04-樹7 二叉搜尋樹的操作集 (30分)

本題要求實作給定二叉搜尋樹的5種常用操作。

函數接口定義：

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結構定義如下：

typedef struct TNode *Position;

typedef Position BinTree;

struct TNode{

    ElementType Data;

    BinTree Left;

    BinTree Right;

};

函數Insert将X插入二叉搜尋樹BST并傳回結果樹的根結點指針；

函數Delete将X從二叉搜尋樹BST中删除，并傳回結果樹的根結點指針；如果X不在樹中，則列印一行Not Found并傳回原樹的根結點指針；

函數Find在二叉搜尋樹BST中找到X，傳回該結點的指針；如果找不到則傳回空指針；

函數FindMin傳回二叉搜尋樹BST中最小元結點的指針；

函數FindMax傳回二叉搜尋樹BST中最大元結點的指針。

輸入樣例：

10

5 8 6 2 4 1 0 10 9 7

5

6 3 10 0 5

5

5 7 0 10 3

輸出樣例：

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;
			else
				BST = BST->Left;
			free(Tmp);
		}
	}
	return BST;
}

Position Find(BinTree BST, ElementType X) {
	while (BST && (X != BST->Data)) {
		if (X < BST->Data)
			BST = BST->Left;
		else
			BST = 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;
}