩子，用后继替换结点，并留下后继的右孩子；(2)、后继位于结点的右子树，但并不是结点的右孩子，则，先用后继的右孩子替换后继，再用后继替换结点

代码：

#include <stdio.h>#include <stdlib.h>#include <string.h>#include <unistd.h>#include <time.h>typedef struct biSearchTreeNode {    int key;    struct biSearchTreeNode *parent;    struct biSearchTreeNode *left;    struct biSearchTreeNode *right;}biSearchTreeNode;typedef struct biSearchTree {    int node_num;    int height;    biSearchTreeNode *root;}biSearchTree;int random_num(){    int a = 1;    int b = 100;    return rand() % ( b - a ) + a;}void postorder_tree_free(    biSearchTreeNode *root ){    if ( root != NULL ) {        postorder_tree_free( root->left );        postorder_tree_free( root->right );        free( root );    }}void inorder_tree_walk(     biSearchTreeNode *root ){    if ( root != NULL ) {        inorder_tree_walk( root->left );        printf("%d ", root->key);        inorder_tree_walk( root->right );    }}void preorder_tree_walk(    biSearchTreeNode *root ){    if ( root != NULL ) {        printf("%d ", root->key);        preorder_tree_walk( root->left );        preorder_tree_walk( root->right );    }}void postorder_tree_walk(    biSearchTreeNode *root ){    if ( root != NULL ) {        postorder_tree_walk( root->left );        postorder_tree_walk( root->right );        printf("%d ", root->key);    }}void print_tree(     biSearchTree *tree ){    printf("中序:");    inorder_tree_walk( tree->root );    printf("\n");    printf("前序:");    preorder_tree_walk( tree->root );    printf("\n");    printf("后序:");    postorder_tree_walk( tree->root );    printf("\n\n");}biSearchTreeNode *tree_search_recursion(     biSearchTreeNode *root,     int key ){    if ( root == NULL || key == root->key ) {        return root;    }    if ( key < root->key )         return tree_search_recursion( root->left, key );    else         return tree_search_recursion( root->right, key );}biSearchTreeNode *tree_search(    biSearchTreeNode *root,    int key ){    while ( root != NULL && key != root->key ) {        if ( key < root->key )             root = root->left;        else             root = root->right;    }    return root;}biSearchTreeNode *tree_minimum(    biSearchTreeNode *root ){    while ( root->left != NULL ) {        root = root->left;    }    return root;}biSearchTreeNode *tree_maximum(    biSearchTreeNode *root ){    while ( root->right != NULL ) {        root = root->right;    }    return root;}// 找前驱 即中序遍历的前一个位置值biSearchTreeNode *tree_predecessor(    biSearchTreeNode *node ){    if ( node->left != NULL )         return tree_maximum( node->left );    biSearchTreeNode *p = node->parent;    while ( p != NULL && node == p->left ) {        node = p;        p = p->parent;    }    return p;}// 找后继 即中序遍历的后一个位置值biSearchTreeNode *tree_successor(    biSearchTreeNode *node ){    if ( node->right != NULL )         return tree_minimum( node->right );    biSearchTreeNode *p = node->parent;    while ( p != NULL && node == p->right ) {        node = p;        p = p->parent;    }    return p;}void tree_insert(     biSearchTree *tree,     biSearchTreeNode *node ){    biSearchTreeNode *root = tree->root;    biSearchTreeNode *p = NULL;    biSearchTreeNode *q = root;    while ( q != NULL ) {        p = q;        if ( node->key < q->key )            q = q->left;        else             q = q->right;    }    node->parent = p;    if ( p == NULL ) {        tree->root = node;    }    else if ( node->key < p->key )         p->left = node;    else        p->right = node;}void transplant(    biSearchTree *tree,    biSearchTreeNode *node_a,    biSearchTreeNode *node_b ){    if ( node_a->parent == NULL )         tree->root = node_b;    else if ( node_a == node_a->parent->left )         node_a->parent->left = node_b;    else         node_a->parent->right = node_b;    if ( node_b != NULL )        node_b->parent = node_a->parent;}void tree_delete(     biSearchTree *tree,    biSearchTreeNode *node ){    if ( node->left == NULL )         transplant( tree, node, node->right );    else if ( node->right == NULL )        transplant( tree, node, node->left );    else {        biSearchTreeNode *p = tree_minimum( node->right );        if ( p->parent != node ) {            transplant( tree, p, p->right );            p->right = node->right;            p->right->parent = p;        }        transplant( tree, node, p );        p->left = node->left;        p->left->parent = p;    }    free( node );}void free_tree(     biSearchTree *tree ){    biSearchTreeNode *root = tree->root;    postorder_tree_free( root );    free( tree );}int main(     int argc,    char **argv ){    srand((int)time(NULL));     int i = 10;    int len = 10;    int arr[10] = {10,4,15,14,5, 2,8,13,1,19};    biSearchTree *tree = ( biSearchTree * )malloc( sizeof(biSearchTree) );    tree->node_num = 0;    tree->height = 0;    for ( i = 0; i < len; i++ ) {        biSearchTreeNode *node =             ( biSearchTreeNode * )malloc( sizeof(biSearchTreeNode) );        //node->key = random_num();        node->key = arr[i];        node->parent = NULL;        node->left = NULL;        node->right = NULL;        tree_insert( tree, node );    }    print_tree( tree );    for ( i = 0; i < len; i++ ) {        biSearchTreeNode *pre = tree_predecessor( tree_search(tree->root, arr[i]) );        biSearchTreeNode *post = tree_successor( tree_search(tree->root, arr[i]) );        printf("\n");        if ( pre != NULL )            printf("查找%d的中序遍历前驱为:%d\n", arr[i], pre->key);        else             printf("查找%d的中序遍历前驱为空！\n", arr[i]);        if ( post != NULL )            printf("查找%d的中序遍历后继为:%d\n", arr[i], post->key);        else            printf("查找%d的中序遍历后继为空！\n", arr[i]);    }    biSearchTreeNode *delete_node = tree_search( tree->root, 4 );    if ( delete_node != NULL ) {        tree_delete( tree, delete_node );    }    printf("\n删除%d的节点后中序遍历顺序为:", 4);    inorder_tree_walk( tree->root );    printf("\n");    delete_node = tree_search( tree->root, 15 );    if ( delete_node != NULL ) {        tree_delete( tree, delete_node );    }    printf("\n删除%d的节点后中序遍历顺序为:", 15);    inorder_tree_walk( tree->root );    printf("\n");    free_tree( tree );    return 0;}