Glean·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Apr 2026

Summary

Glean SWE interview with a classic two-sorted-arrays problem, but they pushed pretty hard on the optimal solution and edge cases. Not a warmup question by any stretch.

Questions Asked (1)

Given two sorted arrays of integers, find the k-th largest element across both arrays combined. What approaches can you think of, and what are the tradeoffs between them?

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I started with the merge-from-the-back approach, which is fine but they clearly wanted more.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem: confirm whether the arrays are sorted in ascending order and whether k is 1-indexed. Then present a progression of solutions: a naive merge-based approach, a binary search on the k-th element, and an optimal binary search on partitions. For each, discuss time and space complexity, and when each is appropriate.

Pro tip: Mention that the optimal solution can be framed as finding a partition in the smaller array such that the combined left half has exactly k elements and all elements in the left half are ≤ all elements in the right half. This shows deep understanding and often impresses interviewers.

1. Clarify the problem

Ask about array sizes, sorted order, definition of k-th largest (1-indexed or 0-indexed), and whether duplicates are allowed. Confirm that the arrays are sorted in ascending order.

2. Discuss naive approaches

Mention merging the arrays and picking the k-th element (O(m+n) time, O(m+n) space) or using a max-heap (O(k log(m+n)) time). Note their simplicity but suboptimal efficiency.

3. Present binary search on value

Explain that you can binary search on the value range (min to max) and count how many elements are ≤ mid in both arrays using binary search. This gives O(log(range) * (log m + log n)) time, which is good if the range is small.

4. Present optimal partition approach

Describe the O(log(min(m,n))) solution: binary search on the partition of the smaller array, ensuring the left half has k elements and max(left) ≤ min(right). Handle edge cases like empty partitions.

5. Compare tradeoffs

Summarize: naive is simple but slow; value binary search is good for bounded integers; partition method is optimal for large arrays. Mention space complexity and code complexity.

Key Points to Mention

Time and space complexity of each approach
The partition method reduces the problem to finding a split in the smaller array
Handling edge cases: k out of bounds, empty arrays, duplicates
The role of binary search in achieving logarithmic time
When to prefer a simpler approach (e.g., if k is small, a heap might be fine)
The importance of clarifying assumptions before coding

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