In the context of FAANG interviews, how do you approach optimizing time and space complexity when your initial brute-force solution is not sufficient? Walk through a concrete example of a problem you solved where you moved from a naive solution to an optimal one, explaining each optimization step and the trade-offs you considered.

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VirtualInterview.AI · Accepted Answer

In interviews, I’m very explicit about starting with the brute-force, then systematically tightening it. For example, I got a variant of “given an array, find the length of the longest substring without repeating characters.”

I first stated the naive approach: check every substring and verify uniqueness with a set. That’s O(n³): O(n²) substrings and O(n) to check each. I walked through why this wouldn’t scale beyond ~10⁴ characters.

Then I moved to a sliding window with a hash map of last seen indices. I maintain two pointers, expand the right pointer, and when I see a duplicate, I move the left pointer to max(left, lastSeen + 1). That drops it to O(n) time and O(min(n, charset)) space.

I also discussed trade-offs: slightly higher constant factors and more complex code, but in practice it handled inputs 10–100x larger and is the expected FAANG-level solution.

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