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Waymo·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
Jun 2026

Summary

Waymo coding interview for a software engineer role, one algorithmic problem that looks straightforward until you read the O(n) constraint and realize sorting is off the table. The bucket approach isn't something most people reach for instinctively so it's worth knowing cold before you walk in.

Questions Asked (1)

Q1

Given an unsorted array of integers, find the largest gap between any two adjacent elements once the array is sorted. Must run in linear time without using a comparison-based sort.

Algorithms & Data Structures
Author's notes

The problem reads like a basic sorting exercise until you hit the time complexity requirement.

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AI HintsAI Generated

Suggested Approach

Use a linear-time algorithm like radix sort or the pigeonhole principle (bucket sort) to sort or approximate the sorted order, then scan for the maximum adjacent difference. Emphasize that comparison-based sorts are O(n log n) and thus disallowed, so you must leverage integer properties or distribution.

Pro tip: Mention that the pigeonhole principle guarantees the maximum gap is at least (max-min)/(n-1), which justifies using n-1 buckets and ensures the answer lies between buckets, not within them. This shows deep understanding and avoids unnecessary comparisons.

1. Clarify constraints and edge cases

Confirm the array size, integer range, and whether duplicates are allowed. Handle edge cases like n < 2 by returning 0 or throwing an error.

2. Choose a linear-time sorting or bucketing strategy

Decide between radix sort (for bounded integers) or bucket sort based on the pigeonhole principle. Explain why comparison sorts are not allowed.

3. Implement the chosen algorithm

For bucket sort: compute min and max, create n-1 buckets, distribute elements, then scan buckets to find max gap between consecutive non-empty buckets. For radix sort: sort then scan for max adjacent difference.

4. Analyze time and space complexity

State that the algorithm runs in O(n) time and O(n) space. Discuss the trade-offs and why it meets the linear-time requirement.

5. Test with examples and edge cases

Walk through a small example (e.g., [3,6,9,1]) and edge cases like all equal elements or two elements to verify correctness.

Key Points to Mention

  • Comparison-based sorting has a lower bound of Ω(n log n), so it cannot be used.
  • Radix sort is linear for integers with a fixed number of digits, but may not be suitable for arbitrary large integers.
  • The pigeonhole principle: with n elements and n-1 buckets, at least one bucket is empty, so the maximum gap must span at least one empty bucket.
  • Bucket sort approach: create n-1 buckets of equal width, track min and max in each bucket, then compute gaps between consecutive non-empty buckets.
  • Time complexity: O(n) for distribution and scanning; space complexity: O(n) for buckets.
  • Edge cases: empty array, single element, all elements equal, negative numbers, and large ranges.

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