9、二叉排序树的创建、插入、遍历

一、二叉排序树介绍：

　　二叉排序树又称“二叉查找树”、“二叉搜索树”。二叉排序树：或者是一棵空树，或者是具有下列性质的二叉树：

　　1. 若它的左子树不空，则左子树上所有结点的值均小于它的根结点的值；

　　2. 若它的右子树不空，则右子树上所有结点的值均大于它的根结点的值；

　　3. 它的左、右子树也分别为二叉排序树。

二叉排序树通常采用二叉链表作为存储结构。中序遍历二叉排序树可得到一个依据关键字的有序序列，一个无序序列可以通过构造一棵二叉排序树变成一个有序序列，构造树的过程即是对无序序列进行排序的过程。每次插入的新的结点都是二叉排序树上新的叶子结点，在进行插入操作时，不必移动其它结点，只需改动某个结点的指针，由空变为非空即可。搜索、插入、删除的时间复杂度等于树高，期望O(logn)，最坏O(n)（数列有序，树退化成线性表，如右斜树）

二、代码：

// Sort.cpp : 定义控制台应用程序的入口点。
//
#include "stdafx.h"
#include<windows.h>
#include<assert.h>

#if 1

typedef int KEY_VALUE;

struct bstree_node {
    KEY_VALUE data;
    struct bstree_node *left;
    struct bstree_node *right;
};

struct bstree {
    struct bstree_node *root;
};

//创建节点并给key赋值
struct bstree_node *bstree_create_node(KEY_VALUE key) {
    struct bstree_node *node = (struct bstree_node*)malloc(sizeof(struct bstree_node));
    if (node == NULL) {
        assert(0);
    }
    node->data = key;
    node->left = node->right = NULL;

    return node;
}

//把节点插入到二叉顺序树中
int bstree_insert(struct bstree *T, int key) {

    assert(T != NULL);

    if (T->root == NULL) {
        T->root = bstree_create_node(key);
        return 0;
    }

    struct bstree_node *node = T->root;
    struct bstree_node *tmp = T->root;

    //node的父节点为tmp,
    while (node != NULL) {
        tmp = node;
        if (key < node->data) {
            node = node->left;
        }
        else {
            node = node->right;
        }
    }

    if (key < tmp->data) {
        tmp->left = bstree_create_node(key);
    }
    else {
        tmp->right = bstree_create_node(key);
    }

    return 0;
}

//遍历顺序节点，并输出
int bstree_traversal(struct bstree_node *node) {
    if (node == NULL) return 0;

    bstree_traversal(node->left);
    printf("%4d ", node->data);
    bstree_traversal(node->right);
}

#define ARRAY_LENGTH        20
int main() {

    int keyArray[ARRAY_LENGTH] = { 24, 25, 13, 35, 23, 26, 67, 47, 38, 98, 20, 13, 17, 49, 12, 21, 9, 18, 14, 15 };

    struct bstree T = { 0 };
    int i = 0;
    for (i = 0; i < ARRAY_LENGTH; i++) {
        bstree_insert(&T, keyArray[i]);
    }

    bstree_traversal(T.root);

    system("pause");
    printf("
");
}

#else

typedef int KEY_VALUE;


#define BSTREE_ENTRY(name, type)     
    struct name {                    
        struct type *left;            
        struct type *right;            
    }

struct bstree_node {
    KEY_VALUE data;
    BSTREE_ENTRY(, bstree_node) bst;
};

struct bstree {
    struct bstree_node *root;
};

struct bstree_node *bstree_create_node(KEY_VALUE key) {
    struct bstree_node *node = (struct bstree_node*)malloc(sizeof(struct bstree_node));
    if (node == NULL) {
        assert(0);
    }
    node->data = key;
    node->bst.left = node->bst.right = NULL;

    return node;
}

int bstree_insert(struct bstree *T, int key) {

    assert(T != NULL);

    if (T->root == NULL) {
        T->root = bstree_create_node(key);
        return 0;
    }

    struct bstree_node *node = T->root;
    struct bstree_node *tmp = T->root;

    while (node != NULL) {
        tmp = node;
        if (key < node->data) {
            node = node->bst.left;
        }
        else {
            node = node->bst.right;
        }
    }

    if (key < tmp->data) {
        tmp->bst.left = bstree_create_node(key);
    }
    else {
        tmp->bst.right = bstree_create_node(key);
    }

    return 0;
}

int bstree_traversal(struct bstree_node *node) {
    if (node == NULL) return 0;

    bstree_traversal(node->bst.left);
    printf("%4d ", node->data);
    bstree_traversal(node->bst.right);
}

#define ARRAY_LENGTH        20

int _tmain(int argc, _TCHAR* argv[])
{
    int keyArray[ARRAY_LENGTH] = { 24, 25, 13, 35, 23, 26, 67, 47, 38, 98, 20, 13, 17, 49, 12, 21, 9, 18, 14, 15 };

    struct bstree T = { 0 };
    int i = 0;
    for (i = 0; i < ARRAY_LENGTH; i++) {
        bstree_insert(&T, keyArray[i]);
    }

    bstree_traversal(T.root);

    printf("
");

    system("pause");
    return 0;
}

#endif