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(" "); 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 ", X); else { printf("%d is found ", Tmp->Data); if (Tmp==MinP) printf("%d is the smallest key ", Tmp->Data); if (Tmp==MaxP) printf("%d is the largest key ", Tmp->Data); } } scanf("%d", &N); for( i=0; i<N; i++ ) { scanf("%d", &X); BST = Delete(BST, X); } printf("Inorder:"); InorderTraversal(BST); printf(" "); return 0; } /* 你的代码将被嵌在这里 */
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
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 (BST->Data > X) { BST->Left = Insert( BST->Left, X ); } else if (BST->Data < X) { BST->Right = Insert( BST->Right, X ); } return BST; } BinTree Delete( BinTree BST, ElementType X ) { BinTree p; if ( !BST ) { printf("Not Found "); return BST; } if ( BST->Data > X) { BST->Left = Delete( BST->Left, X); } else if ( BST->Data < X) { BST->Right = Delete( BST->Right, X); } else { if ( BST->Right && BST->Left ) { p = FindMax( BST->Left ); BST->Data = p->Data; BST->Left = Delete( BST->Left, BST->Data ); } else { p = BST; if ( !BST->Left ) { BST = BST->Right; } else if ( !BST->Right) { BST = BST->Left; } free(p); } } return BST; } Position Find( BinTree BST, ElementType X ) { if ( !BST ) { return NULL; } if ( BST->Data > X ) { return Find( BST->Left, X ); } else if ( BST->Data < X ) { return Find( BST->Right, X ); } else { 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; }