Amazon·Software Engineer·Online Assessment (OA)·Intermediate

IntermediatePrefer not to say

Jun 2026Remote

Summary

Amazon SWE online assessment, part one was this digit-string greedy problem that looks deceptively clean but has a real trap in the increment-vs-position tradeoff. Part two was apparently an AI assistant question that ate more time than expected, so budget accordingly if you get this OA.

Questions Asked (1)

You're given a string of digits. In one operation, you can remove any digit and reinsert it incremented by 1 (capped at 9) anywhere in the string. You can do this zero or more times. Return the lexicographically smallest string you can produce.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I spent the first few minutes just restating the operation to myself because I kept misreading it as a swap.

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AI HintsAI Generated

Suggested Approach

First, clarify the problem and constraints, then propose a greedy strategy: scan left to right, and for each digit, decide whether incrementing it (by removing and reinserting) and placing it earlier can yield a smaller string. Use a monotonic stack or priority queue to efficiently build the lexicographically smallest result, and analyze time/space complexity.

Pro tip: Demonstrate awareness of edge cases like all 9s or leading zeros, and discuss trade-offs between different approaches (e.g., greedy vs. dynamic programming) to show depth.

1. Clarify the problem

Restate the problem in your own words, ask clarifying questions about constraints (e.g., string length, allowed operations), and confirm the goal: lexicographically smallest string after any number of increment-and-reinsert operations.

2. Explore a greedy strategy

Consider scanning from left to right: for each digit, if incrementing it (capped at 9) and moving it to an earlier position can reduce the lexicographic order, do so. Use a data structure like a monotonic stack to maintain the smallest possible prefix.

3. Design the algorithm

Implement the greedy approach: iterate through the string, and for each digit, while the stack is not empty and the incremented current digit is less than the stack's top, pop and reinsert later. Then push the incremented digit. Finally, append remaining digits in order.

4. Analyze complexity and edge cases

State that the algorithm runs in O(n) time and O(n) space. Discuss edge cases: all digits are 9 (no change), leading zeros after increment (e.g., '9' becomes '0'? Actually capped at 9, so no), and strings with repeated digits.

5. Test with examples

Walk through a few examples (e.g., '123', '909', '999') to verify the algorithm produces the lexicographically smallest string and handles edge cases correctly.

Key Points to Mention

Greedy choice: incrementing a digit and moving it left can only improve lexicographic order if the incremented digit is smaller than the digits it passes.
Use of a monotonic stack to efficiently build the result in O(n) time.
Handling of digit 9: incrementing 9 is capped at 9, so no change; such digits should not be moved unnecessarily.
Comparison of trade-offs: greedy vs. dynamic programming or brute force, and why greedy is optimal here.
Time and space complexity analysis: O(n) time, O(n) space.
Edge cases: all 9s, strings with leading zeros, and very long strings.

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