/ 
Algorithm-Graphs-TransitiveClosure-Tiny-1.03
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/ Algorithm::Graphs::TransitiveClosure::Tiny

NAME

Algorithm::Graphs::TransitiveClosure::Tiny - Calculate the transitive closure.

VERSION

Version 1.03

SYNOPSIS

use Algorithm::Graphs::TransitiveClosure::Tiny qw(floyd_warshall);

# The hash values here need not to be undef, but floyd_warshall()
# only adds undef.
my $graph = {
             0 => {0 => undef},
             1 => {1 => undef, 2 => undef, 3 => undef},
             2 => {1 => undef, 2 => undef},
             3 => {0 => undef, 2 => undef, 3 => undef},
            };

floyd_warshall $graph;

print "There is a path from 2 to 0.\n" if
    exists($graph->{2}) && exists($graph->{2}->{0});

The latter can also be written shorter provided you accept autovivification:

print "There is a path from 2 to 0.\n" if exists($graph->{2}->{0});

DESCRIPTION

This module provides a single function, floyd_warshall, which is exported on demand. It is an implementation of the well known Floyd-Warshall algorithm for computing the transitive closure of a graph.

The code is taken from Algorithm::Graphs::TransitiveClosure but has been modified. The difference is that this implementation of floyd_warshall():

  • works on hashes only,

  • uses undef for hash values, so an incidence must be checked with exists() (but for the input hash you are not forced to use undef),

  • fixes following problem of Algorithm::Graphs::TransitiveClosure:

    Example:

    my $g = {
         0 => { 2 => 1},
         1 => { 0 => 1},
        };

    There is an edge from 0 to 2 and an edge from 1 to 0. So the transitive closure would contain an edge from 1 to 2. But calling floyd_warshall($g) from Algorithm::Graphs::TransitiveClosure results in:

    {
 0 => { 2 => 1},
 1 => { 0 => 1},
}

    No change. The edge from 1 to 2 is missing (you would need to add 2=>{} to $g to get it right). But if you call floyd_warshall($g) from Algorithm::Graphs::TransitiveClosure::Tiny, then the result is correct:

    {
 0 => { 2 => 1},
 1 => { 0 => 1,
        2 => undef},
}

    Edge from 1 to 2 has been added! (Also note that it was possible to use 1 instead of undef as hash value. This value is kept, but the value added by the function is still undef!)

  • By default, floyd_warshall($graph) removes empty subhashes from $graph, e.g.

    my $graph = {
             this => {that => undef},
             that => {}
            };
floyd_warshall($graph);

    will result in

    {
 this => {that => undef}
}

    This behavior can be changed by setting optional second argument of floyd_warshall to a true value, i.e., calling floyd_warshall($graph, 1) with the above example hash will not remove that => {}.

For convenience, floyd_warshall returns $graph.

For further information refer to Algorithm::Graphs::TransitiveClosure.

AUTHOR

Abdul al Hazred, <451 at gmx.eu>

BUGS

Please report any bugs or feature requests to bug-algorithm-graphs-transitiveclosure-tiny at rt.cpan.org, or through the web interface at https://rt.cpan.org/NoAuth/ReportBug.html?Queue=Algorithm-Graphs-TransitiveClosure-Tiny. I will be notified, and then you'll automatically be notified of progress on your bug as I make changes.

SEE ALSO

Algorithm::Graphs::TransitiveClosure, Text::Table::Read::RelationOn::Tiny

SUPPORT

You can find documentation for this module with the perldoc command.

perldoc Algorithm::Graphs::TransitiveClosure::Tiny

You can also look for information at:

LICENSE AND COPYRIGHT

This software is copyright (c) 2022 by Abdul al Hazred.

This is free software; you can redistribute it and/or modify it under the same terms as the Perl 5 programming language system itself.