Is Smallest Subtree with all the Deepest Nodes easy or hard?

Smallest Subtree with all the Deepest Nodes is considered a Medium difficulty problem. The challenge comes from recognizing that the answer is the lowest common ancestor of the deepest nodes and implementing that logic efficiently with DFS.

Smallest Subtree with all the Deepest Nodes Python/Java solution

Python, Java, and C++ implementations usually use recursive DFS. Each function call returns the deepest depth and the node representing the smallest subtree. The logic remains the same across languages with only syntax differences.

How to solve Smallest Subtree with all the Deepest Nodes in O(n)?

Perform a DFS that returns a pair: the depth of the deepest node in the subtree and the subtree root containing those nodes. If left and right depths are equal, return the current node. If one side is deeper, propagate that subtree upward. Since every node is processed once, the total runtime is O(n).

What is the best approach for Smallest Subtree with all the Deepest Nodes?

The best approach is a bottom-up Depth First Search that returns both subtree depth and the candidate node. During recursion, compare the depths of the left and right subtrees. If both depths are equal, the current node becomes the smallest subtree containing all deepest nodes. This solution runs in O(n) time and uses O(h) recursion stack space.

Is Smallest Subtree with all the Deepest Nodes asked at Google/Amazon/Meta?

Tree recursion and Lowest Common Ancestor style problems appear frequently in interviews at companies like Google, Amazon, and Meta. Variations of this problem test understanding of DFS traversal, subtree depth calculations, and LCA concepts in binary trees.

What data structure is used in Smallest Subtree with all the Deepest Nodes?

The problem uses a binary tree as the primary data structure. The solution typically applies Depth First Search recursion and Lowest Common Ancestor logic to determine the subtree containing all deepest nodes.

What is the time complexity of Smallest Subtree with all the Deepest Nodes?

The optimal solution runs in O(n) time where n is the number of nodes in the binary tree. Each node is visited exactly once during the DFS traversal. The space complexity is O(h), where h is the height of the tree due to the recursion stack.

Description Solution Video 42:25

865. Smallest Subtree with all the Deepest Nodes

Medium77.5% acceptance4 companies

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/

Asked at 4 companies

Topics

42:25

Still stuck?Read 3 approaches, or watch a walkthrough.

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LanguageLoading editor…

1# Definition for a binary tree node.
2# class TreeNode:
3#     def __init__(self, val=0, left=None, right=None):
4#         self.val = val
5#         self.left = left
6#         self.right = right
7class Solution:
8    def subtreeWithAllDeepest(self, root: Optional[TreeNode]) -> Optional[TreeNode]:
9        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2Case 3

Input

[3,5,1,6,2,0,8,null,null,7,4]

Input

[1]

Input

[0,1,3,null,2]

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