How do you implement a solution to find the longest common subsequence?
This DSA question tests dynamic programming skills and pattern recognition.
Why Interviewers Ask This
LCS is a classic problem that evaluates a candidate's ability to optimize recursive solutions using memoization. It tests logical thinking and proficiency in DP. Mastery here indicates readiness for complex algorithmic challenges in production code.
How to Answer This Question
Describe the recursive approach first, highlighting overlapping subproblems. Introduce the DP table to store intermediate results. Explain the recurrence relation: if characters match, add 1 to diagonal; else take max of left or top. Analyze time and space complexity.
Key Points to Cover
- Recursive base case
- DP table construction
- Recurrence relation
- Complexity analysis
Sample Answer
To solve LCS, we use dynamic programming to avoid recalculating subproblems. We create a 2D table where dp[i][j] stores the length of LCS for the first i characters of string X and j of string Y. If characters match, dp[i][j] = 1 + dp[i-1][j-1]. Otherwise, it is max(dp[i-1][j], dp[i][j-1]). This reduces complexity from exponential to O(m*n), making it efficient for large inputs.
Common Mistakes to Avoid
- Using pure recursion
- Incorrect indexing
- Forgetting to reconstruct the sequence
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