Count minimum cost in graph
Last updated: December 17, 2025
Quick Overview
Given a weighted, directed graph represented by an adjacency list, write a function to calculate the minimum cost to traverse from a specified source node to a target node. The function should return the minimum cost as an integer, or -1 if there is no valid path. You may assume that the graph does not contain negative weight cycles.
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Given a weighted, directed graph represented by an adjacency list, write a function to calculate the minimum cost to traverse from a specified source node to a target node. The function should return the minimum cost as an integer, or -1 if there is no valid path. You may assume that the graph does not contain negative weight cycles.
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
- 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?
- How would your solution change if the input was sorted?
- Can you solve this iteratively instead of recursively (or vice versa)?
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Problem Analysis
This problem can be effectively solved using Dijkstra's algorithm, which is optimal for finding the shortest path in a weighted graph with non-negative weights. The algorithm employs a priority queue ...
Approach
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Graph Representation: First, represent the graph as an adjacency list. Each node will map to a list of tuples, where each tuple contains a neighboring node and the cost to reach it.
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**Init...
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