04-树7 二叉搜索树的操作集 (30分)

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。

输入样例：
10
5 8 6 2 4 1 0 10 9 7
5
6 3 10 0 5
5
5 7 0 10 3
输出样例：
Preorder: 5 2 1 0 4 8 6 7 10 9
6 is found
3 is not found
10 is found
10 is the largest key
0 is found
0 is the smallest key
5 is found
Not Found
Inorder: 1 2 4 6 8 9

#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); void InorderTraversal(BinTree BT);  void PostorderTraversal(BinTree BT);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("Postorder:");PostorderTraversal(BST);printf("\n");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;}void PreorderTraversal(BinTree BT) {if (!BT) return;printf(" %d", BT->Data);PreorderTraversal(BT->Left);PreorderTraversal(BT->Right);}void InorderTraversal(BinTree BT) {if (!BT) return;PreorderTraversal(BT->Left);printf(" %d", BT->Data);PreorderTraversal(BT->Right);}void PostorderTraversal(BinTree BT) {if (BT) {PostorderTraversal(BT->Left);PostorderTraversal(BT->Right);printf(" %d", BT->Data);}}BinTree Insert(BinTree BST, ElementType X) {if (!BST) {BST = (BinTree)malloc(sizeof(struct TNode));BST->Data = X;BST->Left = NULL;BST->Right = NULL;}else if (X < BST->Data)BST->Left = Insert(BST->Left, X);else if (X > BST->Data)BST->Right = Insert(BST->Right, X);return BST;}BinTree Delete(BinTree BST, ElementType X) {Position Tmp;if (!BST) {printf("Not Found\n");}else if (X < BST->Data)BST->Left = Delete(BST->Left, X);else if (X > BST->Data)BST->Right = Delete(BST->Right, X);else {if (BST->Left && BST->Right) {Tmp = FindMax(BST->Left);BST->Data = Tmp->Data;BST->Left= Delete(BST->Left, Tmp->Data);}else {Tmp = BST;if (!BST->Left)BST = BST->Right;elseBST = BST->Left;free(Tmp);}}return BST;}Position Find(BinTree BST, ElementType X) {while (BST && (X != BST->Data)) {if (X < BST->Data)BST = BST->Left;elseBST = BST->Right;}return BST;}Position FindMin(BinTree BST) {if (BST) {while (BST->Left)BST = BST->Left;}return BST;}Position FindMax(BinTree BST) {if (BST) {while (BST->Right)BST = BST->Right;}return BST;}