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)

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