9、二叉排序樹的創建、插入、遍歷

一、二叉排序樹介紹：

　　二叉排序樹又稱“二叉查找樹”、“二叉搜索樹”。二叉排序樹：或者是一棵空樹，或者是具有下列性質的二叉樹：

　　1. 若它的左子樹不空，則左子樹上所有結點的值均小於它的根結點的值；

　　2. 若它的右子樹不空，則右子樹上所有結點的值均大於它的根結點的值；

　　3. 它的左、右子樹也分別為二叉排序樹。

二叉排序樹通常采用二叉鏈表作為存儲結構。中序遍歷二叉排序樹可得到一個依據關鍵字的有序序列，一個無序序列可以通過構造一棵二叉排序樹變成一個有序序列，構造樹的過程即是對無序序列進行排序的過程。每次插入的新的結點都是二叉排序樹上新的葉子結點，在進行插入操作時，不必移動其它結點，只需改動某個結點的指針，由空變為非空即可。搜索、插入、刪除的時間復雜度等於樹高，期望O(logn)，最壞O(n)（數列有序，樹退化成線性表，如右斜樹）

二、代碼：

// Sort.cpp : 定義控制台應用程序的入口點。
//
#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;
};

//創建節點並給key賦值
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;
}

//把節點插入到二叉順序樹中
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的父節點為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;
}

//遍歷順序節點，並輸出
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("\n");
}

#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("\n");

    system("pause");
    return 0;
}

#endif