Amplitude·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Apr 2026

Summary

Amplitude SWE interview that focused on extending a recursive employee validator with cycle detection. The problem sounds straightforward until you're actually in it trying to juggle DFS state and API contract decisions at the same time.

Questions Asked (2)

You have a recursive employee validator that traverses a hierarchy of employee objects. Malformed input can contain cycles (e.g. A reports to B, B reports to C, C reports to A). Add cycle detection to the existing validate() function using DFS coloring or an ancestor-tracking set, in O(N) time and space.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I went with the ancestor-set approach because it felt more readable than juggling three color states mid-interview.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

First, clarify the problem and constraints, then propose adding a 'visiting' set to track nodes in the current recursion stack. During DFS, if a node is encountered that is already in the visiting set, a cycle is detected; otherwise, mark it visiting, recurse, and unmark. This achieves O(N) time and space.

Pro tip: Mention that the ancestor-tracking set is essentially the 'gray' set in DFS coloring, and that you can optimize space by using a single set with node states if the graph is large. Also, discuss how to handle cycles gracefully (e.g., return an error or log) rather than crashing.

1. Clarify requirements and constraints

Ask about the expected behavior on cycle detection (throw error, return false, etc.) and confirm that the hierarchy is a directed graph where each employee has at most one manager (tree-like but with possible cycles).

2. Choose cycle detection strategy

Decide between DFS coloring (white/gray/black) or ancestor-tracking set. Explain that both are O(N) time and space, but ancestor-tracking is simpler to implement within the existing recursive validate function.

3. Integrate into existing validate function

Modify validate to accept an additional parameter (the visiting set) or use a closure. Before recursing into reports, check if the current node is in the visiting set; if so, cycle detected. Otherwise, add to set, recurse, then remove.

4. Handle edge cases and complexity

Discuss handling of null/undefined nodes, self-loops, and multiple disconnected components. Confirm that time and space remain O(N) since each node is visited once and the set holds at most N nodes.

5. Test and validate

Walk through a simple example (A->B->C->A) to show detection, and a valid hierarchy to show no false positives. Mention potential unit tests.

Key Points to Mention

DFS coloring: white (unvisited), gray (visiting), black (visited) – cycle if encounter gray.
Ancestor-tracking set: maintain a set of nodes in current recursion stack; cycle if node already in set.
Time complexity O(N) because each node is visited once; space O(N) for the set in worst case (skewed tree).
Integration with existing recursive validate: pass the set as an argument or use a helper function.
Handling cycles: throw an error, return false, or log and continue depending on requirements.
Edge cases: self-loop (A reports to A), multiple cycles, and disconnected components.

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

When cycle detection fires, what should the validator do: return false or mark the offending nodes as invalid, versus raising or reporting a structured error with the cycle's node IDs? Walk through the trade-offs and defend a choice.

Technical Trade-offsSystem Design

Author's notes

This is the part I fumbled a bit.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Start by clarifying the validator's contract and the caller's needs, then compare the three options (boolean, invalid marking, structured error) across dimensions like debuggability, API stability, and performance. Defend a choice that balances actionable feedback with system resilience, typically favoring a structured error with cycle node IDs for internal validation and a boolean for simple public APIs.

Pro tip: Emphasize that the best choice depends on the consumer: a boolean is fine for a quick check, but a structured error is essential for debugging and automated remediation. Mention that you'd log the cycle details even if returning a boolean, to avoid losing critical information.

1. Clarify the validator's contract and caller expectations

Determine who calls the validator and what they need: a simple pass/fail, detailed diagnostics, or programmatic handling. Consider whether the validator is part of a public API or internal tooling.

2. Analyze the three options against key criteria

Compare returning false, marking nodes invalid, and raising/reporting a structured error on dimensions like debuggability, API stability, performance, and error handling complexity.

3. Consider the broader system context

Think about how the validator fits into the larger system: will the error be caught and handled? Is there a need for automated recovery or alerting? What are the logging and monitoring implications?

4. Defend a choice with trade-offs

Pick one approach (e.g., structured error with cycle node IDs) and justify it by explaining why its benefits outweigh its drawbacks for the given context, acknowledging the alternatives.

5. Propose a hybrid or adaptive solution if appropriate

Suggest a design that combines approaches, such as returning a boolean for simple checks but also logging a structured error, or making the behavior configurable.

Key Points to Mention

Debuggability: structured errors with node IDs pinpoint the cycle, while a boolean gives no context.
API stability: changing return types can break callers; structured errors may require exception handling.
Performance: raising exceptions can be costly; marking nodes may mutate state unexpectedly.
Error handling: structured errors allow programmatic handling and automated remediation.
Logging and monitoring: even if returning a boolean, log cycle details for observability.
Consumer needs: public APIs often favor booleans for simplicity, internal tools benefit from rich errors.

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