目录
题目
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
五种操作
1.插入操作
BinTree Insert(BinTree BST,ElementType X)
{
if(!BST)/*如果树是空的*/
{
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);/*如果小于根结点键值就递归插入左子树*/
}
else if(X > BST->Data)
{
BST->Right = Insert(BST->Right,X);/*如果大于根结点键值就递归插入右子树*/
}
}
return BST;
}
2. 删除操作
BinTree Delete(BinTree BST,ElementType X)
{
Position T;
if(!BST)
{
printf("Not Found\n");
}
else if(X < BST->Data) BST->Left = Delete(BST->Left,X);/*如果小于根结点键值*/
else if(X > BST->Data) BST->Right = Delete(BST->Right,X);/*如果大于根结点键值*/
else/*如果找到要删除的结点*/
{
if(BST->Left && BST->Right)/*如果左右都不为空*/
{
T = FindMin(BST->Right);/*就在右子树中找最小的元素来替代*/
BST->Data = T->Data;
BST->Right = Delete(BST->Right,BST->Data);/*并删除右子树的最小元*/
/*T = FindMax(BST->Left);
BST->Data = T->Data;
BST->Left = Delete(BST->Right,BST->Data);*/
//或者在左子树中找到最大值来替代并删除最大值
}
else
{
T = BST;
if(!BST->Left)/*如果右子树不为空*/
{
BST = BST->Right;
}
else if(!BST->Right)/*如果左子树不为空*/
{
BST = BST->Left;
}
free(T);
}
}
return BST;
}
3. 查找操作
(1)效率高的迭代函数
Position Find(BinTree BST, ElementType X)
{
while(BST)
{
if(X > BST->Data)
{
BST = BST->Right;
}
else if(X < BST->Data)
{
BST = BST->Left;
}
else
{
return BST;
}
}
return NULL;
}
(2)效率低的递归函数
Position FindMin(BinTree BST)
{
if(!BST) return NULL;/*空的二叉搜索树,返回NULL*/
else if(!BESt->Left)
{
return BST;/*找到最左叶结点并返回*/
}
else
{
return FindMin(BST->Left);
}
}
4. 查找最小值
(1)递归
Position FindMin(BinTree BST)
{
if(!BST) return NULL;/*如果是空树返回NULL*/
else if(!BST->Left) return BST;/*如果到达最左边*/
else
{
FindMin(BST->Left);
}
}
(2)迭代
Position FindMin(BinTree BST)
{
if(BST)
{
while(BST->Left)
{
BST = BSt->Left;
}
}
return BST;
}
5.查找最大值
(1)递归
Position FindMax(BinTree BST)
{
if(!BST) return NULL;/*如果是空树返回NULL*/
else if(!BST->Right) return BST;/*如果到达最左边*/
else
{
FindMin(BST->Right);
}
}
(2)迭代
Position FindMax(BinTree BST)
{
if(BST)
{
while(BST->Right)
{
BST = BSt->Right;
}
}
return BST;
}
完整代码
#include <iostream>
#include <cstdlib>
#include <cstdio>
#include <stack>
using namespace std;
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;
BST = NULL;
cin >> N;/*结点个数*/
for (int i = 0; i < N; i++ )
{
cin >> X;
BST = Insert(BST, X);/*将输入的结点插入二叉搜索树中*/
}
printf("Preorder:"); /*先序遍历*/
PreorderTraversal(BST);
printf("\n");
MinP = FindMin(BST);/*找到最小值并返回其所在指针*/
MaxP = FindMax(BST);/*找到最大值并返回其所在指针*/
cin >> N;/*输入待查找数目*/
for( int i = 0; i < N; i++ )
{
cin >> X;/*输入要查找的数*/
Tmp = Find(BST, X);
if (Tmp == NULL) printf("%d is not found\n", X);/*如果没找到*/
else
{
printf("%d is found\n", Tmp->Data);/*如果找到了*/
if (Tmp==MinP) printf("%d is the smallest key\n", Tmp->Data);/*如果是最小值*/
if (Tmp==MaxP) printf("%d is the largest key\n", Tmp->Data);/*如果是最大值*/
}
}
cin >> N;/*输入待删除的数量*/
for( int i = 0; i < N; i++ )
{
cin >> X;/*输入要删除的结点*/
BST = Delete(BST, X);
}
printf("Inorder:"); /*中序遍历一遍*/
InorderTraversal(BST);
printf("\n");
return 0;
}
BinTree Insert(BinTree BST,ElementType X)
{
if(!BST)/*如果树是空的*/
{
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);/*如果小于根结点键值就递归插入左子树*/
}
else if(X > BST->Data)
{
BST->Right = Insert(BST->Right,X);/*如果大于根结点键值就递归插入右子树*/
}
}
return BST;
}
BinTree Delete(BinTree BST,ElementType X)
{
Position T;
if(!BST)
{
printf("Not Found\n");
}
else if(X < BST->Data) BST->Left = Delete(BST->Left,X);/*如果小于根结点键值*/
else if(X > BST->Data) BST->Right = Delete(BST->Right,X);/*如果大于根结点键值*/
else/*如果找到要删除的结点*/
{
if(BST->Left && BST->Right)/*如果左右都不为空*/
{
T = FindMin(BST->Right);/*就在右子树中找最小的元素来替代*/
BST->Data = T->Data;
BST->Right = Delete(BST->Right,BST->Data);/*并删除右子树的最小元*/
}
else
{
T = BST;
if(!BST->Left)/*如果左子树不为空*/
{
BST = BST->Right;
}
else if(!BST->Right)/*如果右子树不为空*/
{
BST = BST->Left;
}
free(T);
}
}
return BST;
}
Position Find(BinTree BST, ElementType X)
{
while(BST)
{
if(X > BST->Data)
{
BST = BST->Right;
}
else if(X < BST->Data)
{
BST = BST->Left;
}
else
{
return BST;
}
}
return NULL;
}
Position FindMin(BinTree BST)
{
if(!BST) return NULL;/*如果是空树返回NULL*/
else if(!BST->Left) return BST;/*如果到达最左边*/
else
{
FindMin(BST->Left);
}
}
Position FindMax(BinTree BST)
{
if(!BST) return NULL;/*如果是空树返回NULL*/
else if(!BST->Right) return BST;/*如果到达最左边*/
else
{
FindMax(BST->Right);
}
}
void PreorderTraversal(BinTree BST)
{
if(BST)
{
cout << BST->Data << " ";
PreorderTraversal(BST->Left);
PreorderTraversal(BST->Right);
}
}
void InorderTraversal(BinTree BST)
{
if(BST)
{
InorderTraversal(BST->Left);
cout << BST->Data << " ";
InorderTraversal(BST->Right);
}
}