Aurora·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Aurora coding round, one problem the whole session. It's a sliding window minimum variant but with a twist on the output size that I almost missed entirely.

Questions Asked (1)

Given an array of length n and a window size k, implement a streaming sliding window minimum that outputs n values total. For indices before the window fills, output the running minimum so far. Once the window is full, output the standard sliding window minimum. Solve in O(n).

Algorithms & Data Structures

Author's notes

I knew the monotonic deque approach for the standard sliding window max/min problem.

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AI HintsAI Generated

Suggested Approach

Use a monotonic deque to maintain indices of potential minimums in the current window. For the first k-1 elements, output the minimum so far; once the window is full, slide it by removing outdated indices and maintaining the deque property to output the window minimum in O(1) amortized time.

Pro tip: Clarify the streaming aspect: the algorithm should process elements one by one, outputting after each element. Emphasize that the deque stores indices, not values, to efficiently check if the front is out of the window.

1. Understand the problem and edge cases

Restate the problem: for each index i, output the minimum of the last min(i+1, k) elements. Consider edge cases like k=1, k>n, and empty array.

2. Choose the right data structure

Explain that a monotonic deque (double-ended queue) is ideal because it allows O(1) amortized insertion and removal while maintaining the minimum at the front.

3. Design the algorithm step-by-step

For each element, remove indices from the back while the corresponding values are >= current, then add current index. Remove front if it's out of the window. Output the front's value.

4. Handle the initial window fill

For the first k-1 elements, the window isn't full, so the minimum is simply the minimum of all elements seen so far, which is the front of the deque.

5. Analyze complexity and test

Each element is added and removed at most once, so O(n) time and O(k) space. Walk through a small example to verify correctness.

Key Points to Mention

Monotonic deque maintains indices in increasing order of their values.
Amortized O(1) per element due to each index being pushed and popped at most once.
Space complexity O(k) for the deque.
Handling the initial window fill: output running minimum until index k-1.
Removing outdated indices from the front when they fall outside the window.
Streaming nature: process elements one by one and output after each.

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