Find longest subsequence in matrix
Last updated: October 8, 2025
Quick Overview
Given a matrix of integers, write a function to find the longest increasing subsequence that can be formed by moving only right or down from the top-left corner to the bottom-right corner. The function should return the length of this subsequence. The input will be a 2D array of integers, and the output should be a single integer representing the length of the longest subsequence.
Booking.com
October 8, 20254
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4,017 solved
Given a matrix of integers, write a function to find the longest increasing subsequence that can be formed by moving only right or down from the top-left corner to the bottom-right corner. The function should return the length of this subsequence. The input will be a 2D array of integers, and the output should be a single integer representing the length of the longest subsequence.
Booking.com uses this problem in the Onsite 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
- 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?
- What is the worst-case input for your solution?
- Can you solve this iteratively instead of recursively (or vice versa)?
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Problem Analysis
This problem can be viewed as a dynamic programming challenge, where we are tasked with finding the longest increasing subsequence (LIS) in a matrix from the top-left corner to the bottom-right corner...
Approach
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Initialization: Create a 2D dp array of the same dimensions as the input matrix, initialized to 1. This is because each cell can be a subsequence of at least length 1 (itself).
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**Iterate th...
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