1143. Longest Common Subsequence

link to problem

Description:

Given two strings text1 and text2, return the length of their longest common subsequence.

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. (eg, "ace" is a subsequence of "abcde" while "aec" is not). A common subsequence of two strings is a subsequence that is common to both strings.

If there is no common subsequence, return 0.

Solution:

 class Solution:
     def longestCommonSubsequence(self, text1: str, text2: str) -> int:

         n1 = len(text1)
         n2 = len(text2)

         dp = [[0 for i in range(n2+1)] for j in range(n1+1)]
         for i in range(n1):
             for j in range(n2):
                 if text1[i]==text2[j]:
                     dp[i][j] = 1 + dp[i-1][j-1]
                 else:
                     dp[i][j] = max(dp[i-1][j], dp[i][j-1])

         return dp[n1-1][n2-1]

Notes:

2-d Dynamic Programming

O(mn)