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.

/**
 * Definition for binary tree
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
struct TreeNode
{
	int val;
	TreeNode *left;
	TreeNode *right;
	TreeNode(int x) : val(x), left(NULL), right(NULL) {}
};
class Solution {
public:
    int maxPathSum(TreeNode *root) {
		if(root == NULL) return 0;
		maxNode = root->val;
		dfs(root);
		return maxNode;
    }
private:
	int maxNode;
	int dfs(TreeNode *root)
	{
		if(root == NULL) return 0;
		int left = dfs(root->left);
		int right= dfs(root->right);
		int val = root->val;
		if(left > 0) val += left;
		if(right> 0) val += right;
		if(maxNode < val) maxNode = val;
		return std::max(std::max(left,right),0) + root->val;
	}
};