每天学习一算法系列（11） (求二叉树中节点的最大距离)

题目：求二叉树中节点的最大距离.
如果我们把二叉树看成一个图，父子节点之间的连线看成是双向的，我们姑且定义"距离"为两节点之间边的个数。
写一个程序，求一棵二叉树中相距最远的两个节点之间的距离。

 

题目来源于：http://topic.csdn.net/u/20101011/16/2befbfd9-f3e4-41c5-bb31-814e9615832e.html

 

思路一：

题目要求一颗二叉树中两个节点之间的最大距离，由于父子节点之间边是双向的，所以这道题转换为求左子树的最大深度 + 右子树的最大深度就是二叉树中节点的最大距离。

例如：以下一颗树：

          5

         / /

        4  8

           / /

          7  12

             /

           10

那么它的最大距离为4，即：4-->5-->8-->12-->10.其中"-->"的个数就是最大的距离数4.

 

代码如下：

/*--------------------------------求二叉树的最大距离算法.Copyright by yuucyf. 2011.05.06----------------------------------*/#include "stdafx.h"#include <assert.h>#include <iostream>using namespace std;typedef struct tagBSTNode{int nValue;tagBSTNode *psLeft;tagBSTNode *psRight;tagBSTNode(){nValue = 0;psLeft = psRight = NULL;}}S_BSTNode;voidDeleteAllNode(S_BSTNode* pRoot){if (NULL == pRoot)return;DeleteAllNode(pRoot->psLeft);DeleteAllNode(pRoot->psRight);delete pRoot;}voidAddBSTreeNode(S_BSTNode* &pRoot, int nValue){if (NULL == pRoot){pRoot = new S_BSTNode;assert(NULL != pRoot);pRoot->nValue = nValue;return;}if (pRoot->nValue > nValue){AddBSTreeNode(pRoot->psLeft, nValue);}else if ( pRoot->nValue < nValue){AddBSTreeNode(pRoot->psRight, nValue);}}int GetMaxDepth(const S_BSTNode* pRoot){if (NULL == pRoot)return 0;if (NULL == pRoot->psLeft && NULL == pRoot->psRight){return 0;}int nLeftDepth = 0, nRightDepth = 0;if (NULL != pRoot->psLeft){nLeftDepth = GetMaxDepth(pRoot->psLeft) + 1;}if (NULL != pRoot->psRight){nRightDepth = GetMaxDepth(pRoot->psRight) + 1;}if (nRightDepth >= nLeftDepth){return nRightDepth;}else{return nLeftDepth;}}int GetMaxDistance(const S_BSTNode* pRoot){if (NULL == pRoot)return 0;int nLeftDepth = GetMaxDepth(pRoot->psLeft);nLeftDepth += ((pRoot->psLeft != NULL) ? 1 : 0);int nRightDepth =GetMaxDepth(pRoot->psRight);nRightDepth += ((pRoot->psRight != NULL) ? 1 : 0);return nLeftDepth + nRightDepth;}int _tmain(int argc, _TCHAR* argv[]){S_BSTNode *pRoot = NULL;AddBSTreeNode(pRoot, 5);AddBSTreeNode(pRoot, 4);AddBSTreeNode(pRoot, 8);AddBSTreeNode(pRoot, 7);AddBSTreeNode(pRoot, 12);AddBSTreeNode(pRoot, 10);int nMaxDis = GetMaxDistance(pRoot);cout << "Max distance is " << nMaxDis << endl;DeleteAllNode(pRoot);return 0;}

 

 

思路二：

其实想法跟思路一是类似的，具体实现看以下代码，不过你会发现下面的实现没有比思路一中的实现更为容易理解。

 

代码如下：

/*----------------------------------代码来源于书上.Modified by yuucyf. 2011.05.06-----------------------------------*/// 数据结构定义typedef struct NODE{NODE* psLeft; // 左子树NODE* psRight; // 右子树int nMaxLeft; // 左子树中的最长距离int nMaxRight; // 右子树中的最长距离int nValue; // 该节点的值NODE(){nValue = nMaxLeft = nMaxRight = 0;psLeft = psRight = NULL;}}S_BSTNode;voidAddBSTreeNode(S_BSTNode* &pRoot, int nValue){if (NULL == pRoot){pRoot = new S_BSTNode;assert(NULL != pRoot);pRoot->nValue = nValue;return;}if (pRoot->nValue > nValue){AddBSTreeNode(pRoot->psLeft, nValue);}else if ( pRoot->nValue < nValue){AddBSTreeNode(pRoot->psRight, nValue);}}voidDeleteAllNode(S_BSTNode* pRoot){if (NULL == pRoot)return;DeleteAllNode(pRoot->psLeft);DeleteAllNode(pRoot->psRight);delete pRoot;}int g_nMaxLen = 0;// 寻找树中最长的两段距离void FindMaxLen(NODE* pRoot){// 遍历到叶子节点，返回if(NULL == pRoot){return;}// 如果左子树为空，那么该节点的左边最长距离为0if(NULL == pRoot->psLeft){pRoot->nMaxLeft = 0;}// 如果右子树为空，那么该节点的右边最长距离为0if(NULL == pRoot->psRight){pRoot->nMaxRight = 0;}// 如果左子树不为空，递归寻找左子树最长距离if(pRoot->psLeft != NULL){FindMaxLen(pRoot->psLeft);}// 如果右子树不为空，递归寻找右子树最长距离if(pRoot->psRight != NULL){FindMaxLen(pRoot->psRight);}// 计算左子树最长节点距离if(pRoot->psLeft != NULL){int nTempMax = 0;if(pRoot->psLeft->nMaxLeft > pRoot->psLeft->nMaxRight){nTempMax = pRoot->psLeft->nMaxLeft;}else{nTempMax = pRoot->psLeft->nMaxRight;}pRoot->nMaxLeft = nTempMax + 1;}// 计算右子树最长节点距离if(pRoot->psRight != NULL){int nTempMax = 0;if(pRoot->psRight->nMaxLeft > pRoot->psRight->nMaxRight){nTempMax = pRoot->psRight->nMaxLeft;}else{nTempMax = pRoot->psRight->nMaxRight;}pRoot->nMaxRight = nTempMax + 1;}// 更新最长距离if((pRoot->nMaxLeft + pRoot->nMaxRight) > g_nMaxLen){g_nMaxLen = pRoot->nMaxLeft + pRoot->nMaxRight;}}int _tmain(int argc, _TCHAR* argv[]){S_BSTNode *pRoot = NULL;AddBSTreeNode(pRoot, 5);AddBSTreeNode(pRoot, 4);AddBSTreeNode(pRoot, 8);AddBSTreeNode(pRoot, 7);AddBSTreeNode(pRoot, 12);AddBSTreeNode(pRoot, 10);FindMaxLen(pRoot);cout << "Max distance is " << g_nMaxLen << endl;DeleteAllNode(pRoot);return 0;}