Find All Connected Components in an Undirected Graph
Last updated: February 21, 2025
Quick Overview
Given an undirected graph represented as an adjacency list, find all connected components and return them as groups of nodes.
Rivian
February 21, 20256
11
2,326 solved
Given an undirected graph represented as an adjacency list, find all connected components and return them as groups of nodes.
Graph connectivity problems appear in Rivian's phone screens as warm-up problems. In the vehicle domain, this models identifying clusters of connected charging stations, vehicle networks, or sensor groups. The interviewer evaluates your BFS/DFS fluency and code clarity.
What the Interviewer Expects
- Implement using either BFS or DFS with a visited set
- Return all components as a list of node groups
- Handle disconnected graphs, single-node components, and empty graphs
- Write clean, readable code with clear variable naming
- Discuss time and space complexity
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 solve this with Union-Find instead?
- What if the graph is very large and does not fit in memory?
- How would you find the largest connected component efficiently?
- What changes if the graph is directed (strongly connected components)?
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Problem Analysis
To tackle the problem of finding all connected components in an undirected graph, we can utilize the Depth-First Search (DFS) or Breadth-First Search (BFS) algorithms. Both methods allow us to...
Approach
- Initialize Structures: Create a list to hold all connected components and a set to track visited nodes.
- Iterate Through Nodes: For each node in the graph, if it has not been visited, p...
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