# 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
```

```java
public class Solution {
    int max = Integer.MIN_VALUE;

    public int maxPathSum(TreeNode root) {
        helper(root);
        return max;
    }

    // helper returns the max branch
    // plus current node's value
    int helper(TreeNode root) {
        if (root == null)
            return 0;
        // Not considering negative sum in our total
        int left = Math.max(helper(root.left), 0);
        int right = Math.max(helper(root.right), 0);

        max = Math.max(max, root.val + left + right);

        return root.val + Math.max(left, right);
    }
}
```
