[LeetCode] Binary Tree Maximum Path Sum Solution-优快云博客

本文介绍如何解决寻找给定二叉树中最大路径和的问题。通过遍历每个节点，考虑四种可能的最大路径组合，最终返回最大的路径和。

Given a binary tree, find the maximum path sum.

The path may start and end at any node in the tree.

For example:
Given the below binary tree,

       1
      / 
     2   3

Return 6.

» Solve this problem

[Thoughts]
For each node like following, there should be four ways existing for max path:

1. Node only
2. L-sub + Node
3. R-sub + Node
4. L-sub + Node + R-sub

Keep trace the four path and pick up the max one in the end.

[Code]

1:    int maxPathSum(TreeNode *root) {  
2:      // Start typing your C/C++ solution below  
3:      // DO NOT write int main() function  
4:      int maxAcrossRoot=INT_MIN;  
5:      int maxEndByRoot = GetMax(root, maxAcrossRoot);  
6:      return std::max(maxAcrossRoot, maxEndByRoot);  
7:    }  
8:    int GetMax(TreeNode *node, int& maxAcrossRoot)  
9:    {  
10:      if(node == NULL) return 0;  
11:      int left = GetMax(node->left, maxAcrossRoot);  
12:      int right = GetMax(node->right, maxAcrossRoot);  
13:      int cMax = node->val;  
14:      if(left>0)  
15:        cMax+=left;  
16:      if(rifht>0)  
17:        cMax+=right;  
18:      maxAcrossRoot = std::max(maxAcrossRoot, cMax);  
19:      return std::max(  
20:        node->val,   
21:        std::max(node->val+left, node->val+right));  
22:    }