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

Intermediate

May 2026

Summary

Amazon SWE coding round with a string manipulation problem that looks deceptively simple but has some real gotchas once you start tracing through examples.

Questions Asked (1)

You have a string of single-digit box IDs. You can repeatedly pick any digit, remove it, increment it by 1 (capped at 9), and reinsert it anywhere in the string. Return the lexicographically smallest string you can produce.

Algorithms & Data Structures

Author's notes

Spent the first few minutes just staring at the example trying to reverse-engineer the logic.

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AI HintsAI Generated

Suggested Approach

First, clarify the operation: you can increment a digit by 1 (capped at 9) and reinsert it anywhere, but you cannot decrement. The goal is to produce the lexicographically smallest string. The key insight is that incrementing a digit can only make it larger, so you should only increment digits that are followed by a smaller digit, and then move the incremented digit to the left of that smaller digit. A greedy left-to-right scan with a stack can achieve this in O(n) time.

Pro tip: Mention that the operation is equivalent to: for each digit, you may increase it by 1 and move it left, but only if the digit to its left is larger. This simplifies the problem to finding the smallest possible string by selectively incrementing and repositioning digits. Also, note that incrementing a 9 is useless because it stays 9, so skip those.

1. Understand the operation and constraints

Restate the problem: you can pick any digit, increment it by 1 (max 9), and reinsert it anywhere. The goal is lexicographically smallest string. Note that incrementing increases the digit's value, so it's only beneficial if it allows a smaller digit to move left.

2. Identify when incrementing helps

Incrementing a digit d to d+1 is useful only if there is a smaller digit to its right that can be moved left after the increment. Specifically, if you have a pattern like d followed by a smaller digit e (e < d), you can increment d to d+1 and move it after e, making e come earlier. This can be applied repeatedly.

3. Design a greedy algorithm

Process the string from left to right, maintaining a stack of digits that are candidates for incrementing. For each digit, while the top of the stack is greater than the current digit, increment the top and push it back (or handle appropriately). Alternatively, use a two-pass approach: first mark digits that should be incremented, then construct the result.

4. Handle edge cases and implement

Consider digits that are 9 (cannot be incremented further) and ensure that incrementing does not exceed 9. Also, handle cases where multiple increments are needed. Implement the algorithm efficiently, aiming for O(n) time and O(n) space.

5. Verify with examples and analyze complexity

Test with examples like '123' (no change), '321' (increment 3 to 4 and move after 2? Actually, optimal is '231'? Let's check: '321' -> pick 3, increment to 4, reinsert after 2? That gives '241'? Wait, need to verify. Better to test with known cases. Also, analyze time and space complexity.

Key Points to Mention

The operation is equivalent to increasing a digit by 1 and moving it left, but only if it is greater than the digit it moves past.
Greedy approach: scan left to right, and whenever a digit is greater than the next digit, increment it and move it after the next digit.
Use a stack or two-pass method to efficiently determine which digits to increment and where to place them.
Incrementing a 9 is never beneficial because it remains 9 and cannot be moved to improve lexicographic order.
Time complexity can be O(n) with a single pass using a stack, and space O(n) for the result.
Edge cases: all digits same, strictly increasing, strictly decreasing, and strings with 9s.

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