[数据结构与算法] : 二叉查找树

头文件

typedef int ElementType;
#ifndef _TREE_H_
#define _TREE_H_

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

SearchTree MakeEmpty(SearchTree T);
Position Find(ElementType X, SearchTree T);
Position FindMin(SearchTree T);
Position FindMin2(SearchTree T);
Position FindMax2(SearchTree T);
SearchTree Insert(ElementType X, SearchTree T);
SearchTree Delete(ElementType X, SearchTree T);
ElementType Retrieve(Position P);

#endif

 

源文件

#include "tree.h"
#include "fatal.h"
#include <malloc.h>

struct TreeNode
{
    ElementType Element;
    SearchTree  Left;
    SearchTree  Right;
};

// 先清空左子树, 再清空又子树, 再释放自身节点
SearchTree MakeEmpty(SearchTree T)
{
    if(T != NULL)
    {
        MakeEmpty(T->Left);
        MakeEmpty(T->Right);
        free(T);
    }
    return NULL; // 递归终止条件
}

// 查找, 类似二分查找
Position Find(ElementType X, SearchTree T)
{
    if(T == NULL) // 递归终止条件
        return NULL;
    if(X < T->Element)
        return Find(X, T->Left);
    else if(X > T->Element)
        return Find(X, T->Right);
    else
        return T;
}

Position FindMin(SearchTree T) // 递归实现
{
    if(T == NULL) // 防止非法输入
        return NULL;
    if(T->Left == NULL) // 递归终止
        return T;
    else
        return FindMin(T->Left);
}

Position FindMin2(SearchTree T) // 非递归实现
{
    if(T == NULL)
        return NULL;
    while(T->Left != NULL)
        T = T->Left;
    return T;
}

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

Position FindMax2(SearchTree T)
{
    if(T == NULL)
        return NULL;
    while(T->Right != NULL)
        T = T->Right;
    return T;
}

// 插入
SearchTree Insert(ElementType X, SearchTree T)
{
    if(T == NULL) // 如果T为NULL, 创建节点, 递归终止条件
    {
        T = (SearchTree)malloc(sizeof(struct TreeNode));
        if(T == NULL)
            FatalError("Out of space!");
        else
        {
            T->Element = X;
            T->Left = T->Right = NULL;
        }
    }
    else if(X < T->Element)
        T->Left = Insert(X, T->Left);
    else if(X > T->Element)
        T->Right = Insert(X, T->Right);
    // 如果X已经在数中, 则什么也不做
    return T; // Do not forget this line!!
}

// 删除
SearchTree Delete(ElementType X, SearchTree T)
{
    Position TempCell;
    if(T == NULL) // 递归终止
        Error("Element not found!");
    else if(X < T->Element)
        T->Left = Delete(X, T->Left);
    else if(X > T->Element)
        T->Right = Delete(X, T->Right);
    else if(T->Left && T->Right)  // Two children
    {
        TempCell = FindMin(T->Right);// 找一个替身, 右子树的最小值
        T->Element = TempCell->Element;
        T->Right = Delete(T->Element, T->Right);// 替身已经放到T->Element, 再从右子树删除该值即可
    }
    else                          // One or zero childern
    {
        TempCell = T;
        if(T->Left == NULL)
            T = T->Right;
        else if(T->Right = NULL)
            T = T->Left;
        free(TempCell);
    }
    return T; // Do not forget this line!!
}

ElementType Retrieve(Position P)
{
    return P->Element;
}

 

测试文件

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

int main()
{
    SearchTree T;
    Position P;
    int i = 0, j = 0;

    T = MakeEmpty(NULL);
    for( i = 0; i < 50; i++, j = ( j + 7 ) % 50 )
        T = Insert( j, T );
    for( i = 0; i < 50; i++ )
        if( ( P = Find( i, T ) ) == NULL || Retrieve( P ) != i )
            printf( "Error at %d\n", i );

    for( i = 0; i < 50; i += 2 )
        T = Delete( i, T );

    for( i = 1; i < 50; i += 2 )
        if( ( P = Find( i, T ) ) == NULL || Retrieve( P ) != i )
            printf( "Error at %d\n", i );
    for( i = 0; i < 50; i += 2 )
        if( ( P = Find( i, T ) ) != NULL )
            printf( "Error at %d\n", i );

    printf( "Min is %d, Max is %d\n", Retrieve( FindMin2( T ) ),
               Retrieve( FindMax2( T ) ) );

    return 0;
}