LeetCode 104: Maximum Depth of Binary Tree — Python Solution

Solve LeetCode 104: Maximum Depth of Binary Tree in Python with a recursive postorder approach. The key is to make the state invariant explicit, so the implementation and complexity follow naturally.

This guide paraphrases the task and does not reproduce LeetCode’s prompt. Use the official page for the complete statement, examples, constraints, and submission runner.

What the problem is testing

The depth of a node is one plus the larger depth of its children, with an empty subtree contributing zero.

Algorithm

1. The depth of a node is one plus the larger depth of its children, with an empty subtree contributing zero.
2. Maintain this invariant: Each return value is the exact maximum root-to-leaf node count for that subtree.
3. Continue until every input item or reachable state has been resolved, then return the accumulated result.

Python solution

LeetCode provides the list, tree, or graph node definition used by the method.

from collections import Counter, defaultdict, deque, OrderedDict
import random

class Solution:
    def maxDepth(self, root):
        if not root:
            return 0
        return 1 + max(self.maxDepth(root.left), self.maxDepth(root.right))

Why this is correct

The proof follows the maintained state: Each return value is the exact maximum root-to-leaf node count for that subtree. Each iteration preserves that claim while permanently resolving at least one position, node, interval, or search state. When the loop or recursion ends, every candidate required by the problem has therefore been included or ruled out, so the returned value is correct.

Complexity

O(n) time and O(h) recursion space. The stated auxiliary space excludes the returned output unless the output is the data structure being built.

Edge cases

An empty tree has depth zero; a skewed tree uses linear recursion depth.

Tested reference code

This implementation is included in the site’s downloadable 100-solution Python library. The complete suite compiles every solution and runs a behavioral assertion for every problem before publication.

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