Graph BFS on Dependency Chains
Last updated: September 4, 2025
Quick Overview
Given a directed acyclic graph (DAG) representing dependency chains, implement a breadth-first search (BFS) algorithm to traverse the graph and return the nodes in the order they can be processed based on their dependencies. The input will be a list of edges representing the dependencies, and the output should be a list of nodes in the correct execution order. Ensure that your solution handles cases with multiple valid execution orders.
Perplexity
September 4, 20256
12
3,422 solved
Given a directed acyclic graph (DAG) representing dependency chains, implement a breadth-first search (BFS) algorithm to traverse the graph and return the nodes in the order they can be processed based on their dependencies. The input will be a list of edges representing the dependencies, and the output should be a list of nodes in the correct execution order. Ensure that your solution handles cases with multiple valid execution orders.
Standard graph problem that appears in distributed system coding follow-ups. Relevant to Perplexity's crawl scheduling and pipeline orchestration.
What the Interviewer Expects
- Implement topological sort using Kahn's algorithm (BFS)
- Detect cycles in the dependency graph
- Return a valid execution order or indicate impossibility
- Handle disconnected components
- Discuss time and space complexity
Key Topics to Cover
How to Approach This
- Clarify input constraints and edge cases before writing code.
- Walk through your approach verbally and confirm with the interviewer before coding.
- Start with a brute force solution, then optimize. Mention time and space complexity.
- Test your solution with examples, including edge cases like empty input or duplicates.
- Consider common patterns: sliding window, two pointers, hash map, BFS/DFS, dynamic programming.
Possible Follow-up Questions
- How would you parallelize tasks that have no dependencies between them?
- What if dependencies can be added dynamically?
- How would you handle weighted dependencies (some tasks are more expensive)?
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Problem Analysis
To solve the problem of finding an execution order in a directed acyclic graph (DAG) based on dependency chains, we can utilize the BFS approach known as Kahn's Algorithm for topological sorting. This...
Approach
- Input Representation: Start by representing the graph using an adjacency list, and also maintain an array to track the in-degrees of each node (number of incoming edges).
- **Build the Graph...
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