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Graph::UnionFind.3pm

NAME

Graph::UnionFind - union-find data structures

SYNOPSIS

     use Graph::UnionFind;
     my $uf = Graph::UnionFind->new;
 
     # Add the vertices to the data structure.
     $uf->add($u);
     $uf->add($v);
 
     # Join the partitions of the vertices.
     $uf->union( $u, $v );
 
     # Find the partitions the vertices belong to
     # in the union-find data structure.  If they
     # are equal, they are in the same partition.
     # If the vertex has not been seen,
     # undef is returned.
     my $pu = $uf->find( $u );
     my $pv = $uf->find( $v );
     $uf->same($u, $v) # Equal to $pu eq $pv. 
 
     # Has the union-find seen this vertex?
     $uf->has( $v )
 
 

DESCRIPTION

Union-find is a special data structure that can be used to track the partitioning of a set into subsets (a problem known also as disjoint sets).

Graph::UnionFind() is used for Graph::connected_components(), Graph::connected_component(), and Graph::same_connected_components() if you specify a true "union_find" parameter when you create an undirected graph.

Note that union-find is one way: you cannot (easily) 'ununion' vertices once you have 'unioned' them. This means that if you delete edges from a "union_find" graph, you will get wrong results from the Graph::connected_components(), Graph::connected_component(), and Graph::same_connected_components().

API

add

     $uf->add($v)
 
 

Add the vertex v to the union-find.

union

     $uf->union($u, $v)
 
 

Add the edge u-v to the union-find. Also implicitly adds the vertices.

has

     $uf->has($v)
 
 

Return true if the vertex v has been added to the union-find, false otherwise.

find

     $uf->find($v)
 
 

Return the union-find partition the vertex v belongs to, or "undef" if it has not been added.

new

     $uf = Graph::UnionFind->new()
 
 

The constructor.

same

     $uf->same($u, $v)
 
 

Return true of the vertices belong to the same union-find partition the vertex v belongs to, false otherwise.

AUTHOR AND COPYRIGHT

Jarkko Hietaniemi jhi@iki.fi

LICENSE

This module is licensed under the same terms as Perl itself.