6-12 二叉搜索树的操作集
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("\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
插入
错误代码:
BinTree Insert( BinTree BST, ElementType X ){ if(BST==NULL){ BST=(Position)malloc(sizeof(struct TNode)); BST->Data=X; BST->Left=NULL; BST->Right=NULL; } if(BST->Data==X){ } else if(BST->Data>X){ Insert(BST->Left, X);
} else { Insert(BST->Right, X); } return BST; }
正确代码
BinTree Insert( BinTree BST, ElementType X ){
if(BST==NULL){
BST=(Position)malloc(sizeof(struct TNode));
BST->Data=X;
BST->Left=NULL;
BST->Right=NULL;
}
else{
if(BST->Data==X){
}
else if(BST->Data>X){
BST->Left=Insert(BST->Left, X);
}
else {
BST->Right=Insert(BST->Right, X);
}
}
return BST;
}
查找
错误代码:
Position Find( BinTree BST, ElementType X ){ if(BST==NULL){ return NULL; } if(BST->Data==X){ return BST; } else if(BST->Data>X){ Find(BST->Left,X); } else { Find(BST->Right,X); } return NULL; }
正确代码:
Position Find( BinTree BST, ElementType X ){ if(BST==NULL){ return NULL; } if(BST->Data==X){ return BST; } else if(BST->Data>X){ return Find(BST->Left,X); } else { return Find(BST->Right,X); } return NULL; }
删除
注意此处是否free空间都可以通过(AC)。
错误代码:
BinTree Delete( BinTree BST, ElementType X ){ if(BST==NULL){ printf("Not Found\n"); } else{ if(BST->Data==X){ if(BST->Left==NULL&&BST->Right==NULL){ Position tmp; tmp=BST; BST=NULL; free(tmp); } if((BST->Left==NULL&&BST->Right!=NULL)){ Position tmp; tmp=BST; BST=BST->Right; free(tmp); } if((BST->Left!=NULL&&BST->Right==NULL)){ Position tmp; tmp=BST; BST=BST->Left; free(tmp); } if(BST->Left!=NULL && BST->Right!=NULL){ BinTree tmp=FindMax(BST->Left); BST->Data=tmp->Data; BST->Left=Delete(BST->Left, tmp->Data); } } else if(BST->Data>X){ BST->Left=Delete(BST->Left, X); } else { BST->Right=Delete(BST->Right, X); } } return BST; }
正确代码:
BinTree Delete( BinTree BST, ElementType X ){ if(BST==NULL){ printf("Not Found\n"); } else{ if(BST->Data==X){ if(BST->Left==NULL&&BST->Right==NULL){ Position tmp; tmp=BST; BST=NULL; free(tmp); } else if((BST->Left==NULL&&BST->Right!=NULL)){ Position tmp; tmp=BST; BST=BST->Right; free(tmp); } else if((BST->Left!=NULL&&BST->Right==NULL)){ Position tmp; tmp=BST; BST=BST->Left; free(tmp); } else if(BST->Left!=NULL && BST->Right!=NULL){ BinTree tmp=FindMax(BST->Left); BST->Data=tmp->Data; BST->Left=Delete(BST->Left, tmp->Data); } } else if(BST->Data>X){ BST->Left=Delete(BST->Left, X); } else { BST->Right=Delete(BST->Right, X); } } return BST; }
查找最大和最小:
错误代码:
Position FindMin( BinTree BST ){ while(BST->Left!=NULL){ BST=BST->Left; } return BST; } Position FindMax( BinTree BST ){ while(BST->Right!=NULL){ BST=BST->Right; } return BST; }
正确代码:
Position FindMin( BinTree BST ){ if(BST==NULL){ return NULL; } while(BST->Left!=NULL){ BST=BST->Left; } return BST; } Position FindMax( BinTree BST ){ if(BST==NULL){ return NULL; } while(BST->Right!=NULL){ BST=BST->Right; } return BST; }