Count minimum cost in graph
Last updated: February 6, 2026
Quick Overview
Given a weighted, directed graph represented as an adjacency list, write a function to calculate the minimum cost to travel 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 path between the two nodes.
DE Shaw
February 6, 202623
5
3,827 solved
Given a weighted, directed graph represented as an adjacency list, write a function to calculate the minimum cost to travel 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 path between the two nodes.
Coding interviews at DE Shaw 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
- 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
- What if the input doesn't fit in memory?
- Can you solve this in a single pass?
- What is the worst-case input for your solution?
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Practice DSA ProblemsSample Answer
Problem Analysis
This problem can be effectively solved using Dijkstra’s algorithm, which is designed for finding the shortest paths in a graph with non-negative edge weights. Here, we want to find the minimum cost to...
Approach
- Graph Representation: First, represent the graph using an adjacency list, where each key is a node and its value is a list of tuples representing the neighboring nodes and their respective edge...
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