Dynamic Programming on graph
Last updated: October 11, 2025
Quick Overview
Given a directed graph represented as an adjacency list, implement a dynamic programming solution to find the longest path from a given starting node to any other node in the graph. The function should return the length of the longest path, or -1 if no path exists.
Redfin
October 11, 20251
11
2,602 solved
Given a directed graph represented as an adjacency list, implement a dynamic programming solution to find the longest path from a given starting node to any other node in the graph. The function should return the length of the longest path, or -1 if no path exists.
Coding interviews at Redfin focus on problem-solving approach as much as the final solution. The interviewer wants to see you break down the problem, consider edge cases, and optimize iteratively. Communication throughout the process is key.
What the Interviewer Expects
- Identify the correct data structure and algorithm for the problem
- Write clean, bug-free code with proper variable naming
- Analyze time and space complexity correctly
- Handle basic edge cases (empty input, single element)
- Communicate your thought process while coding
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 optimize the space complexity of your solution?
- What happens if the input contains duplicates?
- How would you parallelize this solution?
Sharpen Your Skills on Codemia
Practice similar problems with our interactive workspace, get AI feedback, and track your progress.
Practice DSA ProblemsSample Answer
Problem Analysis
To find the longest path in a directed graph, we can apply a topological sorting approach combined with dynamic programming. This is because the longest path problem in a directed acyclic graph (DAG) ...
Approach
- Topological Sort: Use Kahn's algorithm to perform a topological sort of the graph. Maintain an in-degree list for all nodes and a queue to process nodes with zero in-degrees. 2. **Initializ...
Submit Your Answer
