Binary Tree Maximum Path Sum
<p>A <strong>path</strong> 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 <strong>at most once</strong>. Note that the path does not need to pass through the root.</p>

<p>The <strong>path sum</strong> of a path is the sum of the node&#39;s values in the path.</p>

<p>Given the <code>root</code> of a binary tree, return <em>the maximum <strong>path sum</strong> of any <strong>non-empty</strong> path</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0100-0199/0124.Binary%20Tree%20Maximum%20Path%20Sum/images/exx1.jpg" style="width: 322px; height: 182px;" />
<pre>
<strong>Input:</strong> root = [1,2,3]
<strong>Output:</strong> 6
<strong>Explanation:</strong> The optimal path is 2 -&gt; 1 -&gt; 3 with a path sum of 2 + 1 + 3 = 6.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0100-0199/0124.Binary%20Tree%20Maximum%20Path%20Sum/images/exx2.jpg" />
<pre>
<strong>Input:</strong> root = [-10,9,20,null,null,15,7]
<strong>Output:</strong> 42
<strong>Explanation:</strong> The optimal path is 15 -&gt; 20 -&gt; 7 with a path sum of 15 + 20 + 7 = 42.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 3 * 10<sup>4</sup>]</code>.</li>
	<li><code>-1000 &lt;= Node.val &lt;= 1000</code></li>
</ul>
Tree; Depth-First Search; Dynamic Programming; Binary Tree
// Definition for a binary tree node.
// #[derive(Debug, PartialEq, Eq)]
// pub struct TreeNode {
//   pub val: i32,
//   pub left: Option<Rc<RefCell<TreeNode>>>,
//   pub right: Option<Rc<RefCell<TreeNode>>>,
// }
//
// impl TreeNode {
//   #[inline]
//   pub fn new(val: i32) -> Self {
//     TreeNode {
//       val,
//       left: None,
//       right: None
//     }
//   }
// }
use std::cell::RefCell;
use std::rc::Rc;
impl Solution {
    fn dfs(root: &Option<Rc<RefCell<TreeNode>>>, res: &mut i32) -> i32 {
        if root.is_none() {
            return 0;
        }
        let node = root.as_ref().unwrap().borrow();
        let left = (0).max(Self::dfs(&node.left, res));
        let right = (0).max(Self::dfs(&node.right, res));
        *res = (node.val + left + right).max(*res);
        node.val + left.max(right)
    }

    pub fn max_path_sum(root: Option<Rc<RefCell<TreeNode>>>) -> i32 {
        let mut res = -1000;
        Self::dfs(&root, &mut res);
        res
    }
}
