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

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 Subsequence?

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 Subsequence?

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 Subsequence?

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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Longest Common Subsequence

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

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Problem Statement

Medium

Given two strings text1 and text2, return the length of their longest common subsequence. If there is no common subsequence, return 0.

A subsequence of a string is a new string generated from the original string with some characters (can be none) deleted without changing the relative order of the remaining characters. (For example, "ace" is a subsequence of "abcde").

Write a function longestCommonSubsequence(text1: str, text2: str) -> int.

Constraints

•1 <= len(text1), len(text2) <= 1000
•text1 and text2 consist of only lowercase English characters

Examples

Example 1

Input

text1 = "abcde", text2 = "ace"

Output

Explanation

The longest common subsequence is "ace" and its length is 3.

Example 2

Input

text1 = "abc", text2 = "abc"

Output

Explanation

The longest common subsequence is "abc" and its length is 3.

Example 3

Input

text1 = "abc", text2 = "def"

Output

Explanation

There is no common subsequence, so the result is 0.

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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