Introduction

In this blog post, we will explore how to solve the LeetCode problem "865" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

Given the root of a binary tree, the depth of each node is the shortest distance to the root. Return the smallest subtree such that it contains all the deepest nodes in the original tree. A node is called the deepest if it has the largest depth possible among any node in the entire tree. The subtree of a node is a tree consisting of that node, plus the set of all descendants of that node. Example 1: 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. Example 2: Input: root = [1] Output: [1] Explanation: The root is the deepest node in the tree. Example 3: 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. Constraints: The number of nodes in the tree will be in the range [1, 500]. 0 <= Node.val <= 500 The values of the nodes in the tree are unique. Note: This question is the same as 1123: https://leetcode.com/problems/lowest-common-ancestor-of-deepest-leaves/

Explanation

Here's the solution to find the smallest subtree containing all the deepest nodes in a binary tree:

• Find the Maximum Depth: Traverse the tree to determine the maximum depth of any node.
• Identify Deepest Nodes and LCA: Use a recursive function that returns both the depth of a node and the smallest subtree containing all deepest nodes. If a node's left and right subtrees both contain deepest nodes, then that node is the smallest subtree. If only one subtree contains deepest nodes, that subtree is the answer. If a node is a deepest node, it is the answer.

• Return the Subtree: The recursive function propagates the smallest subtree containing all the deepest nodes up to the root.

• Time Complexity: O(N), where N is the number of nodes in the tree.

• Space Complexity: O(H), where H is the height of the tree (O(log N) for a balanced tree, O(N) in the worst case).

Code

    from typing import Optional

# Definition for a binary tree node.
class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

class Solution:
    def subtreeWithAllDeepest(self, root: Optional[TreeNode]) -> Optional[TreeNode]:
        """
        Finds the smallest subtree containing all the deepest nodes in a binary tree.

        Args:
            root: The root of the binary tree.

        Returns:
            The root of the smallest subtree containing all the deepest nodes.
        """

        def deepest_subtree(node):
            if not node:
                return None, 0

            left_subtree, left_depth = deepest_subtree(node.left)
            right_subtree, right_depth = deepest_subtree(node.right)

            if left_depth > right_depth:
                return left_subtree, left_depth + 1
            elif right_depth > left_depth:
                return right_subtree, right_depth + 1
            else:
                return node, left_depth + 1

        return deepest_subtree(root)[0]