二叉查找树

二叉查找树在查找中有着重要的应用，一个二叉树变成一个二叉查找树后所具有的性质是：对于树中的所有结点，它的左子树中的所有关键字的值小于该结点的关键字值，它的右子树中所有关键字的值大于该结点关键字的值。这就是二叉查找树。自己脑补一下什么是二叉查找树，什么是普通二叉树。由于树的递归定义，通常是递归地编写这些操作的例程。
下面是二叉查找树的操作例程，注：由于这里的所有操作函数都使用了递归，所以我把这些代码的详细总结放在了我的一篇专门用来总结递归的文章里-------------递归算法设计总结
头文件

#ifndef TREE_H_INCLUDED
#define TREE_H_INCLUDED

typedef struct tree_node{
    int data;
    struct tree_node *left;
    struct tree_node *right;
}Search_Tree;

void Make_Empty(Search_Tree *T);
Search_Tree *Find(Search_Tree *T, int X);
Search_Tree *Find_Min(Search_Tree *T);
Search_Tree *Find_Max(Search_Tree *T);
Search_Tree *Insert_Node(Search_Tree *T, int X);
Search_Tree *Delete_Node(Search_Tree *T, int X);
#endif // TREE_H_INCLUDED

C文件

#include <stdio.h>
#include <stdlib.h>
#include "tree.h"

int main()
{
    Search_Tree *tree = NULL;
    Make_Empty(tree);
    tree = Insert_Node(tree, 5);
//    tree = Insert_Node(tree, 4);
//    tree = Insert_Node(tree, 6);
//    tree = Insert_Node(tree, 3);
//    tree = Insert_Node(tree, 7);
      Delete_Node(tree, 5);
//    printf("%d\n", tree->left->left->data);
//    printf("%d\n", tree->left->data);
//    printf("%d\n", tree->data);
//    printf("%d\n", tree->right->data);
    //printf("%d\n", tree->right->right->data);


}

void Make_Empty(Search_Tree *T)
{
    if(T != NULL){
        Make_Empty(T->left);
        Make_Empty(T->right);
        free(T);
    }
}


Search_Tree *Find(Search_Tree *T, int X)
{
    if(T == NULL)
        return NULL;
    else{
        if(X == T->data)
            return T;
        else if(X < T->data)
            return Find(T->left, X);
        else
            return Find(T->right, X);
    }
}

Search_Tree *Find_Min(Search_Tree *T)
{
    if(T == NULL)
        return NULL;
    else if(T->left == NULL)
        return T;
    else
        return Find_Min(T->left);
}

Search_Tree *Find_Max(Search_Tree *T)
{
    if(T == NULL)
        return NULL;
    else
        while(T->right != NULL)
            T = T->right;

    return T;
}


Search_Tree *Insert_Node(Search_Tree *T, int X)
{
    if(T == NULL)
    {
        T = (Search_Tree *)malloc(sizeof(Search_Tree));
        if(T == NULL)
            exit(1);
        T->data = X;
        T->left = NULL;
        T->right = NULL;
    }
    else if(T->data > X)
    {
        T->left = Insert_Node(T->left, X);
    }
    else if(T->data < X)
    {
        T->right = Insert_Node(T->right, X);
    }

    return T;
}

Search_Tree *Delete_Node(Search_Tree *T, int X)
{
    Search_Tree *temp_cell;
    if(T == NULL)
    {
        printf("End!!");
        exit(1);
    }
    else if(X < T->data)
    {
        T->left = Delete_Node(T->left, X);
    }
    else if(X > T->data)
    {
        T->right = Delete_Node(T->right, X);
    }
    else if(T->left && T->right)
    {
        temp_cell = Find_Min(T->right);
        T->data = temp_cell->data;
        T->right = Delete_Node(T->right, T->data);
    }
    else
    {
        temp_cell = T;
        if(T->left == NULL)
            T = T->right;
        else
            T = T->left;
        free(temp_cell);
    }
    return T;
}