Dynamic Programming on graph
Last updated: August 17, 2025
Quick Overview
Given a directed graph represented by an adjacency list, implement a function that uses dynamic programming to find the longest path from a starting node to a target node. The function should return the length of the longest path, or -1 if no path exists.
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Given a directed graph represented by an adjacency list, implement a function that uses dynamic programming to find the longest path from a starting node to a target node. The function should return the length of the longest path, or -1 if no path exists.
Coding interviews at LinkedIn 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
- How would you test this solution thoroughly?
- How would you modify your solution to handle streaming input?
- How would your solution change if the input was sorted?
- What is the worst-case input for your solution?
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Practice DSA ProblemsSample Answer
Problem Analysis
In this problem, we need to find the longest path in a directed graph from a starting node to a target node. The key characteristic of the problem is that it involves finding paths in a graph, which i...
Approach
We will use a Depth-First Search (DFS) approach combined with dynamic programming. The steps are as follows:
- Initialize a memoization dictionary to store the longest path lengths from each node. 2....
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