Smallest Subtree with all the Deepest Nodes
<p>Given the <code>root</code> of a binary tree, the depth of each node is <strong>the shortest distance to the root</strong>.</p>

<p>Return <em>the smallest subtree</em> such that it contains <strong>all the deepest nodes</strong> in the original tree.</p>

<p>A node is called <strong>the deepest</strong> if it has the largest depth possible among any node in the entire tree.</p>

<p>The <strong>subtree</strong> of a node is a tree consisting of that node, plus the set of all descendants of that node.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0800-0899/0865.Smallest%20Subtree%20with%20all%20the%20Deepest%20Nodes/images/sketch1.png" style="width: 600px; height: 510px;" />
<pre>
<strong>Input:</strong> root = [3,5,1,6,2,0,8,null,null,7,4]
<strong>Output:</strong> [2,7,4]
<strong>Explanation:</strong> We return the node with value 2, colored in yellow in the diagram.
The nodes coloured in blue are the deepest nodes of the tree.
Notice that nodes 5, 3 and 2 contain the deepest nodes in the tree but node 2 is the smallest subtree among them, so we return it.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> root = [1]
<strong>Output:</strong> [1]
<strong>Explanation:</strong> The root is the deepest node in the tree.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> root = [0,1,3,null,2]
<strong>Output:</strong> [2]
<strong>Explanation:</strong> The deepest node in the tree is 2, the valid subtrees are the subtrees of nodes 2, 1 and 0 but the subtree of node 2 is the smallest.
</pre>

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

<ul>
	<li>The number of nodes in the tree will be in the range <code>[1, 500]</code>.</li>
	<li><code>0 &lt;= Node.val &lt;= 500</code></li>
	<li>The values of the nodes in the tree are <strong>unique</strong>.</li>
</ul>

<p>&nbsp;</p>
<p><strong>Note:</strong> This question is the same as 1123: <a href="https://leetcode.com/problems/lowest-common-ancestor-of-deepest-leaves/" target="_blank">https://leetcode.com/problems/lowest-common-ancestor-of-deepest-leaves/</a></p>
Tree; Depth-First Search; Breadth-First Search; Hash Table; 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 subtreeWithAllDeepest(root: TreeNode | null): TreeNode | null {
    const dfs = (root: TreeNode | null): [TreeNode, number] => {
        if (!root) {
            return [null, 0];
        }
        const [l, ld] = dfs(root.left);
        const [r, rd] = dfs(root.right);
        if (ld > rd) {
            return [l, ld + 1];
        }
        if (ld < rd) {
            return [r, rd + 1];
        }
        return [root, ld + 1];
    };
    return dfs(root)[0];
}
