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Longest Common Subsequence

Problem Statement​

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.

Leetcode link

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 such common subsequence, so the result is 0.

Constraints​

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

Code​

Python3 Code

class Solution:
    def longestCommonSubsequence(self, text1: str, text2: str) -> int:
        row,col=1+len(text1),1+len(text2)
        prev=[0]*col

        for i in range(1,row):
            curr=[0]*col
            for j in range(1,col):
                if text1[i-1]==text2[j-1]:
                    curr[j]=1+prev[j-1]
                else:
                    curr[j]=max(curr[j-1],prev[j])
            prev=curr
        return prev[-1]