How do you solve Maximum Depth of N-ary Tree on LeetCode?

Maximum Depth of N-ary Tree (LeetCode #559) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Understanding tree traversal is crucial for depth calculations.

What is the brute force solution for Maximum Depth of N-ary Tree?

The brute force approach for Maximum Depth of N-ary Tree is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves traversing the entire tree and calculating the depth by counting the levels. This method is straightforward but inefficient, as it may require multiple passes through the tree. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Maximum Depth of N-ary Tree?

Maximum Depth of N-ary Tree uses the following concepts: Tree, Depth-First Search, Breadth-First Search. The recommended patterns to study are: Depth-First Search, Recursion.

What are the interview tips for Maximum Depth of N-ary Tree?

Explain your thought process before coding. Consider edge cases like empty trees. Use recursion wisely to simplify your code.

What are common mistakes when solving Maximum Depth of N-ary Tree?

Not handling the case when the tree is empty (null root). Forgetting to add 1 for the current node when calculating depth.

#559

Maximum Depth of N-ary Tree

Easy

TreeDepth-First SearchBreadth-First SearchDepth-First SearchRecursion

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

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Intuition

Time O(n)Space O(n)

The optimal solution uses Depth-First Search (DFS) to traverse the tree in a single pass, calculating the depth as we go. This is efficient because we only visit each node once.

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Algorithm

4 steps

1Step 1: If the root is null, return 0.
2Step 2: Initialize a variable to keep track of the maximum depth.
3Step 3: For each child of the root, recursively calculate the depth and update the maximum depth.
4Step 4: Return the maximum depth found plus one for the current node.

solution.py10 lines

1class Node:
2    def __init__(self, val=None, children=None):
3        self.val = val
4        self.children = children if children is not None else []
5
6class Solution:
7    def maxDepth(self, root: Node) -> int:
8        if not root:
9            return 0
10        return 1 + max((self.maxDepth(child) for child in root.children), default=0)

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Complexity note: The time complexity is O(n) because we visit each node exactly once. The space complexity is O(n) due to the recursion stack in the worst case (for a completely unbalanced tree).

1Understanding tree traversal is crucial for depth calculations.
2Recursion can simplify the implementation of depth calculations.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.