Binary Search on graph
Last updated: July 8, 2025
Quick Overview
Given a directed graph represented as an adjacency list, implement a binary search algorithm to determine if there exists a path between two specified nodes. The input will consist of the graph's adjacency list, the starting node, and the target node. The output should be a boolean indicating whether such a path exists.
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Given a directed graph represented as an adjacency list, implement a binary search algorithm to determine if there exists a path between two specified nodes. The input will consist of the graph's adjacency list, the starting node, and the target node. The output should be a boolean indicating whether such a path exists.
This coding problem is frequently asked during Take-home Project at LinkedIn. The interviewer is testing your ability to translate a problem into clean, working code while discussing time and space complexity. LinkedIn expects candidates to write production-quality code, not just solve the puzzle.
What the Interviewer Expects
- Recognize the underlying problem pattern (sliding window, two pointers, BFS/DFS, etc.)
- Discuss multiple approaches and trade-offs before coding
- Implement an optimal solution with clean, production-quality code
- Handle all edge cases including boundary conditions and invalid input
- Optimize both time and space complexity with clear justification
- Test your solution systematically with well-chosen examples
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 your solution change if the input was sorted?
- What if the input doesn't fit in memory?
- Can you solve this in a single pass?
- What happens if the input contains duplicates?
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Problem Analysis
This problem requires determining if there exists a path between two specified nodes in a directed graph represented as an adjacency list. The nature of the problem suggests using a graph traversal al...
Approach
- Graph Representation: Represent the graph using an adjacency list. For example, for a graph with edges A -> B, A -> C, B -> D, it can be represented as: `{'A': ['B', 'C'], 'B': ['D'], 'C': [],...
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