Longest Common Subsequence (LCS)

Algorithms
Medium
Airbnb
51.3K views

Given two strings $text1$ and $text2$, return the length of their longest common subsequence. Use Dynamic Programming.

Why Interviewers Ask This

Airbnb asks the Longest Common Subsequence problem to evaluate a candidate's ability to recognize overlapping subproblems and apply dynamic programming efficiently. They are testing whether you can transition from brute-force recursion to an optimized DP solution, demonstrating logical structuring skills essential for building scalable infrastructure that handles complex data matching tasks.

How to Answer This Question

1. Clarify constraints: Immediately ask about string lengths and character sets to determine if O(N*M) space is acceptable or if space optimization is needed. 2. Define the state: Explicitly state your DP table definition, such as dp[i][j] representing the LCS length of text1[0...i] and text2[0...j]. 3. Establish the recurrence relation: Explain the logic clearly—if characters match, add 1 to the diagonal; otherwise, take the max of the top or left cell. 4. Walk through an example: Use small strings like 'abc' and 'ac' to trace the table filling process verbally before writing code. 5. Optimize and analyze: Discuss time complexity O(N*M) and space complexity, mentioning how to reduce space to O(min(N,M)) if asked, mimicking Airbnb's focus on resource efficiency.

Key Points to Cover

  • Explicitly define the DP state and recurrence relation before coding
  • Demonstrate understanding of why brute force fails due to exponential redundancy
  • Walk through a concrete trace with a small example to show logical flow
  • Correctly identify time and space complexities as O(N*M)
  • Connect the algorithmic pattern to real-world data comparison use cases

Sample Answer

I would start by defining the problem as finding the maximum length of a sequence present in both strings without changing relative order. First, I'd validate inputs and check edge cases like empty strings. Then, I'd pro…

Common Mistakes to Avoid

  • Confusing Subsequence with Substring by allowing contiguous characters instead of non-contiguous ones
  • Failing to initialize the DP table correctly, leading to off-by-one errors in indices
  • Implementing only the recursive solution without memoization, resulting in Time Limit Exceeded
  • Neglecting to discuss space optimization when the interviewer hints at memory constraints

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