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【二叉树的递归】05二叉树中找任意起点和终点使他们的路径和最大【Binary Tree Maximum Path Sum】

2014-04-08 17:01 507 查看

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++给定一个二叉树，寻找值最大的路径。这个路径可以从这个树上面的任意一个节点开始，然后在任意一个节点结束。例如：给定下面的二叉树，

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/\
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.++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++Givenabinarytree,findthemaximumpathsum.Thepathmaystartandendatanynodeinthetree.Forexample:
Giventhebelowbinarytree,

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/\
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Return

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

test.cpp:

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#include<iostream>
#include<cstdio>
#include<stack>
#include<vector>
#include"BinaryTree.h"usingnamespacestd;/**
*Definitionforbinarytree
*structTreeNode{
*intval;
*TreeNode*left;
*TreeNode*right;
*TreeNode(intx):val(x),left(NULL),right(NULL){}
*};
*/
intmax_sum;
intdfs(constTreeNode*root)
{
if(root==NULL)
{
return0;
}
intl=dfs(root->left);
intr=dfs(root->right);
intsum=root->val;
if(l>0)
{
sum+=l;
}
if(r>0)
{
sum+=r;
}
max_sum=max(max_sum,sum);
returnmax(r,l)>0?max(r,l)+root->val:root->val;
}
intmaxPathSum(TreeNode*root)
{max_sum=-0xffff;
dfs(root);
returnmax_sum;
}//树中结点含有分叉，
//8
///\
//61
///\
//92
///\
//47
intmain()
{
TreeNode*pNodeA1=CreateBinaryTreeNode(8);
TreeNode*pNodeA2=CreateBinaryTreeNode(6);
TreeNode*pNodeA3=CreateBinaryTreeNode(1);
TreeNode*pNodeA4=CreateBinaryTreeNode(9);
TreeNode*pNodeA5=CreateBinaryTreeNode(2);
TreeNode*pNodeA6=CreateBinaryTreeNode(4);
TreeNode*pNodeA7=CreateBinaryTreeNode(7);ConnectTreeNodes(pNodeA1,pNodeA2,pNodeA3);
ConnectTreeNodes(pNodeA2,pNodeA4,pNodeA5);
ConnectTreeNodes(pNodeA5,pNodeA6,pNodeA7);PrintTree(pNodeA1);cout<<maxPathSum(pNodeA1)<<endl;DestroyTree(pNodeA1);
return0;
}

结果输出：

BinaryTree.h:

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#ifndef_BINARY_TREE_H_
#define_BINARY_TREE_H_structTreeNode
{
intval;
TreeNode*left;
TreeNode*right;
TreeNode(intx):val(x),left(NULL),right(NULL){}
};TreeNode*CreateBinaryTreeNode(intvalue);
voidConnectTreeNodes(TreeNode*pParent,
TreeNode*pLeft,TreeNode*pRight);
voidPrintTreeNode(TreeNode*pNode);
voidPrintTree(TreeNode*pRoot);
voidDestroyTree(TreeNode*pRoot);#endif/*_BINARY_TREE_H_*/

BinaryTree.cpp:

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#include<iostream>
#include<cstdio>
#include"BinaryTree.h"usingnamespacestd;/**
*Definitionforbinarytree
*structTreeNode{
*intval;
*TreeNode*left;
*TreeNode*right;
*TreeNode(intx):val(x),left(NULL),right(NULL){}
*};
*///创建结点
TreeNode*CreateBinaryTreeNode(intvalue)
{
TreeNode*pNode=newTreeNode(value);returnpNode;
}//连接结点
voidConnectTreeNodes(TreeNode*pParent,TreeNode*pLeft,TreeNode*pRight)
{
if(pParent!=NULL)
{
pParent->left=pLeft;
pParent->right=pRight;
}
}//打印节点内容以及左右子结点内容
voidPrintTreeNode(TreeNode*pNode)
{
if(pNode!=NULL)
{
printf("valueofthisnodeis:%d\n",pNode->val);if(pNode->left!=NULL)
printf("valueofitsleftchildis:%d.\n",pNode->left->val);
else
printf("leftchildisnull.\n");if(pNode->right!=NULL)
printf("valueofitsrightchildis:%d.\n",pNode->right->val);
else
printf("rightchildisnull.\n");
}
else
{
printf("thisnodeisnull.\n");
}printf("\n");
}//前序遍历递归方法打印结点内容
voidPrintTree(TreeNode*pRoot)
{
PrintTreeNode(pRoot);if(pRoot!=NULL)
{
if(pRoot->left!=NULL)
PrintTree(pRoot->left);if(pRoot->right!=NULL)
PrintTree(pRoot->right);
}
}voidDestroyTree(TreeNode*pRoot)
{
if(pRoot!=NULL)
{
TreeNode*pLeft=pRoot->left;
TreeNode*pRight=pRoot->right;deletepRoot;
pRoot=NULL;DestroyTree(pLeft);
DestroyTree(pRight);
}
}

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