(Hope no one minds me making a second reply -- updating gets tiresome after a while...)

Well, a lot really hinges on what you mean, exactly, when you say:

...search for the longest matching substrings between the members of the array...

If what you mean is something like this:

$string[0] = "abc  fghijklmn ";
$string[1] = " b d fgh jklmno";
# correct answer  is: "jklmn", 5 chars long;
# (next longest common substring is " fgh",
#  but you're not interested in that)
[download]

then Algorithm::Diff can be used to arrive at that answer for each pair-wise string comarison as follows:

#!/usr/bin/perl

use strict;
use Algorithm::Diff qw/traverse_sequences/;

my @strings = <>;
chomp @strings;

my ( $longestMatch, $currentMatch );
my ( @seq1, @seq2 );

for my $i ( 0 .. $#strings-1 ) {
    @seq1 = split //, $strings[$i];
    for my $j ( $i+1 .. $#strings ) {
        @seq2 = split //, $strings[$j];
        $longestMatch = $currentMatch = "";
        traverse_sequences( \@seq1, \@seq2,
                          { MATCH => \&add2match,
                            DISCARD_A => \&end_match,
                            DISCARD_B => \&end_match }
                          );

### update: add a direct call to "end_match()" here,
### in case traverse was still matching at end-of-string:
        end_match( 'EOS' );

        print "LCS for $i :: $j = |$longestMatch|\n";
    }
}

sub add2match {
    my ( $ptrA, $ptrB ) = @_;
    $currentMatch .= $seq1[$ptrA];
#    warn "match at i=$ptrA, j=$ptrB : =$seq1[$ptrA]= ; cm=$currentMat
+ch=\n";
}

sub end_match {
    $longestMatch = $currentMatch
        if ( length( $longestMatch ) < length( $currentMatch ));
    $currentMatch = "";
#    warn "match ended at @_ : lm=$longestMatch=\n";
}
[download]

If you take out the comment marks on the "warn" statements in the two callbacks, you'll be able to watch what's going on. With those commented out, a file of 382 lines (between 2 and 73 characters per line, about 73K pair-wise comparisons) was finished in about 6 minutes.

I expect there are cleaner ways to do it (e.g. that don't involve global-scope variables), but this was fairly quick and easy (fun, even) for a first-time A::D user.

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