Binary Tree Maximum Path Sum.cpp

/*
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:
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.

Constraints:
The number of nodes in the tree is in the range [1, 3 * 104].
-1000 <= Node.val <= 1000
*/

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */

class Solution
{
public:
  vector<int> dfs(TreeNode *root, int &ans)
  {
    // {root, root + left, root + right}
    if (!root)
      return {0, 0, 0};

    auto left = dfs(root->left, ans);
    auto right = dfs(root->right, ans);

    int left_max = max({left[0], left[1], left[2]});
    int right_max = max({right[0], right[1], right[2]});

    // {root, root + left, root + right, root + left + right}
    ans = max({ans,
               root->val,
               left_max + root->val,
               right_max + root->val,
               root->val + left_max + right_max});

    return {root->val, left_max + root->val, right_max + root->val};
  }

  int maxPathSum(TreeNode *root)
  {
    int ans = INT_MIN;
    dfs(root, ans);
    return ans;
  }
};