Count maximum path in graph
Last updated: December 25, 2025
Quick Overview
Given a directed graph represented as an adjacency list, write a function to count the number of distinct maximum paths from a specified starting node to any other node in the graph. The function should take the graph as input and return an integer representing the count of these maximum paths.
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December 25, 2025138
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2,508 solved
Given a directed graph represented as an adjacency list, write a function to count the number of distinct maximum paths from a specified starting node to any other node in the graph. The function should take the graph as input and return an integer representing the count of these maximum paths.
Snapchat uses this problem in the Technical Screen to evaluate your algorithmic thinking. They expect you to discuss multiple approaches, analyze trade-offs between them, and implement the optimal solution with clean, readable code.
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
- Can you solve this in a single pass?
- Can you optimize the space complexity of your solution?
- Can you solve this iteratively instead of recursively (or vice versa)?
- How would your solution change if the input was sorted?
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Problem Analysis
This problem can be approached using Depth-First Search (DFS) combined with dynamic programming. The essence of the problem lies in finding the longest path in a directed acyclic graph (DAG), where ea...
Approach
- Graph Representation: First, represent the graph as an adjacency list. For example, if the input graph is represented as
graph = {0: [1, 2], 1: [3], 2: [3], 3: []}, this indicates that from n...
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