1：判断是否为平衡二叉树：

//方法1：int TreeDepth(BTree* pRoot){	if (pRoot == NULL)		return 0;	int nLeftDepth = TreeDepth(pRoot->m_pLeft);	int nRightDepth = TreeDepth(pRoot->m_pRight);	return (nLeftDepth > nRightDepth)? (nLeftDepth+1):(nRightDepth+1);}bool IsBalanced(BTree* pRoot){	if (pRoot == NULL)		return true;	int nLeftDepth = TreeDepth(pRoot->m_pLeft);	int nRightDepth = TreeDepth(pRoot->m_pRight);	int diff = nRightDepth - nLeftDepth;	if (diff > 1 || diff < -1)		return false;	return IsBalanced(pRoot->m_pLeft)&&IsBalanced(pRoot->m_pRight);	}/*上面的方法：在求该节点的左右子树的深度的时候遍历一遍树，再次判断子树的平衡性的时候又要遍历一遍树结构，造成遍历多次！*/bool IsBalanced3(BTree* pRoot, int& depth){	if(pRoot== NULL)	{		depth = 0;		return true;	}	int nLeftDepth;	bool bLeft= IsBalanced3(pRoot->m_pLeft, nLeftDepth);	int nRightDepth;	bool bRight = IsBalanced3(pRoot->m_pRight, nRightDepth);		if (bLeft && bRight && abs(nLeftDepth - nRightDepth) <=1)	{		depth = 1+(nLeftDepth > nRightDepth ? nLeftDepth : nRightDepth);		return true;		}	else	{		return false;	}}bool IsBalanced3(BTree* pRoot){	int depth = 0;	return IsBalanced3(pRoot, depth);}

2：求二叉树的镜像

/*求二叉树的镜像：方法1： 前序遍历每个节点，如果遍历到的节点有子节点，就交换它的两个子节点。（先交换左子树和右子树，再对左子树和右子树进行镜像操作）方法2： 如果二叉树不为空，求左子树和右子树的镜像，然后再交换左子树和右子树*/void Mirror(BTree* &pRoot){	if(pRoot == NULL)		return;	if(pRoot->m_pLeft ==NULL && pRoot->m_pRight == NULL)		return;	BTree* pTemp = pRoot->m_pLeft;	pRoot->m_pLeft = pRoot->m_pRight;	pRoot->m_pRight = pTemp;	if(pRoot->m_pLeft)		Mirror(pRoot->m_pLeft);	if(pRoot->m_pRight)		Mirror(pRoot->m_pRight);}BTree* Mirror2(BTree* pRoot){	if(pRoot == NULL)		return NULL;	BTree*  pLeft = Mirror2(pRoot->m_pLeft);	BTree*  pRight = Mirror2(pRoot->m_pRight);	pRoot->m_pLeft = pRight;	pRoot->m_pRight = pLeft;	return pRoot;}

完整测试代码：

// BalanceOfBT.cpp : 定义控制台应用程序的入口点。//#include "stdafx.h"#include <iostream>using namespace std;class BTree{public:	int     m_nValue;	BTree*  m_pLeft;	BTree*  m_pRight;	BTree(int m):m_nValue(m)	{		m_pLeft = m_pRight = NULL;	}};//二叉树的插入实现void Insert(int value, BTree* &root){	if (root == NULL)	{		root = new BTree(value);	}	else if(value < root->m_nValue)		Insert(value,root->m_pLeft);	else if(value > root->m_nValue)		Insert(value,root->m_pRight);	else		;}//方法1：int TreeDepth(BTree* pRoot){	if (pRoot == NULL)		return 0;	int nLeftDepth = TreeDepth(pRoot->m_pLeft);	int nRightDepth = TreeDepth(pRoot->m_pRight);	return (nLeftDepth > nRightDepth)? (nLeftDepth+1):(nRightDepth+1);}bool IsBalanced(BTree* pRoot){	if (pRoot == NULL)		return true;	int nLeftDepth = TreeDepth(pRoot->m_pLeft);	int nRightDepth = TreeDepth(pRoot->m_pRight);	int diff = nRightDepth - nLeftDepth;	if (diff > 1 || diff < -1)		return false;	return IsBalanced(pRoot->m_pLeft)&&IsBalanced(pRoot->m_pRight);	}/*上面的方法：在求该节点的左右子树的深度的时候遍历一遍树，再次判断子树的平衡性的时候又要遍历一遍树结构，造成遍历多次！*/bool IsBalanced3(BTree* pRoot, int& depth){	if(pRoot== NULL)	{		depth = 0;		return true;	}	int nLeftDepth;	bool bLeft= IsBalanced3(pRoot->m_pLeft, nLeftDepth);	int nRightDepth;	bool bRight = IsBalanced3(pRoot->m_pRight, nRightDepth);		if (bLeft && bRight && abs(nLeftDepth - nRightDepth) <=1)	{		depth = 1+(nLeftDepth > nRightDepth ? nLeftDepth : nRightDepth);		return true;		}	else	{		return false;	}}bool IsBalanced3(BTree* pRoot){	int depth = 0;	return IsBalanced3(pRoot, depth);}/*求二叉树的镜像：方法1： 前序遍历每个节点，如果遍历到的节点有子节点，就交换它的两个子节点。（先交换左子树和右子树，再对左子树和右子树进行镜像操作）方法2： 如果二叉树不为空，求左子树和右子树的镜像，然后再交换左子树和右子树*/void Mirror(BTree* &pRoot){	if(pRoot == NULL)		return;	if(pRoot->m_pLeft ==NULL && pRoot->m_pRight == NULL)		return;	BTree* pTemp = pRoot->m_pLeft;	pRoot->m_pLeft = pRoot->m_pRight;	pRoot->m_pRight = pTemp;	if(pRoot->m_pLeft)		Mirror(pRoot->m_pLeft);	if(pRoot->m_pRight)		Mirror(pRoot->m_pRight);}BTree* Mirror2(BTree* pRoot){	if(pRoot == NULL)		return NULL;	BTree*  pLeft = Mirror2(pRoot->m_pLeft);	BTree*  pRight = Mirror2(pRoot->m_pRight);	pRoot->m_pLeft = pRight;	pRoot->m_pRight = pLeft;	return pRoot;}void PrintPrev(BTree* pRoot){	if(pRoot == NULL)		return;	cout<<pRoot->m_nValue<<" ";	PrintPrev(pRoot->m_pLeft);	PrintPrev(pRoot->m_pRight);}int _tmain(int argc, _TCHAR* argv[]){	BTree* m_pRoot = new BTree(9);	Insert(3,m_pRoot);	Insert(6,m_pRoot);	Insert(1,m_pRoot);	Insert(2,m_pRoot);	Insert(5,m_pRoot);	Insert(8,m_pRoot);	Insert(7,m_pRoot);	Insert(10,m_pRoot);	cout<<IsBalanced(m_pRoot)<<endl;	cout<<"原来的树:"<<endl;	PrintPrev(m_pRoot);	cout<<endl<<"镜像的树:"<<endl;	Mirror(m_pRoot);	//Mirror2(m_pRoot);	PrintPrev(m_pRoot);  	/*	BTree* m_pRoot2 = new BTree(96);	Insert(3,m_pRoot2);	Insert(6,m_pRoot2);	Insert(1,m_pRoot2);	Insert(2,m_pRoot2);	Insert(5,m_pRoot2);	Insert(8,m_pRoot2);	Insert(7,m_pRoot2);	Insert(10,m_pRoot2);	int depth;	cout<<endl<<IsBalanced3(m_pRoot2)<<endl;	*/	getchar();	return 0;}

C++算法之 判断是否为平衡二叉树 求二叉树的镜像