Dynamic Programming on graph
Last updated: July 23, 2025
Quick Overview
Given a directed graph represented as an adjacency matrix, implement a dynamic programming solution to find the longest path in the graph where each node can only be visited once. The function should return the length of the longest path and the path itself as a list of nodes. The input will be the adjacency matrix and the output should be the length of the longest path and the corresponding node sequence.
Lyft
July 23, 2025119
8
1,298 solved
Given a directed graph represented as an adjacency matrix, implement a dynamic programming solution to find the longest path in the graph where each node can only be visited once. The function should return the length of the longest path and the path itself as a list of nodes. The input will be the adjacency matrix and the output should be the length of the longest path and the corresponding node sequence.
This coding problem is frequently asked during Technical Screen at Lyft. The interviewer is testing your ability to translate a problem into clean, working code while discussing time and space complexity. Lyft expects candidates to write production-quality code, not just solve the puzzle.
What the Interviewer Expects
- Quickly identify the optimal approach and its theoretical basis
- Handle complex algorithm design with multiple interacting components
- Write concise, elegant code under time pressure
- Prove correctness of your approach and discuss alternative solutions
- Optimize beyond the obvious: discuss constant factor improvements
- Address follow-up variations and explain how the solution generalizes
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?
- What is the worst-case input for your solution?
- How would you parallelize this solution?
- Can you solve this iteratively instead of recursively (or vice versa)?
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Practice DSA ProblemsSample Answer
Problem Analysis
This problem involves finding the longest path in a directed graph represented as an adjacency matrix. The key characteristics of this problem suggest using dynamic programming coupled with depth-firs...
Approach
- Initialize Variables: Create a memoization array to store the longest path length from each node, and an array to keep track of the actual path taken.
- DFS Function: Implement a DFS fun...
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