Longest common subsequence

Not to be confused with Longest common substring.

A longest common subsequence (LCS) is the longest subsequence common to all sequences in a set of sequences (often just two sequences). It differs from the longest common substring: unlike substrings, subsequences are not required to occupy consecutive positions within the original sequences. The problem of computing longest common subsequences is a classic computer science problem. Because it is polynomial and has an efficient algorithm to solve it, it is employed to compare data and merge changes to files in programs such as the diff utility and revision control systems such as Git. It has similar applications in computational linguistics and bioinformatics.

For example, consider the sequences (ABCD) and (ACBAD). They have five length-2 common subsequences: (AB), (AC), (AD), (BD), and (CD); two length-3 common subsequences: (ABD) and (ACD); and no longer common subsequences. So (ABD) and (ACD) are their longest common subsequences.

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