# Binary Tree Maximum Path Sum

[124. Binary Tree Maximum Path Sum]

Given a 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.

For example:
Given the below binary tree,

``````
1
/ \
2   3
``````

Return 6.

``````/**
* Definition for a binary tree node.
* public class TreeNode {
*     int val;
*     TreeNode left;
*     TreeNode right;
*     TreeNode(int x) { val = x; }
* }
*/
public class Solution {
int max = Integer.MIN_VALUE;

public int maxPathSum(TreeNode root) {
helper(root);

return max;
}

int helper(TreeNode root) {
if (root == null) {
return 0;
}

int leftSum = Math.max(helper(root.left), 0);
int rightSum = Math.max(helper(root.right), 0);

max = Math.max(max, root.val + leftSum + rightSum);

return root.val + Math.max(leftSum, rightSum);
}
}
``````

Hope this helps,
Michael 