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.
 * class TreeNode {
 *     val: number
 *     left: TreeNode | null
 *     right: TreeNode | null
 *     constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
 *         this.val = (val===undefined ? 0 : val)
 *         this.left = (left===undefined ? null : left)
 *         this.right = (right===undefined ? null : right)
 *     }
 * }
 */

function maxPathSum(root: TreeNode | null): number {
    let ans = -1001;
    const dfs = (root: TreeNode | null): number => {
        if (!root) {
            return 0;
        }
        const left = Math.max(0, dfs(root.left));
        const right = Math.max(0, dfs(root.right));
        ans = Math.max(ans, left + right + root.val);
        return Math.max(left, right) + root.val;
    };
    dfs(root);
    return ans;
}
