Longest Common Subsequence

Statement

Suppose you are given two strings. You need to find the length of the longest common subsequence between these two strings.

A subsequence is a string formed by removing some characters from the original string, while maintaining the relative position of the remaining characters. For example, “abd” is a subsequence of “abcd”, where the removed character is “c”.

If there is no common subsequence, then return 0.

Let’s say you have the following two strings:

• “cloud”
• “found”

The longest common subsequence between these two strings is “oud”, which has a length of $3$.

Constraints:

• $1 \leq$ str1.length $\leq 2.5 \times 10^3$
• $1 \leq$ str2.length $\leq 2.5 \times 10^3$
• str1 and str2 contain only lowercase English characters.

Examples