Longest Common Subsequence

Longest Common Subsequence

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", but "aec" is not.

A common subsequence of two strings is a subsequence that is common to both strings.

Examples

Example 1:

Input: text1 = "abcde", text2 = "ace"
Output: 3
Explanation: The longest common subsequence is "ace" and its length is 3.

Example 2:

Input: text1 = "abc", text2 = "abc"
Output: 3
Explanation: The longest common subsequence is "abc" and its length is 3.

Example 3:

Input: text1 = "abc", text2 = "def"
Output: 0
Explanation: There is no common subsequence, so the result is 0.

Constraints

• 1 <= text1.length, text2.length <= 1000
• text1 and text2 consist of only lowercase English characters.

Expected Complexity

• Time: O(m * n) where m and n are the lengths of the two strings
• Space: O(m * n) for the DP table, or O(min(m, n)) with space optimization