Amazon·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Jun 2026Remote

Summary

Amazon coding round, one problem the whole session. It looked like a string DP thing at first glance but the cost function made it messier than expected.

Questions Asked (1)

You have a string of '0's, '1's, and '!' characters, where each '!' must be replaced by either '0' or '1'. The total cost is (number of '01' subsequences) * x plus (number of '10' subsequences) * y. Find the replacement assignment that minimizes total cost.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I stared at the example for longer than I'd like to admit.

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AI HintsAI Generated

Suggested Approach

First, clarify the problem and constraints, then derive a greedy strategy based on the relative costs x and y. Explain that if x < y, we want to minimize '01' subsequences by placing '0's before '1's, and if y < x, we want to minimize '10' subsequences by placing '1's before '0's. Handle ties by noting any assignment works.

Pro tip: Mention that the optimal assignment can be found in O(n) time by counting existing characters and making local decisions for each '!', and that this greedy choice is provably optimal due to the monotonic effect of each replacement.

1. Understand the problem and define cost

Restate the problem: each '!' can be replaced by '0' or '1', and the cost is x*(#01) + y*(#10). Clarify that subsequences are counted over the final string.

2. Analyze the effect of replacements

Determine how replacing a '!' with '0' or '1' affects the number of '01' and '10' subsequences, considering the existing characters before and after the position.

3. Derive greedy strategy based on costs

If x < y, prioritize minimizing '01' by placing '0's before '1's; if y < x, prioritize minimizing '10' by placing '1's before '0's. If x = y, any assignment yields the same cost.

4. Implement and verify

Scan the string, count existing '0's and '1's, and for each '!' decide its replacement based on the greedy rule. Compute the final cost to verify optimality.

Key Points to Mention

Time complexity: O(n) with a single pass, space complexity O(1) if we count on the fly.
Greedy choice property: local optimal decisions lead to global optimum because the cost function is linear and monotonic.
Edge cases: all '!' characters, no '!' characters, x = y, x = 0 or y = 0.
Proof of optimality: exchange argument showing that swapping a suboptimal assignment increases cost.
Comparison with dynamic programming: DP would be O(n^2) or O(n) with states, but greedy is simpler and faster.
Amazon leadership principles: customer obsession (minimizing cost), dive deep (analyzing trade-offs), deliver results (efficient solution).

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