标签：
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;
}
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原文地址：http://blog.csdn.net/djb100316878/article/details/42496843
