Leetcode #559: Maximum Depth of N-ary Tree
In this guide, we solve Leetcode #559 Maximum Depth of N-ary Tree in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
Given a n-ary tree, find its maximum depth. The maximum depth is the number of nodes along the longest path from the root node down to the farthest leaf node.
Quick Facts
- Difficulty: Easy
- Premium: No
- Tags: Tree, Depth-First Search, Breadth-First Search
Intuition
We need to explore a structure deeply before backing up, which suits DFS.
DFS keeps local context on the call stack and is easy to implement recursively.
Approach
Define a recursive DFS that carries the necessary state.
Combine child results as the recursion unwinds.
Steps:
- Define a recursive DFS with state.
- Visit children and combine results.
- Return the final aggregation.
Example
Input: root = [1,null,3,2,4,null,5,6]
Output: 3
Python Solution
"""
# Definition for a Node.
class Node:
def __init__(self, val: Optional[int] = None, children: Optional[List['Node']] = None):
self.val = val
self.children = children
"""
class Solution:
def maxDepth(self, root: "Node") -> int:
if root is None:
return 0
mx = 0
for child in root.children:
mx = max(mx, self.maxDepth(child))
return 1 + mx
Complexity
The time complexity is , and the space complexity is , where is the number of nodes. The space complexity is , where is the number of nodes.
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.