Amazon·Software Engineer·Onsite - Coding / Algorithms·Intermediate

IntermediatePrefer not to say

Apr 2026

Summary

Amazon SWE coding round with a string manipulation problem that had a greedy twist to it. Nothing too wild but the optimization angle took me a second to see clearly.

Questions Asked (1)

You're given a string containing '0', '1', and '!' characters. Each '!' can be independently replaced with '0' or '1'. After substitution, every '10' subsequence contributes x errors and every '01' subsequence contributes y errors. Return the total error count modulo 10^9 + 7. (Variant: minimize or maximize the total.)

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was to try all combinations of replacements which is obviously wrong the moment you think about input size.

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AI HintsAI Generated

Suggested Approach

Clarify whether the goal is to compute the total over all possible substitutions (sum), or to find the minimum/maximum error count. Then derive a formula for the total error contribution of each pair of positions, and use dynamic programming or greedy strategies to handle '!' characters efficiently, considering modulo arithmetic.

Pro tip: For the sum variant, linearity of expectation over all 2^k substitutions simplifies the problem: each pair contributes based on the number of '!' between them. For min/max, a greedy assignment (e.g., all '!' to '0' or '1') often works, but verify with small cases.

1. Clarify the problem variant

Ask the interviewer whether the task is to compute the sum of errors over all possible substitutions, or to minimize/maximize the total error. This determines the algorithmic approach.

2. Analyze contribution of fixed pairs

For any two positions i < j with fixed characters, the pair contributes x if s[i]='1' and s[j]='0', y if s[i]='0' and s[j]='1', and 0 otherwise. Count these contributions directly.

3. Handle '!' characters

For sum variant, each '!' independently becomes '0' or '1' with equal probability; compute expected contribution per pair and multiply by 2^k. For min/max, decide optimal assignment for each '!' based on surrounding fixed characters.

4. Derive efficient formula

Use prefix counts of '0's, '1's, and '!'s to compute total contributions in O(n) time. For sum variant, account for the number of '!' between positions to get the multiplier.

5. Implement with modulo

Compute the result modulo 10^9+7, using modular arithmetic for large powers and sums. Test with small examples to verify correctness.

Key Points to Mention

Linearity of expectation for the sum variant: total sum = sum over pairs of expected contribution × 2^(number of '!')
For min/max, greedy assignment: all '!' to '0' minimizes '10' but may increase '01'; need to balance based on x and y
Use prefix sums to count fixed '0's and '1's efficiently
Modular exponentiation for 2^k mod 10^9+7
Edge cases: all '!', no '!', x or y zero, large string length
Time complexity: O(n) for sum variant, O(n) for min/max with careful greedy

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