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

class Solution {
public:
    int maxPathSum(TreeNode* root) {    // root != nulllptr
        return maxPathSumHelper(root).first;
    }
private:
    pair<int, int> maxPathSumHelper(TreeNode *root) {
        if (!root) return {INT_MIN, 0};
        
        auto left = maxPathSumHelper(root->left);
        auto right = maxPathSumHelper(root->right);
        left.second = max(left.second, 0);
        right.second = max(right.second, 0);
        
        return {max(max(left.first, right.first),  left.second + right.second + root->val),
                max(left.second, right.second) + root->val};
    }
};