Longest Common Subsequence The Longest Common Subsequence (LCS) is the longest subsequence that appears in every substring of a given string. It's like...
Longest Common Subsequence
The Longest Common Subsequence (LCS) is the longest subsequence that appears in every substring of a given string. It's like the longest shared "backbone" among all smaller sub-strings.
Example:
Longest Common Subsequence of "abcabcdd": "abc"
Longest Common Subsequence of "agctcagtcagc": "agt"
Longest Common Subsequence of "aaabbccccaaa": "abc"
Algorithm:
If the length of the string is 0, the LCS is also an empty string.
Otherwise, the LCS is equal to the first character of the string.
For each character in the string, find the longest common subsequence of the substring that ends with that character.
This can be calculated by recursively finding the LCSs of the substring with the first character removed, and the substring without the last character.
Applications:
Pattern matching: The LCS can be used to find the longest common substring between two strings.
Bioinformatics: It can be used to find the longest common sequence of DNA or RNA sequences.
Software development: It can be used to find the longest common substring between two strings used in a string manipulation algorithm.
Time Complexity:
Additional Notes:
The LCS is also known as the longest common substring problem or the longest common subsequence algorithm.
The LCS problem is a dynamic programming problem, which means that it can be solved efficiently by using a recursive algorithm.
The LCS problem can be solved using dynamic programming in O(n) time, where n is the length of the string