LeetCode 637: Average of Levels in Binary Tree — Python Solution

Solve LeetCode 637: Average of Levels in Binary Tree in Python with a level aggregation 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

For each BFS level, sum exactly its current queue length and divide by that length.

Algorithm

1. For each BFS level, sum exactly its current queue length and divide by that length.
2. Maintain this invariant: Before moving to the next level, every node from the current level contributes once to its sum.
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 averageOfLevels(self, root):
        queue, answer = deque([root]), []
        while queue:
            level_size = len(queue)
            total = 0
            for _ in range(level_size):
                node = queue.popleft(); total += node.val
                if node.left: queue.append(node.left)
                if node.right: queue.append(node.right)
            answer.append(total / level_size)
        return answer

Why this is correct

The proof follows the maintained state: Before moving to the next level, every node from the current level contributes once to its sum. 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(w) space. The stated auxiliary space excludes the returned output unless the output is the data structure being built.

Edge cases

Use numeric division; values may be negative.

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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