What is the optimal time complexity of solving Longest Common Sequence?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Longest Common Sequence?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Longest Common Sequence?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Longest Common Sequence?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Competitive ProgrammingEasy

Longest Common Sequence

Learn how to solve the 'Longest Common Sequence' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function lcs(s1, s2) that returns the length of the longest common subsequence of two strings s1 and s2.

Constraints

•0 <= len(s1), len(s2) <= 1000
•Strings consist of uppercase English letters.

Examples

Example 1

Input

lcs('ABCDGH', 'AEDFHR')

Output

Explanation

The longest common subsequence is 'ADH' which has length 3.

Example 2

Input

lcs('AGGTAB', 'GXTXAYB')

Output

Explanation

The longest common subsequence is 'GTAB' which has length 4.

Need a Hint?

Define subproblem states, establish the recurrence relation, and use memoization (top-down) or tabulation (bottom-up).

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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