二叉搜索树的操作集

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

输出样例：

Preorder: 5 2 1 0 4 8 6 7 10 96 is found3 is not found10 is found10 is the largest key0 is found0 is the smallest key5 is foundNot FoundInorder: 1 2 4 6 8 9

---

BinTree Insert(BinTree BST, ElementType X) {if (!BST) {BST = (BinTree)malloc(sizeof(struct TNode));BST->Data = X;BST->Left = NULL;BST->Right = NULL;}//递归建树else if (X < BST->Data)BST->Left = Insert(BST->Left, X);else if (X > BST->Data)BST->Right = Insert(BST->Right, X);//如果相等，什么也不做return BST;//返回树的根节点地址}BinTree Delete(BinTree BTS, ElementType X) {Position Tmp;if (!BTS)printf("Not Found\n");else {if (X < BTS->Data) {BTS->Left = Delete(BTS->Left, X);//左子树递归删除}else if (X > BTS->Data) {BTS->Right = Delete(BTS->Right, X);//右子树递归删除}else {//若此节点为叶子节点，直接删除//若节点有一个儿子节点，直接使其父节点指向要删除的结点的非空的儿子节点//当有两个儿子节点时，用右子树的最小数据（很容易找到）代替该节点的数据并递归的删除那个节点（变为NULL）if (BTS->Left && BTS->Right) {//被删除的结点有左右两个子结点 Tmp = FindMin(BTS->Right);//在右子树中找到最小的元素来填充删除的结点  BTS->Data = Tmp->Data;BTS->Right = Delete(BTS->Right, BTS->Data);//在删除结点的右子树中递归删除最小元素 }else {//被删除结点有一个或0个子结点  Tmp = BTS;if (!BTS->Left) {BTS = BTS->Right;}else if (!BTS->Right) {BTS = BTS->Left;}free(Tmp);}}}return BTS;}Position Find(BinTree BST, ElementType X) {if (BST == NULL) return NULL;if (BST->Data == X) return BST;else {if (X < BST->Data)BST = Find(BST->Left, X);else if (X > BST->Data)BST = Find(BST->Right, X);}}Position FindMin(BinTree BST) {//从根节点开始，只要有左儿子就向左递归查找，终止点即为最小元素if (!BST)return NULL;else {if (BST->Left) FindMin(BST->Left);elsereturn BST;}}Position FindMax(BinTree BST) {//一直向右查找if (!BST)return NULL;else {if (BST->Right != NULL)FindMax(BST->Right);elsereturn BST;}/*if (BST) {while (BST->Right) {BST = BST->Right;}}return BST;*/}