DFS on matrix
Last updated: January 3, 2026
Quick Overview
Implement a Depth-First Search (DFS) algorithm to traverse a given 2D matrix, where each cell contains either a 0 or a 1. Your task is to count the number of connected components of 1s in the matrix, treating adjacent 1s (horizontally or vertically) as part of the same component. The input will be a binary matrix, and the output should be an integer representing the total number of connected components.
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January 3, 202626
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Implement a Depth-First Search (DFS) algorithm to traverse a given 2D matrix, where each cell contains either a 0 or a 1. Your task is to count the number of connected components of 1s in the matrix, treating adjacent 1s (horizontally or vertically) as part of the same component. The input will be a binary matrix, and the output should be an integer representing the total number of connected components.
Coding interviews at Instacart 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
- 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?
- Can you optimize the space complexity of your solution?
- What if the input doesn't fit in memory?
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Practice DSA ProblemsSample Answer
Problem Analysis
The problem requires us to count the number of connected components of 1s in a 2D matrix. Each component consists of 1s that are directly adjacent either horizontally or vertically. This problem is be...
Approach
- Initialize a count to keep track of connected components.
- Iterate through each cell in the matrix. If a cell contains a '1' and has not been visited:
- Increment the count of connecte...
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