6-12 二叉搜索樹的操作集（30 分）

本題要求實現給定二叉搜索樹的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將X插入二叉搜索樹BST并返回結果樹的根結點指針；
• 函數Delete將X從二叉搜索樹BST中刪除，并返回結果樹的根結點指針；如果X不在樹中，則打印一行Not Found并返回原樹的根結點指針；
• 函數Find在二叉搜索樹BST中找到X，返回該結點的指針；如果找不到則返回空指針；
• 函數FindMin返回二叉搜索樹BST中最小元結點的指針；
• 函數FindMax返回二叉搜索樹BST中最大元結點的指針。

裁判測試程序樣例：

#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 ); /* 先序遍歷，由裁判實現，細節不表 */
void InorderTraversal( BinTree BT );  /* 中序遍歷，由裁判實現，細節不表 */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;
}
/* 你的代碼將被嵌在這里 */

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

思路：二叉搜索樹忘了?，看完之后曾國強不想用遞歸。

BinTree Insert(BinTree BST, ElementType X)
{if (BST == NULL){BST = (BinTree)malloc(sizeof(struct TNode));BST->Data = X;BST->Left = NULL;BST->Right = NULL;return BST;}BinTree bin = BST;while (bin){if (X < bin->Data){if (bin->Left == NULL){bin->Left = (BinTree)malloc(sizeof(struct TNode));bin->Left->Data = X;bin->Left->Left = NULL;bin->Left->Right = NULL;break;}else bin = bin->Left;}else if (bin->Data < X) {if (bin->Right == NULL){bin->Right = (BinTree)malloc(sizeof(struct TNode));bin->Right->Data = X;bin->Right->Left = NULL;bin->Right->Right = NULL;break;}else bin = bin->Right; }}return BST;
}
BinTree Delete(BinTree BST, ElementType X)
{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){Position pos = FindMin(BST->Right);BST->Data = pos->Data;BST->Right = Delete(BST->Right, BST->Data);}else if (!BST->Left){Position pos = BST;BST = BST->Right;free(pos);}else if (!BST->Right){Position pos = BST;BST = BST->Left;free(pos);}}}return BST;
}
Position Find(BinTree BST, ElementType X)
{if (!BST)return BST;Position pos = BST;while (pos){if (pos->Data == X)return pos;if (pos->Data > X){if (pos->Left == NULL)return pos->Left;else pos = pos->Left;}if (pos->Data < X){if (pos->Right == NULL)return pos->Right;else pos = pos->Right;}}
}
Position FindMin(BinTree BST)
{if (!BST)return BST;Position pos = BST;while (pos->Left)pos = pos->Left;return pos;
}
Position FindMax(BinTree BST)
{if (!BST)return BST;Position pos = BST;while (pos->Right)pos = pos->Right;return pos;
}

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轉載于:https://www.cnblogs.com/zengguoqiang/p/8401272.html

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