Smallest Subtree with all the Deepest Nodes

lcpy gen -n 865   # by problem number
lcpy gen -s smallest_subtree_with_all_the_deepest_nodes   # by problem name

Input: root = [3,5,1,6,2,0,8,null,null,7,4]
Output: [2,7,4]
Explanation: 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.

Input: root = [1]
Output: [1]
Explanation: The root is the deepest node in the tree.

Input: root = [0,1,3,null,2]
Output: [2]
Explanation: 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.

from leetcode_py import TreeNode


class Solution:
    # Time: O(n) single DFS over all nodes
    # Space: O(h) recursion stack, h = tree height
    def subtree_with_all_deepest(self, root: TreeNode[int] | None) -> TreeNode[int] | None:
        if root is None:
            return None

        def dfs(node: TreeNode[int]) -> tuple[int, TreeNode[int]]:
            left = dfs(node.left) if node.left else (0, node)
            right = dfs(node.right) if node.right else (0, node)
            if left[0] > right[0]:
                return left[0] + 1, left[1]
            if left[0] < right[0]:
                return right[0] + 1, right[1]
            return left[0] + 1, node

        return dfs(root)[1]