4-12 二叉搜索树的操作集*

本题要求实现给定二叉搜索树的5种常用操作。

函数接口定义：

BinTree Insert( BinTree BST, ElementType X );BinTree Delete( BinTree BST, ElementType X );Position Find( BinTree BST, ElementType X );Position FindMin( BinTree BST );Position FindMax( BinTree BST );

其中BinTree结构定义如下：

typedef struct TNode *Position;typedef Position BinTree;struct TNode{    ElementType Data;    BinTree Left;    BinTree Right;};

• 函数Insert将X插入二叉搜索树BST并返回结果树的根结点指针；
• 函数Delete将X从二叉搜索树BST中删除，并返回结果树的根结点指针；如果X不在树中，则打印一行Not Found并返回原树的根结点指针；
• 函数Find在二叉搜索树BST中找到X，返回该结点的指针；如果找不到则返回空指针；
• 函数FindMin返回二叉搜索树BST中最小元结点的指针；
• 函数FindMax返回二叉搜索树BST中最大元结点的指针。

裁判测试程序样例：

#include <stdio.h>#include <stdlib.h>typedef int ElementType;typedef struct TNode *Position;typedef Position BinTree;struct TNode{    ElementType Data;    BinTree Left;    BinTree Right;};void PreorderTraversal( BinTree BT ); /* 先序遍历，由裁判实现，细节不表 */void InorderTraversal( BinTree BT );  /* 中序遍历，由裁判实现，细节不表 */BinTree Insert( BinTree BST, ElementType X );BinTree Delete( BinTree BST, ElementType X );Position Find( BinTree BST, ElementType X );Position FindMin( BinTree BST );Position FindMax( BinTree BST );int main(){    BinTree BST, MinP, MaxP, Tmp;    ElementType X;    int N, i;    BST = NULL;    scanf("%d", &N);    for ( i=0; i<N; i++ ) {        scanf("%d", &X);        BST = Insert(BST, X);    }    printf("Preorder:"); PreorderTraversal(BST); printf("\n");    MinP = FindMin(BST);    MaxP = FindMax(BST);    scanf("%d", &N);    for( i=0; i<N; i++ ) {        scanf("%d", &X);        Tmp = Find(BST, X);        if (Tmp == NULL) printf("%d is not found\n", X);        else {            printf("%d is found\n", Tmp->Data);            if (Tmp==MinP) printf("%d is the smallest key\n", Tmp->Data);            if (Tmp==MaxP) printf("%d is the largest key\n", Tmp->Data);        }    }    scanf("%d", &N);    for( i=0; i<N; i++ ) {        scanf("%d", &X);        BST = Delete(BST, X);    }    printf("Inorder:"); InorderTraversal(BST); printf("\n");    return 0;}/* 你的代码将被嵌在这里 */

输入样例：

105 8 6 2 4 1 0 10 9 756 3 10 0 555 7 0 10 3

#include #include typedef int ElementType;typedef struct TNode *Position;typedef Position BinTree;struct TNode{ElementType Data;BinTree Left;BinTree Right;};void PreorderTraversal(BinTree BT) /* 先序遍历，由裁判实现，细节不表 */{BinTree tmp = BT;if (!tmp)return;else{{printf(" %d", tmp->Data);}PreorderTraversal(tmp->Left);PreorderTraversal(tmp->Right);}}void InorderTraversal(BinTree BT)  /* 中序遍历，由裁判实现，细节不表 */{BinTree tmp = BT;if (!tmp)return;else{{}InorderTraversal(tmp->Left);printf(" %d", tmp->Data);InorderTraversal(tmp->Right);}}BinTree Insert(BinTree BST, ElementType X);BinTree Delete(BinTree BST, ElementType X);Position Find(BinTree BST, ElementType X);Position FindMin(BinTree BST);Position FindMax(BinTree BST);int main(){BinTree BST, MinP, MaxP, Tmp;ElementType X;int N, i;BST = NULL;scanf("%d", &N);for (i = 0; iData);if (Tmp == MinP) printf("%d is the smallest key\n", Tmp->Data);if (Tmp == MaxP) printf("%d is the largest key\n", Tmp->Data);}}scanf("%d", &N);for (i = 0; iData = X;BST->Left = NULL;BST->Right = NULL;return BST;}else{while (tmp){if (tmp->Data>X){if (!tmp->Left){BinTree newB = (BinTree)malloc(sizeof(struct TNode));newB->Data = X;newB->Left = NULL;newB->Right = NULL;tmp->Left = newB;break;}else{tmp = tmp->Left;}}else{if (!tmp->Right){//printf("tmp->data:%d\n", tmp->Data);//printf("X:%d", X);BinTree newC = (BinTree)malloc(sizeof(struct TNode));newC->Data = X;newC->Left = NULL;newC->Right = NULL;tmp->Right = newC;break;}elsetmp = tmp->Right;}}return BST;}}void createnewBinTree(BinTree BST, ElementType X, BinTree *newtree){BinTree tmp = BST;if (!tmp)return;else{{if (tmp->Data != X)*newtree=Insert(*newtree, tmp->Data);}createnewBinTree(tmp->Left, X, newtree);createnewBinTree(tmp->Right, X, newtree);}}BinTree Delete(BinTree BST, ElementType X){BinTree tmp = Find(BST, X);BinTree newBin = NULL;if (!tmp){ printf("Not Found\n"); return BST; }else{createnewBinTree(BST, X, &newBin);//只有传递指针才能在局部函数里面改变该变量的值return newBin;}}Position Find(BinTree BST, ElementType X){BinTree tmp = BST;if (!tmp)return NULL;if (tmp->Data == X)return tmp;else{if (tmp->Data>X)tmp = Find(tmp->Left, X);elsetmp = Find(tmp->Right, X);}return tmp;}Position FindMin(BinTree BST){BinTree tmp = BST;if (!tmp)return NULL;while (1){if (tmp->Left)tmp = tmp->Left;else return tmp;}}Position FindMax(BinTree BST){BinTree tmp = BST;if (!tmp)return NULL;while (1){if (tmp->Right)tmp = tmp->Right;else return tmp;}}

易错点：//只有传递指针才能在局部函数里面改变该变量的值，所以构造函数前要确定是否要改变数据的值