text: /*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:
  
  
  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:
  
  
  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.*/
  
  
  class Solution {
  public:
      int maxPathSum(TreeNode* root) {
          int max_sum = INT_MIN;
          maxPathSum(root, max_sum);
          return max_sum;
      }
      
      int maxPathSum(TreeNode* root, int& max_sum) {
          if (!root) return 0;
          int left_sum = max(maxPathSum(root->left, max_sum), 0);
          int right_sum = max(maxPathSum(root->right, max_sum), 0);
          max_sum = max(max_sum, left_sum + right_sum + root->val);
          return max(left_sum, right_sum) + root->val;
      }
  };
  
  