C++算法之 判断是否为平衡二叉树 求二叉树的镜像

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;
}