【hard】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

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
private:
    int solution(TreeNode* root, int& best){  // my own solution
        if (!root) return 0;
        int left_sum = root->val + solution(root->left, best);
        int right_sum = root->val + solution(root->right, best);
        int curve_sum = left_sum + right_sum - root->val;
        best = max({best, left_sum, right_sum, curve_sum, root->val});
        
        return max({left_sum, right_sum, root -> val});
    }
    
public:
    int maxPathSum(TreeNode* root) {  // it is the original function
        int best = INT_MIN;
        int eval = solution(root, best);
        return max(best, eval);
    }
    
};