数据结构与算法分析-二叉查找树

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

#define ElementType int　　//节点数据类型

//typedef struct TreeNode *Position;
//typedef struct TreeNode *SearchTree;

struct TreeNode
{
    ElementType Element;
    struct TreeNode *Left;
    struct TreeNode *Right;

};

typedef struct TreeNode *Position;
typedef struct TreeNode *SearchTree;

SearchTree Insert(ElementType X,  SearchTree T);
SearchTree Delete(ElementType X, SearchTree T);
SearchTree MakeEmpty(SearchTree T);
SearchTree PrintTree(SearchTree T);　　　　//使用前序遍历打印树
Position Find(ElementType X, SearchTree T);
Position FindMax(SearchTree T);
Position FindMin(SearchTree T);


SearchTree Insert(ElementType X,  SearchTree T)
{
    if (NULL == T)
    {
        T = (SearchTree)malloc(sizeof(struct TreeNode));    
        if (NULL == T)
        {
            printf("Malloc Error!\n");
            return NULL;
        }
        else
        {
            printf("Insert %d!\n", X);
            T->Element = X;
            T->Left = T->Right = NULL;
        }
    }
    else if (X > T->Element)
    {
        T->Right = Insert(X, T->Right);
    }
    else
    {
        T->Left = Insert(X, T->Left);
    }
    return T;
}

//删除的效率并不高,因为它沿该树进行了两趟搜索以查找和删除右子树中最小的节点.
//经过大量删除操作后,将会导致左子树比右子树深,原因是我们总是用右子树的一个节点来代替删除节点
SearchTree Delete(ElementType X, SearchTree T)　　　　
{
    Position Temp = NULL;
    if (NULL == T)
    {
        printf("Delete Element Not Found!\n");
        return NULL;
    }
    else if (X > T->Element)
    {
        T->Right = Delete(X, T->Right);
    }
    else if (X < T->Element)
    {
        T->Left = Delete(X, T->Left);
    }
    else if (T->Right && T->Left)
    {
        Temp = FindMin(T->Right);
        T->Element = Temp->Element;
        T->Right = Delete(T->Element, T->Right);
    }
    else
    {
        Temp = T;
        if (NULL == T->Right)
        {
            T = T->Left;    
        }
        else if (NULL == T->Left)
        {
            T = T->Right;    
        }
        else
        {}
        free(Temp);
        Temp = NULL;
    }
    return T;
}


SearchTree MakeEmpty(SearchTree T)
{
    if (NULL != T)
    {
        MakeEmpty(T->Right);
        MakeEmpty(T->Left);
        free(T);    
    }
    return NULL;
}


SearchTree PrintTree(SearchTree T)
{
    if (NULL != T)
    {
        printf("%d ", T->Element);
        if (NULL != T->Left)
        {
            PrintTree(T->Left);
        }
        if (NULL != T->Right)
        {
            PrintTree(T->Right);
        }
    }
    return NULL;
}


Position Find(ElementType X, SearchTree T)
{
    if (NULL == T)
    {
        printf("Find Element Not Found!\n");
        return NULL;    
    }
    else if (X < T->Element)
    {
        return Find(X, T->Left);    
    }
    else if (X > T->Element)
    {
        return Find(X, T->Right);    
    }
    else
    {
        return T;
    }
}


Position FindMax(SearchTree T)
{
    if (NULL != T)
    {
        while (NULL != T->Right)
        {
            T = T->Right;
        }
    }
    return T;
}

Position FindMin(SearchTree T)
{
    if (NULL == T)
    {
        return NULL;
    }
    else if (NULL == T->Left)
    {
        return T;
    }
    else 
    {
        return FindMin(T->Left);
    }
}

int main()
{
    SearchTree T = NULL;    
    SearchTree ptmp = NULL;    

    T = Insert(6, T);    
    T = Insert(2, T);    
    T = Insert(8, T);    
    T = Insert(4, T);    
    T = Insert(3, T);    
    T = Insert(1, T);    

    ptmp = FindMin(T);
    if (NULL != ptmp)
    {
        printf("min:%d\n", ptmp->Element);
    }
    ptmp = FindMax(T);
    if (NULL != ptmp)
    {
        printf("max:%d\n", ptmp->Element);
    }
    ptmp = Find(3, T);
    if (NULL != ptmp)
    {
        printf("find:%d\n", ptmp->Element); 
    }
    PrintTree(T);
    printf("\n");    

    T = Delete(3, T);
    PrintTree(T);
    printf("\n");    
    ptmp = Find(3, T);
    if (NULL != ptmp)
    {
        printf("find:%d\n", ptmp->Element); 
    }
    
    T = MakeEmpty(T);
    return 0;    
}