第四周的编程作业：

1.是否同一棵二叉搜索树

#include<stdio.h>
#include<stdlib.h>
typedef struct TreeNode *Tree;
struct TreeNode
{
	int v;
	Tree Left,Right;
	int flag;
};
Tree newNode(int V)
{
	Tree T=(Tree)malloc(sizeof(struct TreeNode));
	T->v=V;
	T->Left=T->Right=NULL;
	T->flag=0;
	return T;
}
Tree Insert(Tree T,int V)
{
	if(!T) T=newNode(V);
	else
	{
		if(V>T->v)
		T->Right=Insert(T->Right,V);
		else
		T->Left=Insert(T->Left,V);
	}
	return T;
}
Tree MakeTree(int n)
{
	Tree T;
	int i,V;
	scanf("%d",&V);
	T=newNode(V);
	for(i=1;i<n;i++)
	{
		scanf("%d",&V);
		T=Insert(T,V);
	}
	return T;
}
int Judge(Tree T,int V)
{
	if(T->flag)
	{
		if(V<T->v)
		return Judge(T->Left,V);
		else if(V>T->v)
		return Judge(T->Right,V);
		else 
		return 0;
	}
	else
	{
		if(V==T->v)
		{
			T->flag=1;
			return 1;
		}
		else return 0;
	}
}
int Check(Tree T,int n)
{
	int i,V,flag=0;
	scanf("%d",&V);
	if(V!=T->v) flag=1;
	else T->flag=1;
	for(i=1;i<n;i++)
	{
		scanf("%d",&V);
		if((!flag)&&(!Judge(T,V)))flag=1;
	}
	if(flag)return 0;
	else return 1;
}
void ResetT(Tree T)
{
	if(T->Left) ResetT(T->Left);
	if(T->Right) ResetT(T->Right);
	T->flag=0;
}
void FreeTree(Tree T)
{
	if(T->Left) FreeTree(T->Left);
	if(T->Right) FreeTree(T->Right);
	free(T);
}
int main()
{
	int n,l,i;
	Tree T;
	while(scanf("%d",&n))
	{
		if(n==0)break;
		scanf("%d",&l);
		T=MakeTree(n);
		while(l--)
		{
			if(Check(T,n))
			printf("Yes\n");
			else 
			printf("No\n");
			ResetT(T);
		}
		FreeTree(T);
	}	
}

2.Root of AVL Tree

//按照输入顺序建立平衡二叉树，输出根节点

//四种情况都要转一下

#include<stdio.h>
#include<stdlib.h>
#include<iostream>
#include<algorithm>
using namespace std;
typedef int ElementType;
typedef struct AVLNode *Position;
typedef Position AVLTree;
typedef struct AVLNode{
	ElementType Data;
	AVLTree Left;
	AVLTree Right;
	int Height;
};
int GetHeight(AVLTree T)
{
	int l,r,maxh;
	if(T)
	{
		l=GetHeight(T->Left);
		r=GetHeight(T->Right);
		maxh=l>r?l:r;
		return (maxh+1);
	}
	else return 0;
}
AVLTree SingleLeftRotation(AVLTree A)
{
	AVLTree B=A->Left;
	A->Left=B->Right;
	B->Right=A;
	A->Height=max(GetHeight(A->Left),GetHeight(A->Right))+1;
	B->Height=max(GetHeight(B->Left),A->Height)+1;
	return B;
}
AVLTree SingleRightRotation(AVLTree A)
{
	AVLTree B=A->Right;
	A->Right=B->Left;
	B->Left=A;
	A->Height=max(GetHeight(A->Left),GetHeight(A->Right))+1;
	B->Height=max(GetHeight(B->Right),A->Height)+1;
	return B;
}
AVLTree DoubleLeftRightRotation(AVLTree A)
{
	A->Left=SingleRightRotation(A->Left);
	return SingleLeftRotation(A);
}
AVLTree DoubleRightLeftRotation(AVLTree A)
{
	A->Right=SingleLeftRotation(A->Right);
	return SingleRightRotation(A);
}
AVLTree Insert(AVLTree T,ElementType x)
{
	if(!T)
	{
		T=(AVLTree)malloc(sizeof(struct AVLNode));
		T->Data=x;
		T->Height=1;
		T->Left=T->Right=NULL;
	}
	else if(x<T->Data)
	{
		T->Left=Insert(T->Left,x);
		if(GetHeight(T->Left)-GetHeight(T->Right)==2)
		{
			if(x<T->Left->Data)
			T=SingleLeftRotation(T);
			else 
			T=DoubleLeftRightRotation(T);
		}
	}
	else if(x>T->Data)
	{
		T->Right=Insert(T->Right,x);
		if(GetHeight(T->Left)-GetHeight(T->Right)==-2)
		{
			if(x>T->Right->Data)
			T=SingleRightRotation(T);
			else 
			T=DoubleRightLeftRotation(T);
		}
	}
	T->Height=max(GetHeight(T->Left),GetHeight(T->Right))+1;
	return T;
}
int main()
{
	int n,i;
	ElementType x;
	AVLTree T;
	T=NULL;
	scanf("%d",&n);
	for(i=0;i<n;i++)
	{
		scanf("%d",&x);
		T=Insert(T,x);
	}
	printf("%d\n",T->Data);
}

3.Complete Binary Search Tree 

#include <stdio.h>
#include <algorithm>
#include <stdlib.h>
using namespace std;
int A[1005],T[1005];
int n,p;
void solve(int root)
{
	if(root<=n)
	{
		solve(root*2);//左 
		T[root]=A[p++];
		solve(root*2+1);//右 
	}
}
int main()
{
	int i;
	p=0;
	scanf("%d",&n);
	for(i=0;i<n;i++)
	scanf("%d",&A[i]);
	sort(A,A+n);
	solve(1);
	for(i=1;i<n;i++)
	printf("%d ",T[i]);
	printf("%d\n",T[n]);
}

4.二叉搜索树的操作集

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