Find connected components in matrix
Last updated: May 26, 2026
Quick Overview
Given a binary matrix, write a function to find and return all connected components of 1s, where connectivity is defined as horizontal or vertical adjacency. The output should be a list of lists, where each inner list contains the coordinates of the cells that form a connected component. Your solution should efficiently handle large matrices using depth-first search (DFS) or breadth-first search (BFS).
HRT
May 26, 20262
7
377 solved
Given a binary matrix, write a function to find and return all connected components of 1s, where connectivity is defined as horizontal or vertical adjacency. The output should be a list of lists, where each inner list contains the coordinates of the cells that form a connected component. Your solution should efficiently handle large matrices using depth-first search (DFS) or breadth-first search (BFS).
HRT uses this problem in the Phone Screen to evaluate your algorithmic thinking. They expect you to discuss multiple approaches, analyze trade-offs between them, and implement the optimal solution with clean, readable code.
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 optimize the space complexity of your solution?
- What is the worst-case input for your solution?
- Can you solve this iteratively instead of recursively (or vice versa)?
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Practice DSA ProblemsSample Answer
Problem Analysis
To solve the problem of finding connected components of 1s in a binary matrix, we can utilize Depth-First Search (DFS) as our primary pattern. DFS is particularly suitable here because it allows us to...
Approach
We can approach the problem with the following steps:
- Initialize a list to store the connected components.
- Create a set to keep track of visited cells to avoid processing the same cell multiple ...
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