Count longest subsequence in matrix
Last updated: January 14, 2026
Quick Overview
Given a matrix of integers, write a function to count the length of the longest increasing subsequence that can be formed by moving only right or down from any starting position in the matrix. The function should take a 2D array as input and return an integer representing the length of the longest subsequence.
Two Sigma
January 14, 2026104
11
1,632 solved
Given a matrix of integers, write a function to count the length of the longest increasing subsequence that can be formed by moving only right or down from any starting position in the matrix. The function should take a 2D array as input and return an integer representing the length of the longest subsequence.
This coding problem is frequently asked during Take-home Project at Two Sigma. The interviewer is testing your ability to translate a problem into clean, working code while discussing time and space complexity. Two Sigma 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
- How would your solution change if the input was sorted?
- What if the input doesn't fit in memory?
- What happens if the input contains duplicates?
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Practice DSA ProblemsSample Answer
Problem Analysis
To tackle the problem of finding the longest increasing subsequence in a matrix while only moving right or down, we can utilize a dynamic programming approach. The matrix naturally lends itself to a g...
Approach
- Initialization: Create a 2D list
dpof the same dimensions as the input matrix, wheredp[i][j]will store the length of the longest increasing subsequence that ends at the cell(i, j). In...
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