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Glean·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
May 2026

Summary

Glean software engineer interview with an algorithms problem involving two sorted arrays. Pretty clean problem statement, nothing too tricky on the surface, but the edge cases are where things get interesting.

Questions Asked (1)

Q1

You're given two sorted arrays and an integer k. Find the kth largest element across both arrays combined, counting duplicates separately.

Algorithms & Data Structures
Author's notes

My first instinct was to just merge and sort, which works but feels lazy.

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AI HintsAI Generated

Suggested Approach

Clarify the problem constraints (array sizes, value ranges, duplicates) and discuss multiple approaches: binary search on value range, binary search on partition, or a heap-based merge. For an optimal solution, use binary search on the value range to count how many elements are ≥ a candidate value, then find the smallest value such that the count is at least k. Alternatively, use a modified binary search on partitions to achieve O(log(min(m,n))) time.

Pro tip: Always start by discussing the brute-force merge approach and its O(m+n) complexity, then optimize; this shows you can iterate and consider trade-offs. Also, explicitly handle edge cases like k=1, k=m+n, and arrays of different lengths.

1. Clarify and Restate

Confirm the problem details: arrays are sorted, duplicates count separately, k is 1-indexed, and what to return if k is invalid. Ask about constraints (array sizes, value ranges) to guide approach selection.

2. Discuss Brute Force

Mention the straightforward merge of both arrays and picking the kth element, which takes O(m+n) time and O(m+n) space (or O(k) with a heap). This sets a baseline and shows you can start simple.

3. Propose Optimal Approach

Explain binary search on the value range: find the minimum value v such that the number of elements ≥ v is at least k. Counting takes O(log m + log n) per step, leading to O((log m + log n) * log(range)) time. Alternatively, describe the partition-based binary search for O(log(min(m,n))) time.

4. Walk Through Example

Trace the algorithm on a small example (e.g., arrays [1,3,5] and [2,4,6], k=4) to demonstrate correctness and handling of duplicates. Show how the count is computed and how the search space narrows.

5. Analyze Complexity and Edge Cases

State time and space complexity clearly. Discuss edge cases: k=1, k=m+n, empty arrays, all elements equal, and negative numbers. Mention that the value-range binary search requires knowing the min and max values.

Key Points to Mention

  • Binary search on the value range: count elements ≥ mid using binary search in each array.
  • Partition-based binary search: find a split in the smaller array such that left half has k elements and max(left) ≤ min(right).
  • Time complexity: O(log(min(m,n))) for partition approach, or O((log m + log n) * log(max-min)) for value-range approach.
  • Space complexity: O(1) for both optimal approaches.
  • Handling duplicates: counting elements ≥ mid naturally includes duplicates.
  • Edge cases: k out of bounds, empty arrays, all elements identical, negative values.

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