---
description: Tree
---

# LeetCode 124. Binary Tree Maximum Path Sum

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`

## Solution

```
class Solution {
    
    int dfs(TreeNode *root, int& result) {
        if (root == nullptr) {
            return 0;
        }

        int l = max(0, dfs(root->left, result));
        int r = max(0, dfs(root->right, result));
        result = max(result, l + r + root->val);

        return root->val + max(l, r);
    }
    
public:
    int maxPathSum(TreeNode *root) {
        int result = INT_MIN;
        dfs(root, result);
        return result;
    }
};
```
