What is the Course Schedule problem and how do you solve it?
This problem asks if it's possible to finish all courses given prerequisites. It tests topological sorting and cycle detection in directed graphs.
Why Interviewers Ask This
Interviewers use this to test graph theory applications, specifically topological sorting. They want to see if you can model dependencies as a directed graph and detect cycles. It demonstrates real-world problem modeling skills.
How to Answer This Question
Explain the problem as detecting a cycle in a directed graph. If a cycle exists, it's impossible to finish all courses. Use Kahn's algorithm (BFS with in-degree counts) or DFS to detect cycles. Count the number of processed nodes; if it equals the total number of courses, a valid order exists. Discuss time complexity.
Key Points to Cover
- Graph representation of dependencies
- Cycle detection necessity
- Kahn's algorithm implementation
- In-degree tracking
Sample Answer
I model the courses and prerequisites as a directed graph where an edge from A to B means A is a prerequisite for B. The problem becomes checking if this graph has a cycle. I can use Kahn's algorithm by calculating in-de…
Common Mistakes to Avoid
- Confusing undirected and directed graph logic
- Not updating in-degrees correctly
- Failing to detect cycles properly
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