> For the complete documentation index, see [llms.txt](https://aaronice.gitbook.io/lintcode/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://aaronice.gitbook.io/lintcode/trees/binary-tree-maximum-path-sum.md).

# 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

```java
/**
 * 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);
    }
}
```


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