Binary Tree Maximum Path Sum

Given a non-empty binary tree, find the maximum path sum.

For this problem, a path is defined as any sequence of nodes from some starting node to any node in the tree along the parent-child connections. The path must contain at least one node and does not need to go through the root.

Example 1:

Input: [1,2,3]

       1
      / \
     2   3

Output: 6

Example 2:

Input: [-10,9,20,null,null,15,7]

   -10
   / \
  9  20
    /  \
   15   7

Output: 42

---

/**
* Definition for a binary tree node.
* struct TreeNode {
* int val;
* TreeNode *left;
* TreeNode *right;
* TreeNode(int x) : val(x), left(NULL), right(NULL) {}
* };
*/
class Solution {
public:
int maxPathSum(TreeNode* root) {
int sum=INT_MIN;
help(root,sum);
return sum;
}
int help(TreeNode* root,int &sum)
{
if(root==NULL)
return 0;
int left=max(help(root->left,sum),0);
int right=max(help(root->right,sum),0);
if((left+right+root->val)>sum)
sum=left+right+root->val;
return max(left,right)+root->val;
}
};