A substring of a string $S$ is a contiguous sequence of the characters appearing in $S$. The empty string is a substring of every string. A subsequence of a string $S$ is a sequence of characters from $S$, which may not be contiguous in $S$. Every substring of $S$ is a subsequence of $S$. For example, $''bc''$ is a substring of $''abc''$, and $''ac''$ is a subsequence of $''abc''$ which is not a substring.

The LongestCommonSubString( s1, s2 ) command returns from its input strings, s1 and s2, a common substring of maximum length.

Many common substrings of maximum length may exist. Which among the candidates is returned depends upon the suffix structure of the pair of strings, but is deterministic.

The LongestCommonSubSequence( s1, s2 ) command is similar, but searches for subsequences of the pair of input strings rather than substrings.

All of the StringTools package commands treat strings as (null-terminated) sequences of $8$-bit (ASCII) characters.  Thus, there is no support for multibyte character encodings, such as unicode encodings.

$\mathbf{use}\mathrm{StringTools}\mathbf{in}\mathrm{LongestCommonSubString}\left(''abax''\,''bax''\right)\mathbf{end\; use}$

$''bax''$

$\mathrm{with}\left(\mathrm{StringTools}\right)\:$

$\mathrm{LongestCommonSubString}\left(''tsaxbaxyz''\,''axcaxy''\right)$

$''axy''$

$\mathrm{LongestCommonSubString}\left(''abcde''\,''uvabxycde''\right)$

$''cde''$

$\mathrm{LongestCommonSubSequence}\left(''abcde''\,''uvabxycde''\right)$

$''abcde''$

$\mathrm{LongestCommonSubString}\left(''abc''\,''xyz''\right)$

$\mathrm{LongestCommonSubSequence}\left(''abc''\,''xyz''\right)$

$\mathrm{seq1}≔''TAAGGTCGGCGCGCACGCTGGCGAGTATGGTGCGGAGGCCCTGGAGAGGTGAGGCTCCCTCCCCTGCTCCGACCCGGGCTCCTCGCCCGCCCGGACCCAC''\:$

$\mathrm{seq2}≔''AAGCGCCGCGCAGTCTGGGCTCCGCACACTTCTGGTCCAGTCCGACTGAGAAGGAACCACCATGGTGCTGTCTCCCGCTGACAAGACCAACATCAAGACTGCCTGGGAAAAGATCGGCAGCCACGGTGGCGAGTATGGCGCCGAGGCCGT''\:$

$\mathrm{LongestCommonSubString}\left(\mathrm{seq1}\,\mathrm{seq2}\right)$

$''TGGCGAGTATGG''$

$\mathrm{LongestCommonSubSequence}\left(\mathrm{seq1}\,\mathrm{seq2}\right)$

$''AAGGCCGCGCAGCTGGCGATTGGTCAGCCCTGGAAGGTGGGCTCTCCCCTGCTCGACCCGGGTCCGCCCGCGGACCCA''$