124. 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

int helper(TreeNode* node, int& res) { // time: O(n); space: O(n)
    if (!node) return 0;
    int left = max(0, helper(node->left, res));
    int right = max(0, helper(node->right, res));
    res = max(res, left + node->val + right);
    return max(left, right) + node->val;
}
int maxPathSum(TreeNode* root) {
    int res = numeric_limits<int>::min();
    helper(root, res);
    return res;
}