Google·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

Jun 2026

Summary

Google ML engineer interview with a coding question that looked trivial but had a specific efficiency angle worth thinking through carefully.

Questions Asked (1)

Given a list of natural numbers, sort both the numbers and their squares as efficiently as possible.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was to just square everything and sort the whole thing, which is fine but misses the point.

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AI HintsAI Generated

Suggested Approach

First, clarify the problem: you need to sort the original list and also sort the list of their squares. The most efficient approach is to sort the original list in O(n log n) time, then generate the squares in sorted order by leveraging the fact that the squares of a sorted list of natural numbers are not necessarily sorted, but can be sorted in O(n) time using a two-pointer technique from both ends of the sorted list. This yields overall O(n log n) time and O(n) space, which is optimal for comparison-based sorting.

Pro tip: Mention that if the input is already sorted or if we can use counting sort due to bounded values, we could achieve O(n) time, but for general natural numbers, O(n log n) is optimal. Also, emphasize that you would discuss trade-offs between time and space, and consider whether the squares need to be stored separately or can be produced on the fly.

1. Clarify requirements and constraints

Ask whether the input list can contain duplicates, whether it's already sorted, and what the expected output format is (two separate sorted lists or one combined). Also, confirm the definition of 'natural numbers' (including zero or not).

2. Sort the original list

Use an efficient comparison-based sort like Timsort (Python's sorted) or quicksort/mergesort, achieving O(n log n) time. This is optimal for arbitrary natural numbers.

3. Generate squares in sorted order

Since the original list is sorted, the squares are not necessarily sorted, but the largest squares come from either the smallest or largest original numbers. Use two pointers (left at start, right at end) to compare absolute values and fill the squares array from the end to the beginning in O(n) time.

4. Analyze complexity and trade-offs

State that the overall time complexity is O(n log n) due to sorting, and space is O(n) for the output. Discuss that if the input is already sorted, the squares can be sorted in O(n) time, and if values are bounded, counting sort could achieve O(n) overall.

5. Consider edge cases and optimizations

Handle empty list, single element, duplicates, and zero. Mention that if the squares need to be sorted in-place or if memory is constrained, alternative approaches might be needed, but the two-pointer method is optimal for time.

Key Points to Mention

Time complexity: O(n log n) for sorting the original list, O(n) for sorting squares using two pointers, overall O(n log n).
Space complexity: O(n) for storing the sorted squares (or O(1) extra if done in-place, but typically O(n)).
Two-pointer technique: compare absolute values from both ends of the sorted list to place squares in descending order.
Trade-offs: if input is already sorted, squares can be sorted in O(n); if values are bounded, counting sort can achieve O(n) overall.
Edge cases: empty list, negative numbers (if allowed), duplicates, and zero.
Stability and in-place considerations: whether the original list can be modified, and if the squares need to be a separate list.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.