# 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

## Solution

/**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode(int x) { val = x; }
* }
*/
class Solution {
int maxSum = Integer.MIN_VALUE;
public int maxPathSum(TreeNode root) {
if (root == null) return 0;
helper(root);
return maxSum;
}
int helper(TreeNode root) {
if (root == null) return 0;
int leftPath = Math.max(helper(root.left), 0);
int rightPath = Math.max(helper(root.right), 0);
maxSum = Math.max(maxSum, root.val + leftPath + rightPath);
return root.val + Math.max(leftPath, rightPath);
}
}