# 0124. Binary Tree Maximum Path Sum

<https://leetcode.com/problems/binary-tree-maximum-path-sum>

## Description

A **path** in a binary tree is a sequence of nodes where each pair of adjacent nodes in the sequence has an edge connecting them. A node can only appear in the sequence **at most once**. Note that the path does not need to pass through the root.

The **path sum** of a path is the sum of the node's values in the path.

Given the `root` of a binary tree, return *the maximum **path sum** of any path*.

**Example 1:**

![](https://assets.leetcode.com/uploads/2020/10/13/exx1.jpg)

```
**Input:** root = [1,2,3]
**Output:** 6
**Explanation:** The optimal path is 2 -> 1 -> 3 with a path sum of 2 + 1 + 3 = 6.
```

**Example 2:**

![](https://assets.leetcode.com/uploads/2020/10/13/exx2.jpg)

```
**Input:** root = [-10,9,20,null,null,15,7]
**Output:** 42
**Explanation:** The optimal path is 15 -> 20 -> 7 with a path sum of 15 + 20 + 7 = 42.
```

**Constraints:**

* The number of nodes in the tree is in the range `[1, 3 * 104]`.
* `-1000 <= Node.val <= 1000`

## ac

```java
/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    int max = Integer.MIN_VALUE;
    public int maxPathSum(TreeNode root) {
        helper(root);
        return max;
    }
    private int helper(TreeNode root) {
        if (root == null) return 0;

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

        if ((root.val + left + right) > max) max = root.val + left + right;

        int maxChild = Math.max(left, right);

        return root.val + maxChild;
    }
}
```