1143. Longest Common Subsequence

Problem Link

Description

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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

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Python3

class Solution:
    def longestCommonSubsequence(self, text1: str, text2: str) -> int:
        N, M = len(text1), len(text2)
 
        @cache
        def go(i, j):
            if i == N or j == M: return 0
 
            if text1[i] == text2[j]:
                return 1 + go(i + 1, j + 1)
            
            return max(go(i + 1, j), go(i, j + 1))
        
        return go(0, 0)