#### Find the Maximum Path Sum in a Binary Tree

This problem asks you to find the maximum path sum in a binary tree. 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.

#### Problem

```Given a 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 input:
[1,2,3]
Output: 6
Explanation: The maximum sum path is [1,2,3].```

#### Solution

This solution is in C++. Our A.I. can create solutions in multiple languages.
```#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

struct TreeNode {
int val;
TreeNode *left;
TreeNode *right;
TreeNode(int x) : val(x), left(NULL), right(NULL) {}
};

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

int main() {
TreeNode* root = new TreeNode(1);
root->left = new TreeNode(2);
root->right = new TreeNode(3);
Solution solution;
cout << solution.maxPathSum(root) << endl;
return 0;
}```

A.I. Evaluation of the Solution

The candidate's solution correctly solves the problem. The approach is to recursively find the maximum path sum for each node in the tree. The path sum for each node is the node's value plus the maximum of the path sums for the node's left and right child nodes. The maximum path sum for the tree is the maximum of the path sums for all nodes in the tree.

Evaluated at: 2022-11-19 20:15:41