树7 二叉搜索树的操作集

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。

# define _CRT_SECURE_NO_WARNINGS
#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*/
{
	if (!BT) return;
	else
	{
		printf(" %d", BT->Data);
		PreorderTraversal(BT->Left);
		PreorderTraversal(BT->Right);
	}
}
void InorderTraversal(BinTree BT) /* 中序遍历*/
{
	if (!BT) return;
	else
	{
		PreorderTraversal(BT->Left);
		printf(" %d", BT->Data);
		PreorderTraversal(BT->Right);
	}
}

BinTree Insert(BinTree BST, ElementType X) {
	if (!BST)
	{
		BST = (BinTree)malloc(sizeof(struct TNode));
		BST->Data = X;
		BST->Left = BST->Right = NULL;
	}
	else
	{
		if (X<BST->Data)
		{
			BST->Left = Insert(BST->Left, X);
		}
		else
		{
			BST->Right = Insert(BST->Right, X);
		}
	}
	return BST;
}
Position Find(BinTree BST, ElementType X) {
	while (BST)
	{
		if (BST->Data < X) BST = BST->Right;
		else if (X < BST->Data) BST = BST->Left;
		else return BST;
	}
	return NULL;
}
Position FindMin(BinTree BST) {
	if (BST)
		while (BST->Left)	 BST = BST->Left;
	return BST;
}
Position FindMax(BinTree BST) {
	if (!BST) return NULL;
	else if (!BST->Right) return BST;
	else return FindMax(BST->Right);
}
BinTree Delete(BinTree BST, ElementType X) {
	Position temp;
	if (!BST) printf("Not Found\n");
	else if (X < BST->Data)  BST->Left = Delete(BST->Left, X);
	else if (BST->Data < X)   BST->Right = Delete(BST->Right, X);
	else
	{
		if (BST->Left&&BST->Right) {
			temp = FindMax(BST->Left);
			BST->Data = temp->Data;
			BST->Left = Delete(BST->Left, temp->Data);
		}
		else
		{
			temp = BST;
			if (!BST->Left)
				BST = BST->Right;
			else if (!BST->Right)
				BST = BST->Left;
			free(temp);
		}
	}
	return 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;
}