Amazon·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Amazon SWE interview covering the Course Schedule problem. Not much context to go on here, but it's a classic graph/topological sort question that shows up a lot in these loops.

Questions Asked (1)

Given a list of courses and their prerequisites, determine whether it's possible to finish all courses (i.e., detect if a cycle exists in the dependency graph).

Algorithms & Data Structures

Author's notes

Classic topological sort / cycle detection problem.

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AI HintsAI Generated

Suggested Approach

Model the courses and prerequisites as a directed graph and detect cycles using either DFS with recursion stack or Kahn's topological sort algorithm. Clearly explain the graph representation, cycle detection logic, and analyze time and space complexity.

Pro tip: Mention that Kahn's algorithm can also produce a valid course order if one exists, and discuss how to handle large inputs with memory-efficient adjacency lists. Also, relate the problem to real-world dependency resolution, showing practical insight.

1. Clarify the problem and assumptions

Confirm input format (e.g., number of courses, prerequisite pairs), whether prerequisites are directed edges, and if all courses must be taken. Ask about constraints like course count and graph density.

2. Choose graph representation and algorithm

Decide between adjacency list or matrix, and select DFS with cycle detection or Kahn's topological sort. Explain why the chosen method is suitable for cycle detection.

3. Walk through the algorithm step-by-step

Describe how to build the graph, then either perform DFS tracking visited and recursion stack, or compute in-degrees and process nodes with zero in-degree. Highlight how a cycle is detected.

4. Analyze complexity and edge cases

State time and space complexity (O(V+E) for both algorithms). Discuss edge cases: empty input, no prerequisites, self-loops, disconnected graphs, and duplicate edges.

5. Conclude with the answer and possible extensions

Return true if no cycle, false otherwise. Optionally mention how to return a valid order or handle dynamic updates.

Key Points to Mention

Directed graph representation with courses as nodes and prerequisites as edges.
Cycle detection using DFS with recursion stack or Kahn's topological sort.
Time and space complexity: O(V+E) for both approaches.
Handling edge cases: empty graph, no prerequisites, self-loops, disconnected components.
Trade-offs between DFS and Kahn's algorithm (e.g., DFS may use recursion stack, Kahn's can produce order).
Real-world relevance: dependency resolution in build systems or course scheduling.

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