## DEV Community

Abhishek Chaudhary

Posted on

# 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"`.

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

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 such common subsequence, so the result is 0.

Constraints:

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

SOLUTION:

``````class Solution:
def lcs(self, text1: str, text2: str, i, j) -> int:
if (i, j) in self.cache:
return self.cache[(i, j)]
if i >= len(text1) or j >= len(text2):
self.cache[(i, j)] = 0
return 0
if text1[i] == text2[j]:
self.cache[(i, j)] = 1 + self.lcs(text1, text2, i + 1, j + 1)
return self.cache[(i, j)]
else:
a = self.lcs(text1, text2, i + 1, j)
b = self.lcs(text1, text2, i, j + 1)
self.cache[(i, j)] = max(a, b)
return self.cache[(i, j)]

def longestCommonSubsequence(self, text1: str, text2: str, i = 0, j = 0) -> int:
self.cache = {}
return self.lcs(text1, text2, 0, 0)
``````