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https://github.com/netwide-assembler/nasm.git
synced 2024-11-27 08:10:07 +08:00
3852 lines
85 KiB
Perl
3852 lines
85 KiB
Perl
package Graph;
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use strict;
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BEGIN {
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if (0) { # SET THIS TO ZERO FOR TESTING AND RELEASES!
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$SIG{__DIE__ } = \&__carp_confess;
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$SIG{__WARN__} = \&__carp_confess;
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}
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sub __carp_confess { require Carp; Carp::confess(@_) }
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}
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use Graph::AdjacencyMap qw(:flags :fields);
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use vars qw($VERSION);
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$VERSION = '0.84';
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require 5.006; # Weak references are absolutely required.
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use Graph::AdjacencyMap::Heavy;
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use Graph::AdjacencyMap::Light;
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use Graph::AdjacencyMap::Vertex;
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use Graph::UnionFind;
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use Graph::TransitiveClosure;
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use Graph::Traversal::DFS;
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use Graph::MSTHeapElem;
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use Graph::SPTHeapElem;
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use Graph::Undirected;
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use Heap071::Fibonacci;
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use List::Util qw(shuffle first);
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use Scalar::Util qw(weaken);
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sub _F () { 0 } # Flags.
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sub _G () { 1 } # Generation.
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sub _V () { 2 } # Vertices.
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sub _E () { 3 } # Edges.
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sub _A () { 4 } # Attributes.
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sub _U () { 5 } # Union-Find.
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my $Inf;
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BEGIN {
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local $SIG{FPE};
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eval { $Inf = exp(999) } ||
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eval { $Inf = 9**9**9 } ||
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eval { $Inf = 1e+999 } ||
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{ $Inf = 1e+99 }; # Close enough for most practical purposes.
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}
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sub Infinity () { $Inf }
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# Graphs are blessed array references.
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# - The first element contains the flags.
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# - The second element is the vertices.
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# - The third element is the edges.
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# - The fourth element is the attributes of the whole graph.
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# The defined flags for Graph are:
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# - _COMPAT02 for user API compatibility with the Graph 0.20xxx series.
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# The vertices are contained in either a "simplemap"
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# (if no hypervertices) or in a "map".
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# The edges are always in a "map".
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# The defined flags for maps are:
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# - _COUNT for countedness: more than one instance
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# - _HYPER for hyperness: a different number of "coordinates" than usual;
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# expects one for vertices and two for edges
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# - _UNORD for unordered coordinates (a set): if _UNORD is not set
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# the coordinates are assumed to be meaningfully ordered
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# - _UNIQ for unique coordinates: if set duplicates are removed,
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# if not, duplicates are assumed to meaningful
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# - _UNORDUNIQ: just a union of _UNORD and UNIQ
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# Vertices are assumed to be _UNORDUNIQ; edges assume none of these flags.
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use Graph::Attribute array => _A, map => 'graph';
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sub _COMPAT02 () { 0x00000001 }
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sub stringify {
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my $g = shift;
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my $o = $g->is_undirected;
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my $e = $o ? '=' : '-';
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my @e =
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map {
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my @v =
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map {
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ref($_) eq 'ARRAY' ? "[" . join(" ", @$_) . "]" : "$_"
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}
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@$_;
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join($e, $o ? sort { "$a" cmp "$b" } @v : @v) } $g->edges05;
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my @s = sort { "$a" cmp "$b" } @e;
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push @s, sort { "$a" cmp "$b" } $g->isolated_vertices;
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join(",", @s);
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}
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sub eq {
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"$_[0]" eq "$_[1]"
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}
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sub ne {
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"$_[0]" ne "$_[1]"
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}
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use overload
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'""' => \&stringify,
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'eq' => \&eq,
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'ne' => \≠
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sub _opt {
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my ($opt, $flags, %flags) = @_;
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while (my ($flag, $FLAG) = each %flags) {
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if (exists $opt->{$flag}) {
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$$flags |= $FLAG if $opt->{$flag};
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delete $opt->{$flag};
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}
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if (exists $opt->{my $non = "non$flag"}) {
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$$flags &= ~$FLAG if $opt->{$non};
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delete $opt->{$non};
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}
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}
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}
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sub is_compat02 {
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my ($g) = @_;
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$g->[ _F ] & _COMPAT02;
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}
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*compat02 = \&is_compat02;
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sub has_union_find {
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my ($g) = @_;
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($g->[ _F ] & _UNIONFIND) && defined $g->[ _U ];
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}
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sub _get_union_find {
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my ($g) = @_;
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$g->[ _U ];
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}
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sub _opt_get {
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my ($opt, $key, $var) = @_;
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if (exists $opt->{$key}) {
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$$var = $opt->{$key};
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delete $opt->{$key};
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}
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}
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sub _opt_unknown {
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my ($opt) = @_;
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if (my @opt = keys %$opt) {
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my $f = (caller(1))[3];
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require Carp;
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Carp::confess(sprintf
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"$f: Unknown option%s: @{[map { qq['$_'] } sort @opt]}",
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@opt > 1 ? 's' : '');
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}
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}
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sub new {
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my $class = shift;
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my $gflags = 0;
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my $vflags;
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my $eflags;
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my %opt = _get_options( \@_ );
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if (ref $class && $class->isa('Graph')) {
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no strict 'refs';
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for my $c (qw(undirected refvertexed compat02
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hypervertexed countvertexed multivertexed
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hyperedged countedged multiedged omniedged)) {
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# $opt{$c}++ if $class->$c; # 5.00504-incompatible
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if (&{"Graph::$c"}($class)) { $opt{$c}++ }
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}
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# $opt{unionfind}++ if $class->has_union_find; # 5.00504-incompatible
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if (&{"Graph::has_union_find"}($class)) { $opt{unionfind}++ }
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}
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_opt_get(\%opt, undirected => \$opt{omniedged});
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_opt_get(\%opt, omnidirected => \$opt{omniedged});
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if (exists $opt{directed}) {
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$opt{omniedged} = !$opt{directed};
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delete $opt{directed};
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}
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my $vnonomni =
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$opt{nonomnivertexed} ||
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(exists $opt{omnivertexed} && !$opt{omnivertexed});
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my $vnonuniq =
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$opt{nonuniqvertexed} ||
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(exists $opt{uniqvertexed} && !$opt{uniqvertexed});
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_opt(\%opt, \$vflags,
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countvertexed => _COUNT,
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multivertexed => _MULTI,
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hypervertexed => _HYPER,
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omnivertexed => _UNORD,
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uniqvertexed => _UNIQ,
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refvertexed => _REF,
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);
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_opt(\%opt, \$eflags,
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countedged => _COUNT,
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multiedged => _MULTI,
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hyperedged => _HYPER,
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omniedged => _UNORD,
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uniqedged => _UNIQ,
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);
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_opt(\%opt, \$gflags,
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compat02 => _COMPAT02,
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unionfind => _UNIONFIND,
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);
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if (exists $opt{vertices_unsorted}) { # Graph 0.20103 compat.
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my $unsorted = $opt{vertices_unsorted};
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delete $opt{vertices_unsorted};
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require Carp;
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Carp::confess("Graph: vertices_unsorted must be true")
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unless $unsorted;
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}
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my @V;
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if ($opt{vertices}) {
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require Carp;
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Carp::confess("Graph: vertices should be an array ref")
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unless ref $opt{vertices} eq 'ARRAY';
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@V = @{ $opt{vertices} };
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delete $opt{vertices};
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}
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my @E;
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if ($opt{edges}) {
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unless (ref $opt{edges} eq 'ARRAY') {
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require Carp;
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Carp::confess("Graph: edges should be an array ref of array refs");
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}
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@E = @{ $opt{edges} };
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delete $opt{edges};
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}
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_opt_unknown(\%opt);
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my $uflags;
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if (defined $vflags) {
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$uflags = $vflags;
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$uflags |= _UNORD unless $vnonomni;
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$uflags |= _UNIQ unless $vnonuniq;
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} else {
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$uflags = _UNORDUNIQ;
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$vflags = 0;
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}
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if (!($vflags & _HYPER) && ($vflags & _UNORDUNIQ)) {
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my @but;
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push @but, 'unordered' if ($vflags & _UNORD);
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push @but, 'unique' if ($vflags & _UNIQ);
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require Carp;
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Carp::confess(sprintf "Graph: not hypervertexed but %s",
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join(' and ', @but));
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}
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unless (defined $eflags) {
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$eflags = ($gflags & _COMPAT02) ? _COUNT : 0;
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}
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if (!($vflags & _HYPER) && ($vflags & _UNIQ)) {
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require Carp;
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Carp::confess("Graph: not hypervertexed but uniqvertexed");
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}
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if (($vflags & _COUNT) && ($vflags & _MULTI)) {
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require Carp;
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Carp::confess("Graph: both countvertexed and multivertexed");
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}
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if (($eflags & _COUNT) && ($eflags & _MULTI)) {
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require Carp;
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Carp::confess("Graph: both countedged and multiedged");
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}
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my $g = bless [ ], ref $class || $class;
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$g->[ _F ] = $gflags;
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$g->[ _G ] = 0;
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$g->[ _V ] = ($vflags & (_HYPER | _MULTI)) ?
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Graph::AdjacencyMap::Heavy->_new($uflags, 1) :
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(($vflags & ~_UNORD) ?
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Graph::AdjacencyMap::Vertex->_new($uflags, 1) :
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Graph::AdjacencyMap::Light->_new($g, $uflags, 1));
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$g->[ _E ] = (($vflags & _HYPER) || ($eflags & ~_UNORD)) ?
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Graph::AdjacencyMap::Heavy->_new($eflags, 2) :
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Graph::AdjacencyMap::Light->_new($g, $eflags, 2);
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$g->add_vertices(@V) if @V;
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if (@E) {
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for my $e (@E) {
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unless (ref $e eq 'ARRAY') {
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require Carp;
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Carp::confess("Graph: edges should be array refs");
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}
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$g->add_edge(@$e);
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}
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}
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if (($gflags & _UNIONFIND)) {
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$g->[ _U ] = Graph::UnionFind->new;
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}
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return $g;
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}
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sub countvertexed { $_[0]->[ _V ]->_is_COUNT }
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sub multivertexed { $_[0]->[ _V ]->_is_MULTI }
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sub hypervertexed { $_[0]->[ _V ]->_is_HYPER }
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sub omnivertexed { $_[0]->[ _V ]->_is_UNORD }
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sub uniqvertexed { $_[0]->[ _V ]->_is_UNIQ }
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sub refvertexed { $_[0]->[ _V ]->_is_REF }
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sub countedged { $_[0]->[ _E ]->_is_COUNT }
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sub multiedged { $_[0]->[ _E ]->_is_MULTI }
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sub hyperedged { $_[0]->[ _E ]->_is_HYPER }
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sub omniedged { $_[0]->[ _E ]->_is_UNORD }
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sub uniqedged { $_[0]->[ _E ]->_is_UNIQ }
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*undirected = \&omniedged;
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*omnidirected = \&omniedged;
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sub directed { ! $_[0]->[ _E ]->_is_UNORD }
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*is_directed = \&directed;
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*is_undirected = \&undirected;
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*is_countvertexed = \&countvertexed;
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*is_multivertexed = \&multivertexed;
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*is_hypervertexed = \&hypervertexed;
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*is_omnidirected = \&omnidirected;
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*is_uniqvertexed = \&uniqvertexed;
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*is_refvertexed = \&refvertexed;
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*is_countedged = \&countedged;
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*is_multiedged = \&multiedged;
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*is_hyperedged = \&hyperedged;
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*is_omniedged = \&omniedged;
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*is_uniqedged = \&uniqedged;
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sub _union_find_add_vertex {
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my ($g, $v) = @_;
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my $UF = $g->[ _U ];
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$UF->add( $g->[ _V ]->_get_path_id( $v ) );
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}
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sub add_vertex {
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my $g = shift;
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if ($g->is_multivertexed) {
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return $g->add_vertex_by_id(@_, _GEN_ID);
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}
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my @r;
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if (@_ > 1) {
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unless ($g->is_countvertexed || $g->is_hypervertexed) {
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require Carp;
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Carp::croak("Graph::add_vertex: use add_vertices for more than one vertex or use hypervertexed");
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}
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for my $v ( @_ ) {
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if (defined $v) {
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$g->[ _V ]->set_path( $v ) unless $g->has_vertex( $v );
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} else {
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require Carp;
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Carp::croak("Graph::add_vertex: undef vertex");
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}
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}
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}
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for my $v ( @_ ) {
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unless (defined $v) {
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require Carp;
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Carp::croak("Graph::add_vertex: undef vertex");
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}
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}
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$g->[ _V ]->set_path( @_ );
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$g->[ _G ]++;
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$g->_union_find_add_vertex( @_ ) if $g->has_union_find;
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return $g;
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}
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sub has_vertex {
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my $g = shift;
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my $V = $g->[ _V ];
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return exists $V->[ _s ]->{ $_[0] } if ($V->[ _f ] & _LIGHT);
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$V->has_path( @_ );
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}
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sub vertices05 {
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my $g = shift;
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my @v = $g->[ _V ]->paths( @_ );
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if (wantarray) {
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return $g->[ _V ]->_is_HYPER ?
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@v : map { ref $_ eq 'ARRAY' ? @$_ : $_ } @v;
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} else {
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return scalar @v;
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}
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}
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sub vertices {
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my $g = shift;
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my @v = $g->vertices05;
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if ($g->is_compat02) {
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wantarray ? sort @v : scalar @v;
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} else {
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if ($g->is_multivertexed || $g->is_countvertexed) {
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if (wantarray) {
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my @V;
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for my $v ( @v ) {
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push @V, ($v) x $g->get_vertex_count($v);
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}
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return @V;
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} else {
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my $V = 0;
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for my $v ( @v ) {
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$V += $g->get_vertex_count($v);
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}
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return $V;
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}
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} else {
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return @v;
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}
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}
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}
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*vertices_unsorted = \&vertices_unsorted; # Graph 0.20103 compat.
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sub unique_vertices {
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my $g = shift;
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my @v = $g->vertices05;
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if ($g->is_compat02) {
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wantarray ? sort @v : scalar @v;
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} else {
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return @v;
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}
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}
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sub has_vertices {
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my $g = shift;
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scalar $g->[ _V ]->has_paths( @_ );
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}
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sub _add_edge {
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my $g = shift;
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my $V = $g->[ _V ];
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my @e;
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if (($V->[ _f ]) & _LIGHT) {
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for my $v ( @_ ) {
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$g->add_vertex( $v ) unless exists $V->[ _s ]->{ $v };
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push @e, $V->[ _s ]->{ $v };
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}
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} else {
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my $h = $g->[ _V ]->_is_HYPER;
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for my $v ( @_ ) {
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my @v = ref $v eq 'ARRAY' && $h ? @$v : $v;
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$g->add_vertex( @v ) unless $V->has_path( @v );
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push @e, $V->_get_path_id( @v );
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}
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}
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return @e;
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}
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sub _union_find_add_edge {
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my ($g, $u, $v) = @_;
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$g->[ _U ]->union($u, $v);
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}
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sub add_edge {
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my $g = shift;
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if ($g->is_multiedged) {
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unless (@_ == 2 || $g->is_hyperedged) {
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require Carp;
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Carp::croak("Graph::add_edge: use add_edges for more than one edge");
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}
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return $g->add_edge_by_id(@_, _GEN_ID);
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}
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unless (@_ == 2) {
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unless ($g->is_hyperedged) {
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require Carp;
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Carp::croak("Graph::add_edge: graph is not hyperedged");
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}
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}
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my @e = $g->_add_edge( @_ );
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$g->[ _E ]->set_path( @e );
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$g->[ _G ]++;
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$g->_union_find_add_edge( @e ) if $g->has_union_find;
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return $g;
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}
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sub _vertex_ids {
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my $g = shift;
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my $V = $g->[ _V ];
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my @e;
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if (($V->[ _f ] & _LIGHT)) {
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for my $v ( @_ ) {
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return () unless exists $V->[ _s ]->{ $v };
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push @e, $V->[ _s ]->{ $v };
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}
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} else {
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my $h = $g->[ _V ]->_is_HYPER;
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for my $v ( @_ ) {
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my @v = ref $v eq 'ARRAY' && $h ? @$v : $v;
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return () unless $V->has_path( @v );
|
|
push @e, $V->_get_path_id( @v );
|
|
}
|
|
}
|
|
return @e;
|
|
}
|
|
|
|
sub has_edge {
|
|
my $g = shift;
|
|
my $E = $g->[ _E ];
|
|
my $V = $g->[ _V ];
|
|
my @i;
|
|
if (($V->[ _f ] & _LIGHT) && @_ == 2) {
|
|
return 0 unless
|
|
exists $V->[ _s ]->{ $_[0] } &&
|
|
exists $V->[ _s ]->{ $_[1] };
|
|
@i = @{ $V->[ _s ] }{ @_[ 0, 1 ] };
|
|
} else {
|
|
@i = $g->_vertex_ids( @_ );
|
|
return 0 if @i == 0 && @_;
|
|
}
|
|
my $f = $E->[ _f ];
|
|
if ($E->[ _a ] == 2 && @i == 2 && !($f & (_HYPER|_REF|_UNIQ))) { # Fast path.
|
|
@i = sort @i if ($f & _UNORD);
|
|
return exists $E->[ _s ]->{ $i[0] } &&
|
|
exists $E->[ _s ]->{ $i[0] }->{ $i[1] } ? 1 : 0;
|
|
} else {
|
|
return defined $E->_get_path_id( @i ) ? 1 : 0;
|
|
}
|
|
}
|
|
|
|
sub edges05 {
|
|
my $g = shift;
|
|
my $V = $g->[ _V ];
|
|
my @e = $g->[ _E ]->paths( @_ );
|
|
wantarray ?
|
|
map { [ map { my @v = $V->_get_id_path($_);
|
|
@v == 1 ? $v[0] : [ @v ] }
|
|
@$_ ] }
|
|
@e : @e;
|
|
}
|
|
|
|
sub edges02 {
|
|
my $g = shift;
|
|
if (@_ && defined $_[0]) {
|
|
unless (defined $_[1]) {
|
|
my @e = $g->edges_at($_[0]);
|
|
wantarray ?
|
|
map { @$_ }
|
|
sort { $a->[0] cmp $b->[0] || $a->[1] cmp $b->[1] } @e
|
|
: @e;
|
|
} else {
|
|
die "edges02: unimplemented option";
|
|
}
|
|
} else {
|
|
my @e = map { ($_) x $g->get_edge_count(@$_) } $g->edges05( @_ );
|
|
wantarray ?
|
|
map { @$_ }
|
|
sort { $a->[0] cmp $b->[0] || $a->[1] cmp $b->[1] } @e
|
|
: @e;
|
|
}
|
|
}
|
|
|
|
sub unique_edges {
|
|
my $g = shift;
|
|
($g->is_compat02) ? $g->edges02( @_ ) : $g->edges05( @_ );
|
|
}
|
|
|
|
sub edges {
|
|
my $g = shift;
|
|
if ($g->is_compat02) {
|
|
return $g->edges02( @_ );
|
|
} else {
|
|
if ($g->is_multiedged || $g->is_countedged) {
|
|
if (wantarray) {
|
|
my @E;
|
|
for my $e ( $g->edges05 ) {
|
|
push @E, ($e) x $g->get_edge_count(@$e);
|
|
}
|
|
return @E;
|
|
} else {
|
|
my $E = 0;
|
|
for my $e ( $g->edges05 ) {
|
|
$E += $g->get_edge_count(@$e);
|
|
}
|
|
return $E;
|
|
}
|
|
} else {
|
|
return $g->edges05;
|
|
}
|
|
}
|
|
}
|
|
|
|
sub has_edges {
|
|
my $g = shift;
|
|
scalar $g->[ _E ]->has_paths( @_ );
|
|
}
|
|
|
|
###
|
|
# by_id
|
|
#
|
|
|
|
sub add_vertex_by_id {
|
|
my $g = shift;
|
|
$g->expect_multivertexed;
|
|
$g->[ _V ]->set_path_by_multi_id( @_ );
|
|
$g->[ _G ]++;
|
|
$g->_union_find_add_vertex( @_ ) if $g->has_union_find;
|
|
return $g;
|
|
}
|
|
|
|
sub add_vertex_get_id {
|
|
my $g = shift;
|
|
$g->expect_multivertexed;
|
|
my $id = $g->[ _V ]->set_path_by_multi_id( @_, _GEN_ID );
|
|
$g->[ _G ]++;
|
|
$g->_union_find_add_vertex( @_ ) if $g->has_union_find;
|
|
return $id;
|
|
}
|
|
|
|
sub has_vertex_by_id {
|
|
my $g = shift;
|
|
$g->expect_multivertexed;
|
|
$g->[ _V ]->has_path_by_multi_id( @_ );
|
|
}
|
|
|
|
sub delete_vertex_by_id {
|
|
my $g = shift;
|
|
$g->expect_multivertexed;
|
|
my $V = $g->[ _V ];
|
|
return unless $V->has_path_by_multi_id( @_ );
|
|
# TODO: what to about the edges at this vertex?
|
|
# If the multiness of this vertex goes to zero, delete the edges?
|
|
$V->del_path_by_multi_id( @_ );
|
|
$g->[ _G ]++;
|
|
return $g;
|
|
}
|
|
|
|
sub get_multivertex_ids {
|
|
my $g = shift;
|
|
$g->expect_multivertexed;
|
|
$g->[ _V ]->get_multi_ids( @_ );
|
|
}
|
|
|
|
sub add_edge_by_id {
|
|
my $g = shift;
|
|
$g->expect_multiedged;
|
|
my $id = pop;
|
|
my @e = $g->_add_edge( @_ );
|
|
$g->[ _E ]->set_path( @e, $id );
|
|
$g->[ _G ]++;
|
|
$g->_union_find_add_edge( @e ) if $g->has_union_find;
|
|
return $g;
|
|
}
|
|
|
|
sub add_edge_get_id {
|
|
my $g = shift;
|
|
$g->expect_multiedged;
|
|
my @i = $g->_add_edge( @_ );
|
|
my $id = $g->[ _E ]->set_path_by_multi_id( @i, _GEN_ID );
|
|
$g->_union_find_add_edge( @i ) if $g->has_union_find;
|
|
$g->[ _G ]++;
|
|
return $id;
|
|
}
|
|
|
|
sub has_edge_by_id {
|
|
my $g = shift;
|
|
$g->expect_multiedged;
|
|
my $id = pop;
|
|
my @i = $g->_vertex_ids( @_ );
|
|
return 0 if @i == 0 && @_;
|
|
$g->[ _E ]->has_path_by_multi_id( @i, $id );
|
|
}
|
|
|
|
sub delete_edge_by_id {
|
|
my $g = shift;
|
|
$g->expect_multiedged;
|
|
my $V = $g->[ _E ];
|
|
my $id = pop;
|
|
my @i = $g->_vertex_ids( @_ );
|
|
return unless $V->has_path_by_multi_id( @i, $id );
|
|
$V->del_path_by_multi_id( @i, $id );
|
|
$g->[ _G ]++;
|
|
return $g;
|
|
}
|
|
|
|
sub get_multiedge_ids {
|
|
my $g = shift;
|
|
$g->expect_multiedged;
|
|
my @id = $g->_vertex_ids( @_ );
|
|
return unless @id;
|
|
$g->[ _E ]->get_multi_ids( @id );
|
|
}
|
|
|
|
###
|
|
# Neighbourhood.
|
|
#
|
|
|
|
sub vertices_at {
|
|
my $g = shift;
|
|
my $V = $g->[ _V ];
|
|
return @_ unless ($V->[ _f ] & _HYPER);
|
|
my %v;
|
|
my @i;
|
|
for my $v ( @_ ) {
|
|
my $i = $V->_get_path_id( $v );
|
|
return unless defined $i;
|
|
push @i, ( $v{ $v } = $i );
|
|
}
|
|
my $Vi = $V->_ids;
|
|
my @v;
|
|
while (my ($i, $v) = each %{ $Vi }) {
|
|
my %i;
|
|
my $h = $V->[_f ] & _HYPER;
|
|
@i{ @i } = @i if @i; # @todo: nonuniq hyper vertices?
|
|
for my $u (ref $v eq 'ARRAY' && $h ? @$v : $v) {
|
|
my $j = exists $v{ $u } ? $v{ $u } : ( $v{ $u } = $i );
|
|
if (defined $j && exists $i{ $j }) {
|
|
delete $i{ $j };
|
|
unless (keys %i) {
|
|
push @v, $v;
|
|
last;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
return @v;
|
|
}
|
|
|
|
sub _edges_at {
|
|
my $g = shift;
|
|
my $V = $g->[ _V ];
|
|
my $E = $g->[ _E ];
|
|
my @e;
|
|
my $en = 0;
|
|
my %ev;
|
|
my $h = $V->[_f ] & _HYPER;
|
|
for my $v ( $h ? $g->vertices_at( @_ ) : @_ ) {
|
|
my $vi = $V->_get_path_id( ref $v eq 'ARRAY' && $h ? @$v : $v );
|
|
next unless defined $vi;
|
|
my $Ei = $E->_ids;
|
|
while (my ($ei, $ev) = each %{ $Ei }) {
|
|
if (wantarray) {
|
|
for my $j (@$ev) {
|
|
push @e, [ $ei, $ev ]
|
|
if $j == $vi && !$ev{$ei}++;
|
|
}
|
|
} else {
|
|
for my $j (@$ev) {
|
|
$en++ if $j == $vi;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
return wantarray ? @e : $en;
|
|
}
|
|
|
|
sub _edges_from {
|
|
my $g = shift;
|
|
my $V = $g->[ _V ];
|
|
my $E = $g->[ _E ];
|
|
my @e;
|
|
my $o = $E->[ _f ] & _UNORD;
|
|
my $en = 0;
|
|
my %ev;
|
|
my $h = $V->[_f ] & _HYPER;
|
|
for my $v ( $h ? $g->vertices_at( @_ ) : @_ ) {
|
|
my $vi = $V->_get_path_id( ref $v eq 'ARRAY' && $h ? @$v : $v );
|
|
next unless defined $vi;
|
|
my $Ei = $E->_ids;
|
|
if (wantarray) {
|
|
if ($o) {
|
|
while (my ($ei, $ev) = each %{ $Ei }) {
|
|
next unless @$ev;
|
|
push @e, [ $ei, $ev ]
|
|
if ($ev->[0] == $vi || $ev->[-1] == $vi) && !$ev{$ei}++;
|
|
}
|
|
} else {
|
|
while (my ($ei, $ev) = each %{ $Ei }) {
|
|
next unless @$ev;
|
|
push @e, [ $ei, $ev ]
|
|
if $ev->[0] == $vi && !$ev{$ei}++;
|
|
}
|
|
}
|
|
} else {
|
|
if ($o) {
|
|
while (my ($ei, $ev) = each %{ $Ei }) {
|
|
next unless @$ev;
|
|
$en++ if ($ev->[0] == $vi || $ev->[-1] == $vi);
|
|
}
|
|
} else {
|
|
while (my ($ei, $ev) = each %{ $Ei }) {
|
|
next unless @$ev;
|
|
$en++ if $ev->[0] == $vi;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
if (wantarray && $g->is_undirected) {
|
|
my @i = map { $V->_get_path_id( $_ ) } @_;
|
|
for my $e ( @e ) {
|
|
unless ( $e->[ 1 ]->[ 0 ] == $i[ 0 ] ) { # @todo
|
|
$e = [ $e->[ 0 ], [ reverse @{ $e->[ 1 ] } ] ];
|
|
}
|
|
}
|
|
}
|
|
return wantarray ? @e : $en;
|
|
}
|
|
|
|
sub _edges_to {
|
|
my $g = shift;
|
|
my $V = $g->[ _V ];
|
|
my $E = $g->[ _E ];
|
|
my @e;
|
|
my $o = $E->[ _f ] & _UNORD;
|
|
my $en = 0;
|
|
my %ev;
|
|
my $h = $V->[_f ] & _HYPER;
|
|
for my $v ( $h ? $g->vertices_at( @_ ) : @_ ) {
|
|
my $vi = $V->_get_path_id( ref $v eq 'ARRAY' && $h ? @$v : $v );
|
|
next unless defined $vi;
|
|
my $Ei = $E->_ids;
|
|
if (wantarray) {
|
|
if ($o) {
|
|
while (my ($ei, $ev) = each %{ $Ei }) {
|
|
next unless @$ev;
|
|
push @e, [ $ei, $ev ]
|
|
if ($ev->[-1] == $vi || $ev->[0] == $vi) && !$ev{$ei}++;
|
|
}
|
|
} else {
|
|
while (my ($ei, $ev) = each %{ $Ei }) {
|
|
next unless @$ev;
|
|
push @e, [ $ei, $ev ]
|
|
if $ev->[-1] == $vi && !$ev{$ei}++;
|
|
}
|
|
}
|
|
} else {
|
|
if ($o) {
|
|
while (my ($ei, $ev) = each %{ $Ei }) {
|
|
next unless @$ev;
|
|
$en++ if $ev->[-1] == $vi || $ev->[0] == $vi;
|
|
}
|
|
} else {
|
|
while (my ($ei, $ev) = each %{ $Ei }) {
|
|
next unless @$ev;
|
|
$en++ if $ev->[-1] == $vi;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
if (wantarray && $g->is_undirected) {
|
|
my @i = map { $V->_get_path_id( $_ ) } @_;
|
|
for my $e ( @e ) {
|
|
unless ( $e->[ 1 ]->[ -1 ] == $i[ -1 ] ) { # @todo
|
|
$e = [ $e->[ 0 ], [ reverse @{ $e->[ 1 ] } ] ];
|
|
}
|
|
}
|
|
}
|
|
return wantarray ? @e : $en;
|
|
}
|
|
|
|
sub _edges_id_path {
|
|
my $g = shift;
|
|
my $V = $g->[ _V ];
|
|
[ map { my @v = $V->_get_id_path($_);
|
|
@v == 1 ? $v[0] : [ @v ] }
|
|
@{ $_[0]->[1] } ];
|
|
}
|
|
|
|
sub edges_at {
|
|
my $g = shift;
|
|
map { $g->_edges_id_path($_ ) } $g->_edges_at( @_ );
|
|
}
|
|
|
|
sub edges_from {
|
|
my $g = shift;
|
|
map { $g->_edges_id_path($_ ) } $g->_edges_from( @_ );
|
|
}
|
|
|
|
sub edges_to {
|
|
my $g = shift;
|
|
map { $g->_edges_id_path($_ ) } $g->_edges_to( @_ );
|
|
}
|
|
|
|
sub successors {
|
|
my $g = shift;
|
|
my $E = $g->[ _E ];
|
|
($E->[ _f ] & _LIGHT) ?
|
|
$E->_successors($g, @_) :
|
|
Graph::AdjacencyMap::_successors($E, $g, @_);
|
|
}
|
|
|
|
sub predecessors {
|
|
my $g = shift;
|
|
my $E = $g->[ _E ];
|
|
($E->[ _f ] & _LIGHT) ?
|
|
$E->_predecessors($g, @_) :
|
|
Graph::AdjacencyMap::_predecessors($E, $g, @_);
|
|
}
|
|
|
|
sub neighbours {
|
|
my $g = shift;
|
|
my $V = $g->[ _V ];
|
|
my @s = map { my @v = @{ $_->[ 1 ] }; shift @v; @v } $g->_edges_from( @_ );
|
|
my @p = map { my @v = @{ $_->[ 1 ] }; pop @v; @v } $g->_edges_to ( @_ );
|
|
my %n;
|
|
@n{ @s } = @s;
|
|
@n{ @p } = @p;
|
|
map { $V->_get_id_path($_) } keys %n;
|
|
}
|
|
|
|
*neighbors = \&neighbours;
|
|
|
|
sub delete_edge {
|
|
my $g = shift;
|
|
my @i = $g->_vertex_ids( @_ );
|
|
return $g unless @i;
|
|
my $i = $g->[ _E ]->_get_path_id( @i );
|
|
return $g unless defined $i;
|
|
$g->[ _E ]->_del_id( $i );
|
|
$g->[ _G ]++;
|
|
return $g;
|
|
}
|
|
|
|
sub delete_vertex {
|
|
my $g = shift;
|
|
my $V = $g->[ _V ];
|
|
return $g unless $V->has_path( @_ );
|
|
my $E = $g->[ _E ];
|
|
for my $e ( $g->_edges_at( @_ ) ) {
|
|
$E->_del_id( $e->[ 0 ] );
|
|
}
|
|
$V->del_path( @_ );
|
|
$g->[ _G ]++;
|
|
return $g;
|
|
}
|
|
|
|
sub get_vertex_count {
|
|
my $g = shift;
|
|
$g->[ _V ]->_get_path_count( @_ ) || 0;
|
|
}
|
|
|
|
sub get_edge_count {
|
|
my $g = shift;
|
|
my @e = $g->_vertex_ids( @_ );
|
|
return 0 unless @e;
|
|
$g->[ _E ]->_get_path_count( @e ) || 0;
|
|
}
|
|
|
|
sub delete_vertices {
|
|
my $g = shift;
|
|
while (@_) {
|
|
my $v = shift @_;
|
|
$g->delete_vertex($v);
|
|
}
|
|
return $g;
|
|
}
|
|
|
|
sub delete_edges {
|
|
my $g = shift;
|
|
while (@_) {
|
|
my ($u, $v) = splice @_, 0, 2;
|
|
$g->delete_edge($u, $v);
|
|
}
|
|
return $g;
|
|
}
|
|
|
|
###
|
|
# Degrees.
|
|
#
|
|
|
|
sub _in_degree {
|
|
my $g = shift;
|
|
return undef unless @_ && $g->has_vertex( @_ );
|
|
my $in = $g->is_undirected && $g->is_self_loop_vertex( @_ ) ? 1 : 0;
|
|
$in += $g->get_edge_count( @$_ ) for $g->edges_to( @_ );
|
|
return $in;
|
|
}
|
|
|
|
sub in_degree {
|
|
my $g = shift;
|
|
$g->_in_degree( @_ );
|
|
}
|
|
|
|
sub _out_degree {
|
|
my $g = shift;
|
|
return undef unless @_ && $g->has_vertex( @_ );
|
|
my $out = $g->is_undirected && $g->is_self_loop_vertex( @_ ) ? 1 : 0;
|
|
$out += $g->get_edge_count( @$_ ) for $g->edges_from( @_ );
|
|
return $out;
|
|
}
|
|
|
|
sub out_degree {
|
|
my $g = shift;
|
|
$g->_out_degree( @_ );
|
|
}
|
|
|
|
sub _total_degree {
|
|
my $g = shift;
|
|
return undef unless @_ && $g->has_vertex( @_ );
|
|
$g->is_undirected ?
|
|
$g->_in_degree( @_ ) :
|
|
$g-> in_degree( @_ ) - $g-> out_degree( @_ );
|
|
}
|
|
|
|
sub degree {
|
|
my $g = shift;
|
|
if (@_) {
|
|
$g->_total_degree( @_ );
|
|
} else {
|
|
if ($g->is_undirected) {
|
|
my $total = 0;
|
|
$total += $g->_total_degree( $_ ) for $g->vertices05;
|
|
return $total;
|
|
} else {
|
|
return 0;
|
|
}
|
|
}
|
|
}
|
|
|
|
*vertex_degree = \°ree;
|
|
|
|
sub is_sink_vertex {
|
|
my $g = shift;
|
|
return 0 unless @_;
|
|
$g->successors( @_ ) == 0 && $g->predecessors( @_ ) > 0;
|
|
}
|
|
|
|
sub is_source_vertex {
|
|
my $g = shift;
|
|
return 0 unless @_;
|
|
$g->predecessors( @_ ) == 0 && $g->successors( @_ ) > 0;
|
|
}
|
|
|
|
sub is_successorless_vertex {
|
|
my $g = shift;
|
|
return 0 unless @_;
|
|
$g->successors( @_ ) == 0;
|
|
}
|
|
|
|
sub is_predecessorless_vertex {
|
|
my $g = shift;
|
|
return 0 unless @_;
|
|
$g->predecessors( @_ ) == 0;
|
|
}
|
|
|
|
sub is_successorful_vertex {
|
|
my $g = shift;
|
|
return 0 unless @_;
|
|
$g->successors( @_ ) > 0;
|
|
}
|
|
|
|
sub is_predecessorful_vertex {
|
|
my $g = shift;
|
|
return 0 unless @_;
|
|
$g->predecessors( @_ ) > 0;
|
|
}
|
|
|
|
sub is_isolated_vertex {
|
|
my $g = shift;
|
|
return 0 unless @_;
|
|
$g->predecessors( @_ ) == 0 && $g->successors( @_ ) == 0;
|
|
}
|
|
|
|
sub is_interior_vertex {
|
|
my $g = shift;
|
|
return 0 unless @_;
|
|
my $p = $g->predecessors( @_ );
|
|
my $s = $g->successors( @_ );
|
|
if ($g->is_self_loop_vertex( @_ )) {
|
|
$p--;
|
|
$s--;
|
|
}
|
|
$p > 0 && $s > 0;
|
|
}
|
|
|
|
sub is_exterior_vertex {
|
|
my $g = shift;
|
|
return 0 unless @_;
|
|
$g->predecessors( @_ ) == 0 || $g->successors( @_ ) == 0;
|
|
}
|
|
|
|
sub is_self_loop_vertex {
|
|
my $g = shift;
|
|
return 0 unless @_;
|
|
for my $s ( $g->successors( @_ ) ) {
|
|
return 1 if $s eq $_[0]; # @todo: hypervertices
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
sub sink_vertices {
|
|
my $g = shift;
|
|
grep { $g->is_sink_vertex($_) } $g->vertices05;
|
|
}
|
|
|
|
sub source_vertices {
|
|
my $g = shift;
|
|
grep { $g->is_source_vertex($_) } $g->vertices05;
|
|
}
|
|
|
|
sub successorless_vertices {
|
|
my $g = shift;
|
|
grep { $g->is_successorless_vertex($_) } $g->vertices05;
|
|
}
|
|
|
|
sub predecessorless_vertices {
|
|
my $g = shift;
|
|
grep { $g->is_predecessorless_vertex($_) } $g->vertices05;
|
|
}
|
|
|
|
sub successorful_vertices {
|
|
my $g = shift;
|
|
grep { $g->is_successorful_vertex($_) } $g->vertices05;
|
|
}
|
|
|
|
sub predecessorful_vertices {
|
|
my $g = shift;
|
|
grep { $g->is_predecessorful_vertex($_) } $g->vertices05;
|
|
}
|
|
|
|
sub isolated_vertices {
|
|
my $g = shift;
|
|
grep { $g->is_isolated_vertex($_) } $g->vertices05;
|
|
}
|
|
|
|
sub interior_vertices {
|
|
my $g = shift;
|
|
grep { $g->is_interior_vertex($_) } $g->vertices05;
|
|
}
|
|
|
|
sub exterior_vertices {
|
|
my $g = shift;
|
|
grep { $g->is_exterior_vertex($_) } $g->vertices05;
|
|
}
|
|
|
|
sub self_loop_vertices {
|
|
my $g = shift;
|
|
grep { $g->is_self_loop_vertex($_) } $g->vertices05;
|
|
}
|
|
|
|
###
|
|
# Paths and cycles.
|
|
#
|
|
|
|
sub add_path {
|
|
my $g = shift;
|
|
my $u = shift;
|
|
while (@_) {
|
|
my $v = shift;
|
|
$g->add_edge($u, $v);
|
|
$u = $v;
|
|
}
|
|
return $g;
|
|
}
|
|
|
|
sub delete_path {
|
|
my $g = shift;
|
|
my $u = shift;
|
|
while (@_) {
|
|
my $v = shift;
|
|
$g->delete_edge($u, $v);
|
|
$u = $v;
|
|
}
|
|
return $g;
|
|
}
|
|
|
|
sub has_path {
|
|
my $g = shift;
|
|
my $u = shift;
|
|
while (@_) {
|
|
my $v = shift;
|
|
return 0 unless $g->has_edge($u, $v);
|
|
$u = $v;
|
|
}
|
|
return $g;
|
|
}
|
|
|
|
sub add_cycle {
|
|
my $g = shift;
|
|
$g->add_path(@_, $_[0]);
|
|
}
|
|
|
|
sub delete_cycle {
|
|
my $g = shift;
|
|
$g->delete_path(@_, $_[0]);
|
|
}
|
|
|
|
sub has_cycle {
|
|
my $g = shift;
|
|
@_ ? ($g->has_path(@_, $_[0]) ? 1 : 0) : 0;
|
|
}
|
|
|
|
sub has_a_cycle {
|
|
my $g = shift;
|
|
my @r = ( back_edge => \&Graph::Traversal::has_a_cycle );
|
|
push @r,
|
|
down_edge => \&Graph::Traversal::has_a_cycle
|
|
if $g->is_undirected;
|
|
my $t = Graph::Traversal::DFS->new($g, @r, @_);
|
|
$t->dfs;
|
|
return $t->get_state('has_a_cycle');
|
|
}
|
|
|
|
sub find_a_cycle {
|
|
my $g = shift;
|
|
my @r = ( back_edge => \&Graph::Traversal::find_a_cycle);
|
|
push @r,
|
|
down_edge => \&Graph::Traversal::find_a_cycle
|
|
if $g->is_undirected;
|
|
my $t = Graph::Traversal::DFS->new($g, @r, @_);
|
|
$t->dfs;
|
|
$t->has_state('a_cycle') ? @{ $t->get_state('a_cycle') } : ();
|
|
}
|
|
|
|
###
|
|
# Attributes.
|
|
|
|
# Vertex attributes.
|
|
|
|
sub set_vertex_attribute {
|
|
my $g = shift;
|
|
$g->expect_non_multivertexed;
|
|
my $value = pop;
|
|
my $attr = pop;
|
|
$g->add_vertex( @_ ) unless $g->has_vertex( @_ );
|
|
$g->[ _V ]->_set_path_attr( @_, $attr, $value );
|
|
}
|
|
|
|
sub set_vertex_attribute_by_id {
|
|
my $g = shift;
|
|
$g->expect_multivertexed;
|
|
my $value = pop;
|
|
my $attr = pop;
|
|
$g->add_vertex_by_id( @_ ) unless $g->has_vertex_by_id( @_ );
|
|
$g->[ _V ]->_set_path_attr( @_, $attr, $value );
|
|
}
|
|
|
|
sub set_vertex_attributes {
|
|
my $g = shift;
|
|
$g->expect_non_multivertexed;
|
|
my $attr = pop;
|
|
$g->add_vertex( @_ ) unless $g->has_vertex( @_ );
|
|
$g->[ _V ]->_set_path_attrs( @_, $attr );
|
|
}
|
|
|
|
sub set_vertex_attributes_by_id {
|
|
my $g = shift;
|
|
$g->expect_multivertexed;
|
|
my $attr = pop;
|
|
$g->add_vertex_by_id( @_ ) unless $g->has_vertex_by_id( @_ );
|
|
$g->[ _V ]->_set_path_attrs( @_, $attr );
|
|
}
|
|
|
|
sub has_vertex_attributes {
|
|
my $g = shift;
|
|
$g->expect_non_multivertexed;
|
|
return 0 unless $g->has_vertex( @_ );
|
|
$g->[ _V ]->_has_path_attrs( @_ );
|
|
}
|
|
|
|
sub has_vertex_attributes_by_id {
|
|
my $g = shift;
|
|
$g->expect_multivertexed;
|
|
return 0 unless $g->has_vertex_by_id( @_ );
|
|
$g->[ _V ]->_has_path_attrs( @_ );
|
|
}
|
|
|
|
sub has_vertex_attribute {
|
|
my $g = shift;
|
|
$g->expect_non_multivertexed;
|
|
my $attr = pop;
|
|
return 0 unless $g->has_vertex( @_ );
|
|
$g->[ _V ]->_has_path_attr( @_, $attr );
|
|
}
|
|
|
|
sub has_vertex_attribute_by_id {
|
|
my $g = shift;
|
|
$g->expect_multivertexed;
|
|
my $attr = pop;
|
|
return 0 unless $g->has_vertex_by_id( @_ );
|
|
$g->[ _V ]->_has_path_attr( @_, $attr );
|
|
}
|
|
|
|
sub get_vertex_attributes {
|
|
my $g = shift;
|
|
$g->expect_non_multivertexed;
|
|
return unless $g->has_vertex( @_ );
|
|
my $a = $g->[ _V ]->_get_path_attrs( @_ );
|
|
($g->is_compat02) ? (defined $a ? %{ $a } : ()) : $a;
|
|
}
|
|
|
|
sub get_vertex_attributes_by_id {
|
|
my $g = shift;
|
|
$g->expect_multivertexed;
|
|
return unless $g->has_vertex_by_id( @_ );
|
|
$g->[ _V ]->_get_path_attrs( @_ );
|
|
}
|
|
|
|
sub get_vertex_attribute {
|
|
my $g = shift;
|
|
$g->expect_non_multivertexed;
|
|
my $attr = pop;
|
|
return unless $g->has_vertex( @_ );
|
|
$g->[ _V ]->_get_path_attr( @_, $attr );
|
|
}
|
|
|
|
sub get_vertex_attribute_by_id {
|
|
my $g = shift;
|
|
$g->expect_multivertexed;
|
|
my $attr = pop;
|
|
return unless $g->has_vertex_by_id( @_ );
|
|
$g->[ _V ]->_get_path_attr( @_, $attr );
|
|
}
|
|
|
|
sub get_vertex_attribute_names {
|
|
my $g = shift;
|
|
$g->expect_non_multivertexed;
|
|
return unless $g->has_vertex( @_ );
|
|
$g->[ _V ]->_get_path_attr_names( @_ );
|
|
}
|
|
|
|
sub get_vertex_attribute_names_by_id {
|
|
my $g = shift;
|
|
$g->expect_multivertexed;
|
|
return unless $g->has_vertex_by_id( @_ );
|
|
$g->[ _V ]->_get_path_attr_names( @_ );
|
|
}
|
|
|
|
sub get_vertex_attribute_values {
|
|
my $g = shift;
|
|
$g->expect_non_multivertexed;
|
|
return unless $g->has_vertex( @_ );
|
|
$g->[ _V ]->_get_path_attr_values( @_ );
|
|
}
|
|
|
|
sub get_vertex_attribute_values_by_id {
|
|
my $g = shift;
|
|
$g->expect_multivertexed;
|
|
return unless $g->has_vertex_by_id( @_ );
|
|
$g->[ _V ]->_get_path_attr_values( @_ );
|
|
}
|
|
|
|
sub delete_vertex_attributes {
|
|
my $g = shift;
|
|
$g->expect_non_multivertexed;
|
|
return undef unless $g->has_vertex( @_ );
|
|
$g->[ _V ]->_del_path_attrs( @_ );
|
|
}
|
|
|
|
sub delete_vertex_attributes_by_id {
|
|
my $g = shift;
|
|
$g->expect_multivertexed;
|
|
return undef unless $g->has_vertex_by_id( @_ );
|
|
$g->[ _V ]->_del_path_attrs( @_ );
|
|
}
|
|
|
|
sub delete_vertex_attribute {
|
|
my $g = shift;
|
|
$g->expect_non_multivertexed;
|
|
my $attr = pop;
|
|
return undef unless $g->has_vertex( @_ );
|
|
$g->[ _V ]->_del_path_attr( @_, $attr );
|
|
}
|
|
|
|
sub delete_vertex_attribute_by_id {
|
|
my $g = shift;
|
|
$g->expect_multivertexed;
|
|
my $attr = pop;
|
|
return undef unless $g->has_vertex_by_id( @_ );
|
|
$g->[ _V ]->_del_path_attr( @_, $attr );
|
|
}
|
|
|
|
# Edge attributes.
|
|
|
|
sub _set_edge_attribute {
|
|
my $g = shift;
|
|
my $value = pop;
|
|
my $attr = pop;
|
|
my $E = $g->[ _E ];
|
|
my $f = $E->[ _f ];
|
|
my @i;
|
|
if ($E->[ _a ] == 2 && @_ == 2 && !($f & (_HYPER|_REF|_UNIQ))) { # Fast path.
|
|
@_ = sort @_ if ($f & _UNORD);
|
|
my $s = $E->[ _s ];
|
|
$g->add_edge( @_ ) unless exists $s->{ $_[0] } && exists $s->{ $_[0] }->{ $_[1] };
|
|
@i = @{ $g->[ _V ]->[ _s ] }{ @_ };
|
|
} else {
|
|
$g->add_edge( @_ ) unless $g->has_edge( @_ );
|
|
@i = $g->_vertex_ids( @_ );
|
|
}
|
|
$g->[ _E ]->_set_path_attr( @i, $attr, $value );
|
|
}
|
|
|
|
sub set_edge_attribute {
|
|
my $g = shift;
|
|
$g->expect_non_multiedged;
|
|
my $value = pop;
|
|
my $attr = pop;
|
|
my $E = $g->[ _E ];
|
|
$g->add_edge( @_ ) unless $g->has_edge( @_ );
|
|
$E->_set_path_attr( $g->_vertex_ids( @_ ), $attr, $value );
|
|
}
|
|
|
|
sub set_edge_attribute_by_id {
|
|
my $g = shift;
|
|
$g->expect_multiedged;
|
|
my $value = pop;
|
|
my $attr = pop;
|
|
# $g->add_edge_by_id( @_ ) unless $g->has_edge_by_id( @_ );
|
|
my $id = pop;
|
|
$g->[ _E ]->_set_path_attr( $g->_vertex_ids( @_ ), $id, $attr, $value );
|
|
}
|
|
|
|
sub set_edge_attributes {
|
|
my $g = shift;
|
|
$g->expect_non_multiedged;
|
|
my $attr = pop;
|
|
$g->add_edge( @_ ) unless $g->has_edge( @_ );
|
|
$g->[ _E ]->_set_path_attrs( $g->_vertex_ids( @_ ), $attr );
|
|
}
|
|
|
|
sub set_edge_attributes_by_id {
|
|
my $g = shift;
|
|
$g->expect_multiedged;
|
|
my $attr = pop;
|
|
$g->add_edge_by_id( @_ ) unless $g->has_edge_by_id( @_ );
|
|
my $id = pop;
|
|
$g->[ _E ]->_set_path_attrs( $g->_vertex_ids( @_ ), $id, $attr );
|
|
}
|
|
|
|
sub has_edge_attributes {
|
|
my $g = shift;
|
|
$g->expect_non_multiedged;
|
|
return 0 unless $g->has_edge( @_ );
|
|
$g->[ _E ]->_has_path_attrs( $g->_vertex_ids( @_ ) );
|
|
}
|
|
|
|
sub has_edge_attributes_by_id {
|
|
my $g = shift;
|
|
$g->expect_multiedged;
|
|
return 0 unless $g->has_edge_by_id( @_ );
|
|
my $id = pop;
|
|
$g->[ _E ]->_has_path_attrs( $g->_vertex_ids( @_ ), $id );
|
|
}
|
|
|
|
sub has_edge_attribute {
|
|
my $g = shift;
|
|
$g->expect_non_multiedged;
|
|
my $attr = pop;
|
|
return 0 unless $g->has_edge( @_ );
|
|
$g->[ _E ]->_has_path_attr( $g->_vertex_ids( @_ ), $attr );
|
|
}
|
|
|
|
sub has_edge_attribute_by_id {
|
|
my $g = shift;
|
|
$g->expect_multiedged;
|
|
my $attr = pop;
|
|
return 0 unless $g->has_edge_by_id( @_ );
|
|
my $id = pop;
|
|
$g->[ _E ]->_has_path_attr( $g->_vertex_ids( @_ ), $id, $attr );
|
|
}
|
|
|
|
sub get_edge_attributes {
|
|
my $g = shift;
|
|
$g->expect_non_multiedged;
|
|
return unless $g->has_edge( @_ );
|
|
my $a = $g->[ _E ]->_get_path_attrs( $g->_vertex_ids( @_ ) );
|
|
($g->is_compat02) ? (defined $a ? %{ $a } : ()) : $a;
|
|
}
|
|
|
|
sub get_edge_attributes_by_id {
|
|
my $g = shift;
|
|
$g->expect_multiedged;
|
|
return unless $g->has_edge_by_id( @_ );
|
|
my $id = pop;
|
|
return $g->[ _E ]->_get_path_attrs( $g->_vertex_ids( @_ ), $id );
|
|
}
|
|
|
|
sub _get_edge_attribute { # Fast path; less checks.
|
|
my $g = shift;
|
|
my $attr = pop;
|
|
my $E = $g->[ _E ];
|
|
my $f = $E->[ _f ];
|
|
if ($E->[ _a ] == 2 && @_ == 2 && !($f & (_HYPER|_REF|_UNIQ))) { # Fast path.
|
|
@_ = sort @_ if ($f & _UNORD);
|
|
my $s = $E->[ _s ];
|
|
return unless exists $s->{ $_[0] } && exists $s->{ $_[0] }->{ $_[1] };
|
|
} else {
|
|
return unless $g->has_edge( @_ );
|
|
}
|
|
my @i = $g->_vertex_ids( @_ );
|
|
$E->_get_path_attr( @i, $attr );
|
|
}
|
|
|
|
sub get_edge_attribute {
|
|
my $g = shift;
|
|
$g->expect_non_multiedged;
|
|
my $attr = pop;
|
|
return undef unless $g->has_edge( @_ );
|
|
my @i = $g->_vertex_ids( @_ );
|
|
return undef if @i == 0 && @_;
|
|
my $E = $g->[ _E ];
|
|
$E->_get_path_attr( @i, $attr );
|
|
}
|
|
|
|
sub get_edge_attribute_by_id {
|
|
my $g = shift;
|
|
$g->expect_multiedged;
|
|
my $attr = pop;
|
|
return unless $g->has_edge_by_id( @_ );
|
|
my $id = pop;
|
|
$g->[ _E ]->_get_path_attr( $g->_vertex_ids( @_ ), $id, $attr );
|
|
}
|
|
|
|
sub get_edge_attribute_names {
|
|
my $g = shift;
|
|
$g->expect_non_multiedged;
|
|
return unless $g->has_edge( @_ );
|
|
$g->[ _E ]->_get_path_attr_names( $g->_vertex_ids( @_ ) );
|
|
}
|
|
|
|
sub get_edge_attribute_names_by_id {
|
|
my $g = shift;
|
|
$g->expect_multiedged;
|
|
return unless $g->has_edge_by_id( @_ );
|
|
my $id = pop;
|
|
$g->[ _E ]->_get_path_attr_names( $g->_vertex_ids( @_ ), $id );
|
|
}
|
|
|
|
sub get_edge_attribute_values {
|
|
my $g = shift;
|
|
$g->expect_non_multiedged;
|
|
return unless $g->has_edge( @_ );
|
|
$g->[ _E ]->_get_path_attr_values( $g->_vertex_ids( @_ ) );
|
|
}
|
|
|
|
sub get_edge_attribute_values_by_id {
|
|
my $g = shift;
|
|
$g->expect_multiedged;
|
|
return unless $g->has_edge_by_id( @_ );
|
|
my $id = pop;
|
|
$g->[ _E ]->_get_path_attr_values( $g->_vertex_ids( @_ ), $id );
|
|
}
|
|
|
|
sub delete_edge_attributes {
|
|
my $g = shift;
|
|
$g->expect_non_multiedged;
|
|
return unless $g->has_edge( @_ );
|
|
$g->[ _E ]->_del_path_attrs( $g->_vertex_ids( @_ ) );
|
|
}
|
|
|
|
sub delete_edge_attributes_by_id {
|
|
my $g = shift;
|
|
$g->expect_multiedged;
|
|
return unless $g->has_edge_by_id( @_ );
|
|
my $id = pop;
|
|
$g->[ _E ]->_del_path_attrs( $g->_vertex_ids( @_ ), $id );
|
|
}
|
|
|
|
sub delete_edge_attribute {
|
|
my $g = shift;
|
|
$g->expect_non_multiedged;
|
|
my $attr = pop;
|
|
return unless $g->has_edge( @_ );
|
|
$g->[ _E ]->_del_path_attr( $g->_vertex_ids( @_ ), $attr );
|
|
}
|
|
|
|
sub delete_edge_attribute_by_id {
|
|
my $g = shift;
|
|
$g->expect_multiedged;
|
|
my $attr = pop;
|
|
return unless $g->has_edge_by_id( @_ );
|
|
my $id = pop;
|
|
$g->[ _E ]->_del_path_attr( $g->_vertex_ids( @_ ), $id, $attr );
|
|
}
|
|
|
|
###
|
|
# Compat.
|
|
#
|
|
|
|
sub vertex {
|
|
my $g = shift;
|
|
$g->has_vertex( @_ ) ? @_ : undef;
|
|
}
|
|
|
|
sub out_edges {
|
|
my $g = shift;
|
|
return unless @_ && $g->has_vertex( @_ );
|
|
my @e = $g->edges_from( @_ );
|
|
wantarray ? map { @$_ } @e : @e;
|
|
}
|
|
|
|
sub in_edges {
|
|
my $g = shift;
|
|
return unless @_ && $g->has_vertex( @_ );
|
|
my @e = $g->edges_to( @_ );
|
|
wantarray ? map { @$_ } @e : @e;
|
|
}
|
|
|
|
sub add_vertices {
|
|
my $g = shift;
|
|
$g->add_vertex( $_ ) for @_;
|
|
}
|
|
|
|
sub add_edges {
|
|
my $g = shift;
|
|
while (@_) {
|
|
my $u = shift @_;
|
|
if (ref $u eq 'ARRAY') {
|
|
$g->add_edge( @$u );
|
|
} else {
|
|
if (@_) {
|
|
my $v = shift @_;
|
|
$g->add_edge( $u, $v );
|
|
} else {
|
|
require Carp;
|
|
Carp::croak("Graph::add_edges: missing end vertex");
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
###
|
|
# More constructors.
|
|
#
|
|
|
|
sub copy {
|
|
my $g = shift;
|
|
my %opt = _get_options( \@_ );
|
|
|
|
my $c = (ref $g)->new(directed => $g->directed ? 1 : 0,
|
|
compat02 => $g->compat02 ? 1 : 0);
|
|
for my $v ($g->isolated_vertices) { $c->add_vertex($v) }
|
|
for my $e ($g->edges05) { $c->add_edge(@$e) }
|
|
return $c;
|
|
}
|
|
|
|
*copy_graph = \©
|
|
|
|
sub deep_copy {
|
|
require Data::Dumper;
|
|
my $g = shift;
|
|
my $d = Data::Dumper->new([$g]);
|
|
use vars qw($VAR1);
|
|
$d->Purity(1)->Terse(1)->Deepcopy(1);
|
|
$d->Deparse(1) if $] >= 5.008;
|
|
eval $d->Dump;
|
|
}
|
|
|
|
*deep_copy_graph = \&deep_copy;
|
|
|
|
sub transpose_edge {
|
|
my $g = shift;
|
|
if ($g->is_directed) {
|
|
return undef unless $g->has_edge( @_ );
|
|
my $c = $g->get_edge_count( @_ );
|
|
my $a = $g->get_edge_attributes( @_ );
|
|
my @e = reverse @_;
|
|
$g->delete_edge( @_ ) unless $g->has_edge( @e );
|
|
$g->add_edge( @e ) for 1..$c;
|
|
$g->set_edge_attributes(@e, $a) if $a;
|
|
}
|
|
return $g;
|
|
}
|
|
|
|
sub transpose_graph {
|
|
my $g = shift;
|
|
my $t = $g->copy;
|
|
if ($t->directed) {
|
|
for my $e ($t->edges05) {
|
|
$t->transpose_edge(@$e);
|
|
}
|
|
}
|
|
return $t;
|
|
}
|
|
|
|
*transpose = \&transpose_graph;
|
|
|
|
sub complete_graph {
|
|
my $g = shift;
|
|
my $c = $g->new( directed => $g->directed );
|
|
my @v = $g->vertices05;
|
|
for (my $i = 0; $i <= $#v; $i++ ) {
|
|
for (my $j = 0; $j <= $#v; $j++ ) {
|
|
next if $i >= $j;
|
|
if ($g->is_undirected) {
|
|
$c->add_edge($v[$i], $v[$j]);
|
|
} else {
|
|
$c->add_edge($v[$i], $v[$j]);
|
|
$c->add_edge($v[$j], $v[$i]);
|
|
}
|
|
}
|
|
}
|
|
return $c;
|
|
}
|
|
|
|
*complement = \&complement_graph;
|
|
|
|
sub complement_graph {
|
|
my $g = shift;
|
|
my $c = $g->new( directed => $g->directed );
|
|
my @v = $g->vertices05;
|
|
for (my $i = 0; $i <= $#v; $i++ ) {
|
|
for (my $j = 0; $j <= $#v; $j++ ) {
|
|
next if $i >= $j;
|
|
if ($g->is_undirected) {
|
|
$c->add_edge($v[$i], $v[$j])
|
|
unless $g->has_edge($v[$i], $v[$j]);
|
|
} else {
|
|
$c->add_edge($v[$i], $v[$j])
|
|
unless $g->has_edge($v[$i], $v[$j]);
|
|
$c->add_edge($v[$j], $v[$i])
|
|
unless $g->has_edge($v[$j], $v[$i]);
|
|
}
|
|
}
|
|
}
|
|
return $c;
|
|
}
|
|
|
|
*complete = \&complete_graph;
|
|
|
|
###
|
|
# Transitivity.
|
|
#
|
|
|
|
sub is_transitive {
|
|
my $g = shift;
|
|
Graph::TransitiveClosure::is_transitive($g);
|
|
}
|
|
|
|
###
|
|
# Weighted vertices.
|
|
#
|
|
|
|
my $defattr = 'weight';
|
|
|
|
sub _defattr {
|
|
return $defattr;
|
|
}
|
|
|
|
sub add_weighted_vertex {
|
|
my $g = shift;
|
|
$g->expect_non_multivertexed;
|
|
my $w = pop;
|
|
$g->add_vertex(@_);
|
|
$g->set_vertex_attribute(@_, $defattr, $w);
|
|
}
|
|
|
|
sub add_weighted_vertices {
|
|
my $g = shift;
|
|
$g->expect_non_multivertexed;
|
|
while (@_) {
|
|
my ($v, $w) = splice @_, 0, 2;
|
|
$g->add_vertex($v);
|
|
$g->set_vertex_attribute($v, $defattr, $w);
|
|
}
|
|
}
|
|
|
|
sub get_vertex_weight {
|
|
my $g = shift;
|
|
$g->expect_non_multivertexed;
|
|
$g->get_vertex_attribute(@_, $defattr);
|
|
}
|
|
|
|
sub has_vertex_weight {
|
|
my $g = shift;
|
|
$g->expect_non_multivertexed;
|
|
$g->has_vertex_attribute(@_, $defattr);
|
|
}
|
|
|
|
sub set_vertex_weight {
|
|
my $g = shift;
|
|
$g->expect_non_multivertexed;
|
|
my $w = pop;
|
|
$g->set_vertex_attribute(@_, $defattr, $w);
|
|
}
|
|
|
|
sub delete_vertex_weight {
|
|
my $g = shift;
|
|
$g->expect_non_multivertexed;
|
|
$g->delete_vertex_attribute(@_, $defattr);
|
|
}
|
|
|
|
sub add_weighted_vertex_by_id {
|
|
my $g = shift;
|
|
$g->expect_multivertexed;
|
|
my $w = pop;
|
|
$g->add_vertex_by_id(@_);
|
|
$g->set_vertex_attribute_by_id(@_, $defattr, $w);
|
|
}
|
|
|
|
sub add_weighted_vertices_by_id {
|
|
my $g = shift;
|
|
$g->expect_multivertexed;
|
|
my $id = pop;
|
|
while (@_) {
|
|
my ($v, $w) = splice @_, 0, 2;
|
|
$g->add_vertex_by_id($v, $id);
|
|
$g->set_vertex_attribute_by_id($v, $id, $defattr, $w);
|
|
}
|
|
}
|
|
|
|
sub get_vertex_weight_by_id {
|
|
my $g = shift;
|
|
$g->expect_multivertexed;
|
|
$g->get_vertex_attribute_by_id(@_, $defattr);
|
|
}
|
|
|
|
sub has_vertex_weight_by_id {
|
|
my $g = shift;
|
|
$g->expect_multivertexed;
|
|
$g->has_vertex_attribute_by_id(@_, $defattr);
|
|
}
|
|
|
|
sub set_vertex_weight_by_id {
|
|
my $g = shift;
|
|
$g->expect_multivertexed;
|
|
my $w = pop;
|
|
$g->set_vertex_attribute_by_id(@_, $defattr, $w);
|
|
}
|
|
|
|
sub delete_vertex_weight_by_id {
|
|
my $g = shift;
|
|
$g->expect_multivertexed;
|
|
$g->delete_vertex_attribute_by_id(@_, $defattr);
|
|
}
|
|
|
|
###
|
|
# Weighted edges.
|
|
#
|
|
|
|
sub add_weighted_edge {
|
|
my $g = shift;
|
|
$g->expect_non_multiedged;
|
|
if ($g->is_compat02) {
|
|
my $w = splice @_, 1, 1;
|
|
$g->add_edge(@_);
|
|
$g->set_edge_attribute(@_, $defattr, $w);
|
|
} else {
|
|
my $w = pop;
|
|
$g->add_edge(@_);
|
|
$g->set_edge_attribute(@_, $defattr, $w);
|
|
}
|
|
}
|
|
|
|
sub add_weighted_edges {
|
|
my $g = shift;
|
|
$g->expect_non_multiedged;
|
|
if ($g->is_compat02) {
|
|
while (@_) {
|
|
my ($u, $w, $v) = splice @_, 0, 3;
|
|
$g->add_edge($u, $v);
|
|
$g->set_edge_attribute($u, $v, $defattr, $w);
|
|
}
|
|
} else {
|
|
while (@_) {
|
|
my ($u, $v, $w) = splice @_, 0, 3;
|
|
$g->add_edge($u, $v);
|
|
$g->set_edge_attribute($u, $v, $defattr, $w);
|
|
}
|
|
}
|
|
}
|
|
|
|
sub add_weighted_edges_by_id {
|
|
my $g = shift;
|
|
$g->expect_multiedged;
|
|
my $id = pop;
|
|
while (@_) {
|
|
my ($u, $v, $w) = splice @_, 0, 3;
|
|
$g->add_edge_by_id($u, $v, $id);
|
|
$g->set_edge_attribute_by_id($u, $v, $id, $defattr, $w);
|
|
}
|
|
}
|
|
|
|
sub add_weighted_path {
|
|
my $g = shift;
|
|
$g->expect_non_multiedged;
|
|
my $u = shift;
|
|
while (@_) {
|
|
my ($w, $v) = splice @_, 0, 2;
|
|
$g->add_edge($u, $v);
|
|
$g->set_edge_attribute($u, $v, $defattr, $w);
|
|
$u = $v;
|
|
}
|
|
}
|
|
|
|
sub get_edge_weight {
|
|
my $g = shift;
|
|
$g->expect_non_multiedged;
|
|
$g->get_edge_attribute(@_, $defattr);
|
|
}
|
|
|
|
sub has_edge_weight {
|
|
my $g = shift;
|
|
$g->expect_non_multiedged;
|
|
$g->has_edge_attribute(@_, $defattr);
|
|
}
|
|
|
|
sub set_edge_weight {
|
|
my $g = shift;
|
|
$g->expect_non_multiedged;
|
|
my $w = pop;
|
|
$g->set_edge_attribute(@_, $defattr, $w);
|
|
}
|
|
|
|
sub delete_edge_weight {
|
|
my $g = shift;
|
|
$g->expect_non_multiedged;
|
|
$g->delete_edge_attribute(@_, $defattr);
|
|
}
|
|
|
|
sub add_weighted_edge_by_id {
|
|
my $g = shift;
|
|
$g->expect_multiedged;
|
|
if ($g->is_compat02) {
|
|
my $w = splice @_, 1, 1;
|
|
$g->add_edge_by_id(@_);
|
|
$g->set_edge_attribute_by_id(@_, $defattr, $w);
|
|
} else {
|
|
my $w = pop;
|
|
$g->add_edge_by_id(@_);
|
|
$g->set_edge_attribute_by_id(@_, $defattr, $w);
|
|
}
|
|
}
|
|
|
|
sub add_weighted_path_by_id {
|
|
my $g = shift;
|
|
$g->expect_multiedged;
|
|
my $id = pop;
|
|
my $u = shift;
|
|
while (@_) {
|
|
my ($w, $v) = splice @_, 0, 2;
|
|
$g->add_edge_by_id($u, $v, $id);
|
|
$g->set_edge_attribute_by_id($u, $v, $id, $defattr, $w);
|
|
$u = $v;
|
|
}
|
|
}
|
|
|
|
sub get_edge_weight_by_id {
|
|
my $g = shift;
|
|
$g->expect_multiedged;
|
|
$g->get_edge_attribute_by_id(@_, $defattr);
|
|
}
|
|
|
|
sub has_edge_weight_by_id {
|
|
my $g = shift;
|
|
$g->expect_multiedged;
|
|
$g->has_edge_attribute_by_id(@_, $defattr);
|
|
}
|
|
|
|
sub set_edge_weight_by_id {
|
|
my $g = shift;
|
|
$g->expect_multiedged;
|
|
my $w = pop;
|
|
$g->set_edge_attribute_by_id(@_, $defattr, $w);
|
|
}
|
|
|
|
sub delete_edge_weight_by_id {
|
|
my $g = shift;
|
|
$g->expect_multiedged;
|
|
$g->delete_edge_attribute_by_id(@_, $defattr);
|
|
}
|
|
|
|
###
|
|
# Error helpers.
|
|
#
|
|
|
|
my %expected;
|
|
@expected{qw(directed undirected acyclic)} = qw(undirected directed cyclic);
|
|
|
|
sub _expected {
|
|
my $exp = shift;
|
|
my $got = @_ ? shift : $expected{$exp};
|
|
$got = defined $got ? ", got $got" : "";
|
|
if (my @caller2 = caller(2)) {
|
|
die "$caller2[3]: expected $exp graph$got, at $caller2[1] line $caller2[2].\n";
|
|
} else {
|
|
my @caller1 = caller(1);
|
|
die "$caller1[3]: expected $exp graph$got, at $caller1[1] line $caller1[2].\n";
|
|
}
|
|
}
|
|
|
|
sub expect_undirected {
|
|
my $g = shift;
|
|
_expected('undirected') unless $g->is_undirected;
|
|
}
|
|
|
|
sub expect_directed {
|
|
my $g = shift;
|
|
_expected('directed') unless $g->is_directed;
|
|
}
|
|
|
|
sub expect_acyclic {
|
|
my $g = shift;
|
|
_expected('acyclic') unless $g->is_acyclic;
|
|
}
|
|
|
|
sub expect_dag {
|
|
my $g = shift;
|
|
my @got;
|
|
push @got, 'undirected' unless $g->is_directed;
|
|
push @got, 'cyclic' unless $g->is_acyclic;
|
|
_expected('directed acyclic', "@got") if @got;
|
|
}
|
|
|
|
sub expect_multivertexed {
|
|
my $g = shift;
|
|
_expected('multivertexed') unless $g->is_multivertexed;
|
|
}
|
|
|
|
sub expect_non_multivertexed {
|
|
my $g = shift;
|
|
_expected('non-multivertexed') if $g->is_multivertexed;
|
|
}
|
|
|
|
sub expect_non_multiedged {
|
|
my $g = shift;
|
|
_expected('non-multiedged') if $g->is_multiedged;
|
|
}
|
|
|
|
sub expect_multiedged {
|
|
my $g = shift;
|
|
_expected('multiedged') unless $g->is_multiedged;
|
|
}
|
|
|
|
sub _get_options {
|
|
my @caller = caller(1);
|
|
unless (@_ == 1 && ref $_[0] eq 'ARRAY') {
|
|
die "$caller[3]: internal error: should be called with only one array ref argument, at $caller[1] line $caller[2].\n";
|
|
}
|
|
my @opt = @{ $_[0] };
|
|
unless (@opt % 2 == 0) {
|
|
die "$caller[3]: expected an options hash, got a non-even number of arguments, at $caller[1] line $caller[2].\n";
|
|
}
|
|
return @opt;
|
|
}
|
|
|
|
###
|
|
# Random constructors and accessors.
|
|
#
|
|
|
|
sub __fisher_yates_shuffle (@) {
|
|
# From perlfaq4, but modified to be non-modifying.
|
|
my @a = @_;
|
|
my $i = @a;
|
|
while ($i--) {
|
|
my $j = int rand ($i+1);
|
|
@a[$i,$j] = @a[$j,$i];
|
|
}
|
|
return @a;
|
|
}
|
|
|
|
BEGIN {
|
|
sub _shuffle(@);
|
|
# Workaround for the Perl bug [perl #32383] where -d:Dprof and
|
|
# List::Util::shuffle do not like each other: if any debugging
|
|
# (-d) flags are on, fall back to our own Fisher-Yates shuffle.
|
|
# The bug was fixed by perl changes #26054 and #26062, which
|
|
# went to Perl 5.9.3. If someone tests this with a pre-5.9.3
|
|
# bleadperl that calls itself 5.9.3 but doesn't yet have the
|
|
# patches, oh, well.
|
|
*_shuffle = $^P && $] < 5.009003 ?
|
|
\&__fisher_yates_shuffle : \&List::Util::shuffle;
|
|
}
|
|
|
|
sub random_graph {
|
|
my $class = (@_ % 2) == 0 ? 'Graph' : shift;
|
|
my %opt = _get_options( \@_ );
|
|
my $random_edge;
|
|
unless (exists $opt{vertices} && defined $opt{vertices}) {
|
|
require Carp;
|
|
Carp::croak("Graph::random_graph: argument 'vertices' missing or undef");
|
|
}
|
|
if (exists $opt{random_seed}) {
|
|
srand($opt{random_seed});
|
|
delete $opt{random_seed};
|
|
}
|
|
if (exists $opt{random_edge}) {
|
|
$random_edge = $opt{random_edge};
|
|
delete $opt{random_edge};
|
|
}
|
|
my @V;
|
|
if (my $ref = ref $opt{vertices}) {
|
|
if ($ref eq 'ARRAY') {
|
|
@V = @{ $opt{vertices} };
|
|
} else {
|
|
Carp::croak("Graph::random_graph: argument 'vertices' illegal");
|
|
}
|
|
} else {
|
|
@V = 0..($opt{vertices} - 1);
|
|
}
|
|
delete $opt{vertices};
|
|
my $V = @V;
|
|
my $C = $V * ($V - 1) / 2;
|
|
my $E;
|
|
if (exists $opt{edges} && exists $opt{edges_fill}) {
|
|
Carp::croak("Graph::random_graph: both arguments 'edges' and 'edges_fill' specified");
|
|
}
|
|
$E = exists $opt{edges_fill} ? $opt{edges_fill} * $C : $opt{edges};
|
|
delete $opt{edges};
|
|
delete $opt{edges_fill};
|
|
my $g = $class->new(%opt);
|
|
$g->add_vertices(@V);
|
|
return $g if $V < 2;
|
|
$C *= 2 if $g->directed;
|
|
$E = $C / 2 unless defined $E;
|
|
$E = int($E + 0.5);
|
|
my $p = $E / $C;
|
|
$random_edge = sub { $p } unless defined $random_edge;
|
|
# print "V = $V, E = $E, C = $C, p = $p\n";
|
|
if ($p > 1.0 && !($g->countedged || $g->multiedged)) {
|
|
require Carp;
|
|
Carp::croak("Graph::random_graph: needs to be countedged or multiedged ($E > $C)");
|
|
}
|
|
my @V1 = @V;
|
|
my @V2 = @V;
|
|
# Shuffle the vertex lists so that the pairs at
|
|
# the beginning of the lists are not more likely.
|
|
@V1 = _shuffle @V1;
|
|
@V2 = _shuffle @V2;
|
|
LOOP:
|
|
while ($E) {
|
|
for my $v1 (@V1) {
|
|
for my $v2 (@V2) {
|
|
next if $v1 eq $v2; # TODO: allow self-loops?
|
|
my $q = $random_edge->($g, $v1, $v2, $p);
|
|
if ($q && ($q == 1 || rand() <= $q) &&
|
|
!$g->has_edge($v1, $v2)) {
|
|
$g->add_edge($v1, $v2);
|
|
$E--;
|
|
last LOOP unless $E;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
return $g;
|
|
}
|
|
|
|
sub random_vertex {
|
|
my $g = shift;
|
|
my @V = $g->vertices05;
|
|
@V[rand @V];
|
|
}
|
|
|
|
sub random_edge {
|
|
my $g = shift;
|
|
my @E = $g->edges05;
|
|
@E[rand @E];
|
|
}
|
|
|
|
sub random_successor {
|
|
my ($g, $v) = @_;
|
|
my @S = $g->successors($v);
|
|
@S[rand @S];
|
|
}
|
|
|
|
sub random_predecessor {
|
|
my ($g, $v) = @_;
|
|
my @P = $g->predecessors($v);
|
|
@P[rand @P];
|
|
}
|
|
|
|
###
|
|
# Algorithms.
|
|
#
|
|
|
|
my $MST_comparator = sub { ($_[0] || 0) <=> ($_[1] || 0) };
|
|
|
|
sub _MST_attr {
|
|
my $attr = shift;
|
|
my $attribute =
|
|
exists $attr->{attribute} ?
|
|
$attr->{attribute} : $defattr;
|
|
my $comparator =
|
|
exists $attr->{comparator} ?
|
|
$attr->{comparator} : $MST_comparator;
|
|
return ($attribute, $comparator);
|
|
}
|
|
|
|
sub _MST_edges {
|
|
my ($g, $attr) = @_;
|
|
my ($attribute, $comparator) = _MST_attr($attr);
|
|
map { $_->[1] }
|
|
sort { $comparator->($a->[0], $b->[0], $a->[1], $b->[1]) }
|
|
map { [ $g->get_edge_attribute(@$_, $attribute), $_ ] }
|
|
$g->edges05;
|
|
}
|
|
|
|
sub MST_Kruskal {
|
|
my ($g, %attr) = @_;
|
|
|
|
$g->expect_undirected;
|
|
|
|
my $MST = Graph::Undirected->new;
|
|
|
|
my $UF = Graph::UnionFind->new;
|
|
for my $v ($g->vertices05) { $UF->add($v) }
|
|
|
|
for my $e ($g->_MST_edges(\%attr)) {
|
|
my ($u, $v) = @$e; # TODO: hyperedges
|
|
my $t0 = $UF->find( $u );
|
|
my $t1 = $UF->find( $v );
|
|
unless ($t0 eq $t1) {
|
|
$UF->union($u, $v);
|
|
$MST->add_edge($u, $v);
|
|
}
|
|
}
|
|
|
|
return $MST;
|
|
}
|
|
|
|
sub _MST_add {
|
|
my ($g, $h, $HF, $r, $attr, $unseen) = @_;
|
|
for my $s ( grep { exists $unseen->{ $_ } } $g->successors( $r ) ) {
|
|
$HF->add( Graph::MSTHeapElem->new( $r, $s, $g->get_edge_attribute( $r, $s, $attr ) ) );
|
|
}
|
|
}
|
|
|
|
sub _next_alphabetic { shift; (sort keys %{ $_[0] })[0] }
|
|
sub _next_numeric { shift; (sort { $a <=> $b } keys %{ $_[0] })[0] }
|
|
sub _next_random { shift; (values %{ $_[0] })[ rand keys %{ $_[0] } ] }
|
|
|
|
sub _root_opt {
|
|
my $g = shift;
|
|
my %opt = @_ == 1 ? ( first_root => $_[0] ) : _get_options( \@_ );
|
|
my %unseen;
|
|
my @unseen = $g->vertices05;
|
|
@unseen{ @unseen } = @unseen;
|
|
@unseen = _shuffle @unseen;
|
|
my $r;
|
|
if (exists $opt{ start }) {
|
|
$opt{ first_root } = $opt{ start };
|
|
$opt{ next_root } = undef;
|
|
}
|
|
if (exists $opt{ get_next_root }) {
|
|
$opt{ next_root } = $opt{ get_next_root }; # Graph 0.201 compat.
|
|
}
|
|
if (exists $opt{ first_root }) {
|
|
if (ref $opt{ first_root } eq 'CODE') {
|
|
$r = $opt{ first_root }->( $g, \%unseen );
|
|
} else {
|
|
$r = $opt{ first_root };
|
|
}
|
|
} else {
|
|
$r = shift @unseen;
|
|
}
|
|
my $next =
|
|
exists $opt{ next_root } ?
|
|
$opt{ next_root } :
|
|
$opt{ next_alphabetic } ?
|
|
\&_next_alphabetic :
|
|
$opt{ next_numeric } ? \&_next_numeric :
|
|
\&_next_random;
|
|
my $code = ref $next eq 'CODE';
|
|
my $attr = exists $opt{ attribute } ? $opt{ attribute } : $defattr;
|
|
return ( \%opt, \%unseen, \@unseen, $r, $next, $code, $attr );
|
|
}
|
|
|
|
sub _heap_walk {
|
|
my ($g, $h, $add, $etc) = splice @_, 0, 4; # Leave %opt in @_.
|
|
|
|
my ($opt, $unseenh, $unseena, $r, $next, $code, $attr) = $g->_root_opt(@_);
|
|
my $HF = Heap071::Fibonacci->new;
|
|
|
|
while (defined $r) {
|
|
# print "r = $r\n";
|
|
$add->($g, $h, $HF, $r, $attr, $unseenh, $etc);
|
|
delete $unseenh->{ $r };
|
|
while (defined $HF->top) {
|
|
my $t = $HF->extract_top;
|
|
# use Data::Dumper; print "t = ", Dumper($t);
|
|
if (defined $t) {
|
|
my ($u, $v, $w) = $t->val;
|
|
# print "extracted top: $u $v $w\n";
|
|
if (exists $unseenh->{ $v }) {
|
|
$h->set_edge_attribute($u, $v, $attr, $w);
|
|
delete $unseenh->{ $v };
|
|
$add->($g, $h, $HF, $v, $attr, $unseenh, $etc);
|
|
}
|
|
}
|
|
}
|
|
return $h unless defined $next;
|
|
$r = $code ? $next->( $g, $unseenh ) : shift @$unseena;
|
|
}
|
|
|
|
return $h;
|
|
}
|
|
|
|
sub MST_Prim {
|
|
my $g = shift;
|
|
$g->expect_undirected;
|
|
$g->_heap_walk(Graph::Undirected->new(), \&_MST_add, undef, @_);
|
|
}
|
|
|
|
*MST_Dijkstra = \&MST_Prim;
|
|
|
|
*minimum_spanning_tree = \&MST_Prim;
|
|
|
|
###
|
|
# Cycle detection.
|
|
#
|
|
|
|
*is_cyclic = \&has_a_cycle;
|
|
|
|
sub is_acyclic {
|
|
my $g = shift;
|
|
return !$g->is_cyclic;
|
|
}
|
|
|
|
sub is_dag {
|
|
my $g = shift;
|
|
return $g->is_directed && $g->is_acyclic ? 1 : 0;
|
|
}
|
|
|
|
*is_directed_acyclic_graph = \&is_dag;
|
|
|
|
###
|
|
# Backward compat.
|
|
#
|
|
|
|
sub average_degree {
|
|
my $g = shift;
|
|
my $V = $g->vertices05;
|
|
|
|
return $V ? $g->degree / $V : 0;
|
|
}
|
|
|
|
sub density_limits {
|
|
my $g = shift;
|
|
|
|
my $V = $g->vertices05;
|
|
my $M = $V * ($V - 1);
|
|
|
|
$M /= 2 if $g->is_undirected;
|
|
|
|
return ( 0.25 * $M, 0.75 * $M, $M );
|
|
}
|
|
|
|
sub density {
|
|
my $g = shift;
|
|
my ($sparse, $dense, $complete) = $g->density_limits;
|
|
|
|
return $complete ? $g->edges / $complete : 0;
|
|
}
|
|
|
|
###
|
|
# Attribute backward compat
|
|
#
|
|
|
|
sub _attr02_012 {
|
|
my ($g, $op, $ga, $va, $ea) = splice @_, 0, 5;
|
|
if ($g->is_compat02) {
|
|
if (@_ == 0) { return $ga->( $g ) }
|
|
elsif (@_ == 1) { return $va->( $g, @_ ) }
|
|
elsif (@_ == 2) { return $ea->( $g, @_ ) }
|
|
else {
|
|
die sprintf "$op: wrong number of arguments (%d)", scalar @_;
|
|
}
|
|
} else {
|
|
die "$op: not a compat02 graph"
|
|
}
|
|
}
|
|
|
|
sub _attr02_123 {
|
|
my ($g, $op, $ga, $va, $ea) = splice @_, 0, 5;
|
|
if ($g->is_compat02) {
|
|
if (@_ == 1) { return $ga->( $g, @_ ) }
|
|
elsif (@_ == 2) { return $va->( $g, @_[1, 0] ) }
|
|
elsif (@_ == 3) { return $ea->( $g, @_[1, 2, 0] ) }
|
|
else {
|
|
die sprintf "$op: wrong number of arguments (%d)", scalar @_;
|
|
}
|
|
} else {
|
|
die "$op: not a compat02 graph"
|
|
}
|
|
}
|
|
|
|
sub _attr02_234 {
|
|
my ($g, $op, $ga, $va, $ea) = splice @_, 0, 5;
|
|
if ($g->is_compat02) {
|
|
if (@_ == 2) { return $ga->( $g, @_ ) }
|
|
elsif (@_ == 3) { return $va->( $g, @_[1, 0, 2] ) }
|
|
elsif (@_ == 4) { return $ea->( $g, @_[1, 2, 0, 3] ) }
|
|
else {
|
|
die sprintf "$op: wrong number of arguments (%d)", scalar @_;
|
|
}
|
|
} else {
|
|
die "$op: not a compat02 graph";
|
|
}
|
|
}
|
|
|
|
sub set_attribute {
|
|
my $g = shift;
|
|
$g->_attr02_234('set_attribute',
|
|
\&Graph::set_graph_attribute,
|
|
\&Graph::set_vertex_attribute,
|
|
\&Graph::set_edge_attribute,
|
|
@_);
|
|
|
|
}
|
|
|
|
sub set_attributes {
|
|
my $g = shift;
|
|
my $a = pop;
|
|
$g->_attr02_123('set_attributes',
|
|
\&Graph::set_graph_attributes,
|
|
\&Graph::set_vertex_attributes,
|
|
\&Graph::set_edge_attributes,
|
|
$a, @_);
|
|
|
|
}
|
|
|
|
sub get_attribute {
|
|
my $g = shift;
|
|
$g->_attr02_123('get_attribute',
|
|
\&Graph::get_graph_attribute,
|
|
\&Graph::get_vertex_attribute,
|
|
\&Graph::get_edge_attribute,
|
|
@_);
|
|
|
|
}
|
|
|
|
sub get_attributes {
|
|
my $g = shift;
|
|
$g->_attr02_012('get_attributes',
|
|
\&Graph::get_graph_attributes,
|
|
\&Graph::get_vertex_attributes,
|
|
\&Graph::get_edge_attributes,
|
|
@_);
|
|
|
|
}
|
|
|
|
sub has_attribute {
|
|
my $g = shift;
|
|
return 0 unless @_;
|
|
$g->_attr02_123('has_attribute',
|
|
\&Graph::has_graph_attribute,
|
|
\&Graph::has_vertex_attribute,
|
|
\&Graph::get_edge_attribute,
|
|
@_);
|
|
|
|
}
|
|
|
|
sub has_attributes {
|
|
my $g = shift;
|
|
$g->_attr02_012('has_attributes',
|
|
\&Graph::has_graph_attributes,
|
|
\&Graph::has_vertex_attributes,
|
|
\&Graph::has_edge_attributes,
|
|
@_);
|
|
|
|
}
|
|
|
|
sub delete_attribute {
|
|
my $g = shift;
|
|
$g->_attr02_123('delete_attribute',
|
|
\&Graph::delete_graph_attribute,
|
|
\&Graph::delete_vertex_attribute,
|
|
\&Graph::delete_edge_attribute,
|
|
@_);
|
|
|
|
}
|
|
|
|
sub delete_attributes {
|
|
my $g = shift;
|
|
$g->_attr02_012('delete_attributes',
|
|
\&Graph::delete_graph_attributes,
|
|
\&Graph::delete_vertex_attributes,
|
|
\&Graph::delete_edge_attributes,
|
|
@_);
|
|
|
|
}
|
|
|
|
###
|
|
# Simple DFS uses.
|
|
#
|
|
|
|
sub topological_sort {
|
|
my $g = shift;
|
|
my %opt = _get_options( \@_ );
|
|
my $eic = $opt{ empty_if_cyclic };
|
|
my $hac;
|
|
if ($eic) {
|
|
$hac = $g->has_a_cycle;
|
|
} else {
|
|
$g->expect_dag;
|
|
}
|
|
delete $opt{ empty_if_cyclic };
|
|
my $t = Graph::Traversal::DFS->new($g, %opt);
|
|
my @s = $t->dfs;
|
|
$hac ? () : reverse @s;
|
|
}
|
|
|
|
*toposort = \&topological_sort;
|
|
|
|
sub undirected_copy {
|
|
my $g = shift;
|
|
|
|
$g->expect_directed;
|
|
|
|
my $c = Graph::Undirected->new;
|
|
for my $v ($g->isolated_vertices) { # TODO: if iv ...
|
|
$c->add_vertex($v);
|
|
}
|
|
for my $e ($g->edges05) {
|
|
$c->add_edge(@$e);
|
|
}
|
|
return $c;
|
|
}
|
|
|
|
*undirected_copy_graph = \&undirected_copy;
|
|
|
|
sub directed_copy {
|
|
my $g = shift;
|
|
$g->expect_undirected;
|
|
my $c = Graph::Directed->new;
|
|
for my $v ($g->isolated_vertices) { # TODO: if iv ...
|
|
$c->add_vertex($v);
|
|
}
|
|
for my $e ($g->edges05) {
|
|
my @e = @$e;
|
|
$c->add_edge(@e);
|
|
$c->add_edge(reverse @e);
|
|
}
|
|
return $c;
|
|
}
|
|
|
|
*directed_copy_graph = \&directed_copy;
|
|
|
|
###
|
|
# Cache or not.
|
|
#
|
|
|
|
my %_cache_type =
|
|
(
|
|
'connectivity' => '_ccc',
|
|
'strong_connectivity' => '_scc',
|
|
'biconnectivity' => '_bcc',
|
|
'SPT_Dijkstra' => '_spt_di',
|
|
'SPT_Bellman_Ford' => '_spt_bf',
|
|
);
|
|
|
|
sub _check_cache {
|
|
my ($g, $type, $code) = splice @_, 0, 3;
|
|
my $c = $_cache_type{$type};
|
|
if (defined $c) {
|
|
my $a = $g->get_graph_attribute($c);
|
|
unless (defined $a && $a->[ 0 ] == $g->[ _G ]) {
|
|
$a->[ 0 ] = $g->[ _G ];
|
|
$a->[ 1 ] = $code->( $g, @_ );
|
|
$g->set_graph_attribute($c, $a);
|
|
}
|
|
return $a->[ 1 ];
|
|
} else {
|
|
Carp::croak("Graph: unknown cache type '$type'");
|
|
}
|
|
}
|
|
|
|
sub _clear_cache {
|
|
my ($g, $type) = @_;
|
|
my $c = $_cache_type{$type};
|
|
if (defined $c) {
|
|
$g->delete_graph_attribute($c);
|
|
} else {
|
|
Carp::croak("Graph: unknown cache type '$type'");
|
|
}
|
|
}
|
|
|
|
sub connectivity_clear_cache {
|
|
my $g = shift;
|
|
_clear_cache($g, 'connectivity');
|
|
}
|
|
|
|
sub strong_connectivity_clear_cache {
|
|
my $g = shift;
|
|
_clear_cache($g, 'strong_connectivity');
|
|
}
|
|
|
|
sub biconnectivity_clear_cache {
|
|
my $g = shift;
|
|
_clear_cache($g, 'biconnectivity');
|
|
}
|
|
|
|
sub SPT_Dijkstra_clear_cache {
|
|
my $g = shift;
|
|
_clear_cache($g, 'SPT_Dijkstra');
|
|
$g->delete_graph_attribute('SPT_Dijkstra_first_root');
|
|
}
|
|
|
|
sub SPT_Bellman_Ford_clear_cache {
|
|
my $g = shift;
|
|
_clear_cache($g, 'SPT_Bellman_Ford');
|
|
}
|
|
|
|
###
|
|
# Connected components.
|
|
#
|
|
|
|
sub _connected_components_compute {
|
|
my $g = shift;
|
|
my %cce;
|
|
my %cci;
|
|
my $cc = 0;
|
|
if ($g->has_union_find) {
|
|
my $UF = $g->_get_union_find();
|
|
my $V = $g->[ _V ];
|
|
my %icce; # Isolated vertices.
|
|
my %icci;
|
|
my $icc = 0;
|
|
for my $v ( $g->unique_vertices ) {
|
|
$cc = $UF->find( $V->_get_path_id( $v ) );
|
|
if (defined $cc) {
|
|
$cce{ $v } = $cc;
|
|
push @{ $cci{ $cc } }, $v;
|
|
} else {
|
|
$icce{ $v } = $icc;
|
|
push @{ $icci{ $icc } }, $v;
|
|
$icc++;
|
|
}
|
|
}
|
|
if ($icc) {
|
|
@cce{ keys %icce } = values %icce;
|
|
@cci{ keys %icci } = values %icci;
|
|
}
|
|
} else {
|
|
my @u = $g->unique_vertices;
|
|
my %r; @r{ @u } = @u;
|
|
my $froot = sub {
|
|
(each %r)[1];
|
|
};
|
|
my $nroot = sub {
|
|
$cc++ if keys %r;
|
|
(each %r)[1];
|
|
};
|
|
my $t = Graph::Traversal::DFS->new($g,
|
|
first_root => $froot,
|
|
next_root => $nroot,
|
|
pre => sub {
|
|
my ($v, $t) = @_;
|
|
$cce{ $v } = $cc;
|
|
push @{ $cci{ $cc } }, $v;
|
|
delete $r{ $v };
|
|
},
|
|
@_);
|
|
$t->dfs;
|
|
}
|
|
return [ \%cce, \%cci ];
|
|
}
|
|
|
|
sub _connected_components {
|
|
my $g = shift;
|
|
my $ccc = _check_cache($g, 'connectivity',
|
|
\&_connected_components_compute, @_);
|
|
return @{ $ccc };
|
|
}
|
|
|
|
sub connected_component_by_vertex {
|
|
my ($g, $v) = @_;
|
|
$g->expect_undirected;
|
|
my ($CCE, $CCI) = $g->_connected_components();
|
|
return $CCE->{ $v };
|
|
}
|
|
|
|
sub connected_component_by_index {
|
|
my ($g, $i) = @_;
|
|
$g->expect_undirected;
|
|
my ($CCE, $CCI) = $g->_connected_components();
|
|
return defined $CCI->{ $i } ? @{ $CCI->{ $i } } : ( );
|
|
}
|
|
|
|
sub connected_components {
|
|
my $g = shift;
|
|
$g->expect_undirected;
|
|
my ($CCE, $CCI) = $g->_connected_components();
|
|
return values %{ $CCI };
|
|
}
|
|
|
|
sub same_connected_components {
|
|
my $g = shift;
|
|
$g->expect_undirected;
|
|
if ($g->has_union_find) {
|
|
my $UF = $g->_get_union_find();
|
|
my $V = $g->[ _V ];
|
|
my $u = shift;
|
|
my $c = $UF->find( $V->_get_path_id ( $u ) );
|
|
my $d;
|
|
for my $v ( @_) {
|
|
return 0
|
|
unless defined($d = $UF->find( $V->_get_path_id( $v ) )) &&
|
|
$d eq $c;
|
|
}
|
|
return 1;
|
|
} else {
|
|
my ($CCE, $CCI) = $g->_connected_components();
|
|
my $u = shift;
|
|
my $c = $CCE->{ $u };
|
|
for my $v ( @_) {
|
|
return 0
|
|
unless defined $CCE->{ $v } &&
|
|
$CCE->{ $v } eq $c;
|
|
}
|
|
return 1;
|
|
}
|
|
}
|
|
|
|
my $super_component = sub { join("+", sort @_) };
|
|
|
|
sub connected_graph {
|
|
my ($g, %opt) = @_;
|
|
$g->expect_undirected;
|
|
my $cg = Graph->new(undirected => 1);
|
|
if ($g->has_union_find && $g->vertices == 1) {
|
|
# TODO: super_component?
|
|
$cg->add_vertices($g->vertices);
|
|
} else {
|
|
my $sc_cb =
|
|
exists $opt{super_component} ?
|
|
$opt{super_component} : $super_component;
|
|
for my $cc ( $g->connected_components() ) {
|
|
my $sc = $sc_cb->(@$cc);
|
|
$cg->add_vertex($sc);
|
|
$cg->set_vertex_attribute($sc, 'subvertices', [ @$cc ]);
|
|
}
|
|
}
|
|
return $cg;
|
|
}
|
|
|
|
sub is_connected {
|
|
my $g = shift;
|
|
$g->expect_undirected;
|
|
my ($CCE, $CCI) = $g->_connected_components();
|
|
return keys %{ $CCI } == 1;
|
|
}
|
|
|
|
sub is_weakly_connected {
|
|
my $g = shift;
|
|
$g->expect_directed;
|
|
$g->undirected_copy->is_connected(@_);
|
|
}
|
|
|
|
*weakly_connected = \&is_weakly_connected;
|
|
|
|
sub weakly_connected_components {
|
|
my $g = shift;
|
|
$g->expect_directed;
|
|
$g->undirected_copy->connected_components(@_);
|
|
}
|
|
|
|
sub weakly_connected_component_by_vertex {
|
|
my $g = shift;
|
|
$g->expect_directed;
|
|
$g->undirected_copy->connected_component_by_vertex(@_);
|
|
}
|
|
|
|
sub weakly_connected_component_by_index {
|
|
my $g = shift;
|
|
$g->expect_directed;
|
|
$g->undirected_copy->connected_component_by_index(@_);
|
|
}
|
|
|
|
sub same_weakly_connected_components {
|
|
my $g = shift;
|
|
$g->expect_directed;
|
|
$g->undirected_copy->same_connected_components(@_);
|
|
}
|
|
|
|
sub weakly_connected_graph {
|
|
my $g = shift;
|
|
$g->expect_directed;
|
|
$g->undirected_copy->connected_graph(@_);
|
|
}
|
|
|
|
sub _strongly_connected_components_compute {
|
|
my $g = shift;
|
|
my $t = Graph::Traversal::DFS->new($g);
|
|
my @d = reverse $t->dfs;
|
|
my @c;
|
|
my $h = $g->transpose_graph;
|
|
my $u =
|
|
Graph::Traversal::DFS->new($h,
|
|
next_root => sub {
|
|
my ($t, $u) = @_;
|
|
my $root;
|
|
while (defined($root = shift @d)) {
|
|
last if exists $u->{ $root };
|
|
}
|
|
if (defined $root) {
|
|
push @c, [];
|
|
return $root;
|
|
} else {
|
|
return;
|
|
}
|
|
},
|
|
pre => sub {
|
|
my ($v, $t) = @_;
|
|
push @{ $c[-1] }, $v;
|
|
},
|
|
@_);
|
|
$u->dfs;
|
|
return \@c;
|
|
}
|
|
|
|
sub _strongly_connected_components {
|
|
my $g = shift;
|
|
my $scc = _check_cache($g, 'strong_connectivity',
|
|
\&_strongly_connected_components_compute, @_);
|
|
return defined $scc ? @$scc : ( );
|
|
}
|
|
|
|
sub strongly_connected_components {
|
|
my $g = shift;
|
|
$g->expect_directed;
|
|
$g->_strongly_connected_components(@_);
|
|
}
|
|
|
|
sub strongly_connected_component_by_vertex {
|
|
my $g = shift;
|
|
my $v = shift;
|
|
$g->expect_directed;
|
|
my @scc = $g->_strongly_connected_components( next_alphabetic => 1, @_ );
|
|
for (my $i = 0; $i <= $#scc; $i++) {
|
|
for (my $j = 0; $j <= $#{ $scc[$i] }; $j++) {
|
|
return $i if $scc[$i]->[$j] eq $v;
|
|
}
|
|
}
|
|
return;
|
|
}
|
|
|
|
sub strongly_connected_component_by_index {
|
|
my $g = shift;
|
|
my $i = shift;
|
|
$g->expect_directed;
|
|
my $c = ( $g->_strongly_connected_components(@_) )[ $i ];
|
|
return defined $c ? @{ $c } : ();
|
|
}
|
|
|
|
sub same_strongly_connected_components {
|
|
my $g = shift;
|
|
$g->expect_directed;
|
|
my @scc = $g->_strongly_connected_components( next_alphabetic => 1, @_ );
|
|
my @i;
|
|
while (@_) {
|
|
my $v = shift;
|
|
for (my $i = 0; $i <= $#scc; $i++) {
|
|
for (my $j = 0; $j <= $#{ $scc[$i] }; $j++) {
|
|
if ($scc[$i]->[$j] eq $v) {
|
|
push @i, $i;
|
|
return 0 if @i > 1 && $i[-1] ne $i[0];
|
|
}
|
|
}
|
|
}
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
sub is_strongly_connected {
|
|
my $g = shift;
|
|
$g->expect_directed;
|
|
my $t = Graph::Traversal::DFS->new($g);
|
|
my @d = reverse $t->dfs;
|
|
my @c;
|
|
my $h = $g->transpose;
|
|
my $u =
|
|
Graph::Traversal::DFS->new($h,
|
|
next_root => sub {
|
|
my ($t, $u) = @_;
|
|
my $root;
|
|
while (defined($root = shift @d)) {
|
|
last if exists $u->{ $root };
|
|
}
|
|
if (defined $root) {
|
|
unless (@{ $t->{ roots } }) {
|
|
push @c, [];
|
|
return $root;
|
|
} else {
|
|
$t->terminate;
|
|
return;
|
|
}
|
|
} else {
|
|
return;
|
|
}
|
|
},
|
|
pre => sub {
|
|
my ($v, $t) = @_;
|
|
push @{ $c[-1] }, $v;
|
|
},
|
|
@_);
|
|
$u->dfs;
|
|
return @{ $u->{ roots } } == 1 && keys %{ $u->{ unseen } } == 0;
|
|
}
|
|
|
|
*strongly_connected = \&is_strongly_connected;
|
|
|
|
sub strongly_connected_graph {
|
|
my $g = shift;
|
|
my %attr = @_;
|
|
|
|
$g->expect_directed;
|
|
|
|
my $t = Graph::Traversal::DFS->new($g);
|
|
my @d = reverse $t->dfs;
|
|
my @c;
|
|
my $h = $g->transpose;
|
|
my $u =
|
|
Graph::Traversal::DFS->new($h,
|
|
next_root => sub {
|
|
my ($t, $u) = @_;
|
|
my $root;
|
|
while (defined($root = shift @d)) {
|
|
last if exists $u->{ $root };
|
|
}
|
|
if (defined $root) {
|
|
push @c, [];
|
|
return $root;
|
|
} else {
|
|
return;
|
|
}
|
|
},
|
|
pre => sub {
|
|
my ($v, $t) = @_;
|
|
push @{ $c[-1] }, $v;
|
|
}
|
|
);
|
|
|
|
$u->dfs;
|
|
|
|
my $sc_cb;
|
|
my $hv_cb;
|
|
|
|
_opt_get(\%attr, super_component => \$sc_cb);
|
|
_opt_get(\%attr, hypervertex => \$hv_cb);
|
|
_opt_unknown(\%attr);
|
|
|
|
if (defined $hv_cb && !defined $sc_cb) {
|
|
$sc_cb = sub { $hv_cb->( [ @_ ] ) };
|
|
}
|
|
unless (defined $sc_cb) {
|
|
$sc_cb = $super_component;
|
|
}
|
|
|
|
my $s = Graph->new;
|
|
|
|
my %c;
|
|
my @s;
|
|
for (my $i = 0; $i < @c; $i++) {
|
|
my $c = $c[$i];
|
|
$s->add_vertex( $s[$i] = $sc_cb->(@$c) );
|
|
$s->set_vertex_attribute($s[$i], 'subvertices', [ @$c ]);
|
|
for my $v (@$c) {
|
|
$c{$v} = $i;
|
|
}
|
|
}
|
|
|
|
my $n = @c;
|
|
for my $v ($g->vertices) {
|
|
unless (exists $c{$v}) {
|
|
$c{$v} = $n;
|
|
$s[$n] = $v;
|
|
$n++;
|
|
}
|
|
}
|
|
|
|
for my $e ($g->edges05) {
|
|
my ($u, $v) = @$e; # @TODO: hyperedges
|
|
unless ($c{$u} == $c{$v}) {
|
|
my ($p, $q) = ( $s[ $c{ $u } ], $s[ $c{ $v } ] );
|
|
$s->add_edge($p, $q) unless $s->has_edge($p, $q);
|
|
}
|
|
}
|
|
|
|
if (my @i = $g->isolated_vertices) {
|
|
$s->add_vertices(map { $s[ $c{ $_ } ] } @i);
|
|
}
|
|
|
|
return $s;
|
|
}
|
|
|
|
###
|
|
# Biconnectivity.
|
|
#
|
|
|
|
sub _make_bcc {
|
|
my ($S, $v, $c) = @_;
|
|
my %b;
|
|
while (@$S) {
|
|
my $t = pop @$S;
|
|
$b{ $t } = $t;
|
|
last if $t eq $v;
|
|
}
|
|
return [ values %b, $c ];
|
|
}
|
|
|
|
sub _biconnectivity_compute {
|
|
my $g = shift;
|
|
my ($opt, $unseenh, $unseena, $r, $next, $code, $attr) =
|
|
$g->_root_opt(@_);
|
|
return () unless defined $r;
|
|
my %P;
|
|
my %I;
|
|
for my $v ($g->vertices) {
|
|
$I{ $v } = 0;
|
|
}
|
|
$I{ $r } = 1;
|
|
my %U;
|
|
my %S; # Self-loops.
|
|
for my $e ($g->edges) {
|
|
my ($u, $v) = @$e;
|
|
$U{ $u }{ $v } = 0;
|
|
$U{ $v }{ $u } = 0;
|
|
$S{ $u } = 1 if $u eq $v;
|
|
}
|
|
my $i = 1;
|
|
my $v = $r;
|
|
my %AP;
|
|
my %L = ( $r => 1 );
|
|
my @S = ( $r );
|
|
my %A;
|
|
my @V = $g->vertices;
|
|
|
|
# print "V : @V\n";
|
|
# print "r : $r\n";
|
|
|
|
my %T; @T{ @V } = @V;
|
|
|
|
for my $w (@V) {
|
|
my @s = $g->successors( $w );
|
|
if (@s) {
|
|
@s = grep { $_ eq $w ? ( delete $T{ $w }, 0 ) : 1 } @s;
|
|
@{ $A{ $w } }{ @s } = @s;
|
|
} elsif ($g->predecessors( $w ) == 0) {
|
|
delete $T{ $w };
|
|
if ($w eq $r) {
|
|
delete $I { $r };
|
|
$r = $v = each %T;
|
|
if (defined $r) {
|
|
%L = ( $r => 1 );
|
|
@S = ( $r );
|
|
$I{ $r } = 1;
|
|
# print "r : $r\n";
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
# use Data::Dumper;
|
|
# print "T : ", Dumper(\%T);
|
|
# print "A : ", Dumper(\%A);
|
|
|
|
my %V2BC;
|
|
my @BR;
|
|
my @BC;
|
|
|
|
my @C;
|
|
my $Avok;
|
|
|
|
while (keys %T) {
|
|
# print "T = ", Dumper(\%T);
|
|
do {
|
|
my $w;
|
|
do {
|
|
my @w = _shuffle values %{ $A{ $v } };
|
|
# print "w = @w\n";
|
|
$w = first { !$U{ $v }{ $_ } } @w;
|
|
if (defined $w) {
|
|
# print "w = $w\n";
|
|
$U{ $v }{ $w }++;
|
|
$U{ $w }{ $v }++;
|
|
if ($I{ $w } == 0) {
|
|
$P{ $w } = $v;
|
|
$i++;
|
|
$I{ $w } = $i;
|
|
$L{ $w } = $i;
|
|
push @S, $w;
|
|
$v = $w;
|
|
} else {
|
|
$L{ $v } = $I{ $w } if $I{ $w } < $L{ $v };
|
|
}
|
|
}
|
|
} while (defined $w);
|
|
# print "U = ", Dumper(\%U);
|
|
# print "P = ", Dumper(\%P);
|
|
# print "L = ", Dumper(\%L);
|
|
if (!defined $P{ $v }) {
|
|
# Do nothing.
|
|
} elsif ($P{ $v } ne $r) {
|
|
if ($L{ $v } < $I{ $P{ $v } }) {
|
|
$L{ $P{ $v } } = $L{ $v } if $L{ $v } < $L{ $P{ $v } };
|
|
} else {
|
|
$AP{ $P{ $v } } = $P{ $v };
|
|
push @C, _make_bcc(\@S, $v, $P{ $v } );
|
|
}
|
|
} else {
|
|
my $e;
|
|
for my $w (_shuffle keys %{ $A{ $r } }) {
|
|
# print "w = $w\n";
|
|
unless ($U{ $r }{ $w }) {
|
|
$e = $r;
|
|
# print "e = $e\n";
|
|
last;
|
|
}
|
|
}
|
|
$AP{ $e } = $e if defined $e;
|
|
push @C, _make_bcc(\@S, $v, $r);
|
|
}
|
|
# print "AP = ", Dumper(\%AP);
|
|
# print "C = ", Dumper(\@C);
|
|
# print "L = ", Dumper(\%L);
|
|
$v = defined $P{ $v } ? $P{ $v } : $r;
|
|
# print "v = $v\n";
|
|
$Avok = 0;
|
|
if (defined $v) {
|
|
if (keys %{ $A{ $v } }) {
|
|
if (!exists $P{ $v }) {
|
|
for my $w (keys %{ $A{ $v } }) {
|
|
$Avok++ if $U{ $v }{ $w };
|
|
}
|
|
# print "Avok/1 = $Avok\n";
|
|
$Avok = 0 unless $Avok == keys %{ $A{ $v } };
|
|
# print "Avok/2 = $Avok\n";
|
|
}
|
|
} else {
|
|
$Avok = 1;
|
|
# print "Avok/3 = $Avok\n";
|
|
}
|
|
}
|
|
} until ($Avok);
|
|
|
|
last if @C == 0 && !exists $S{$v};
|
|
|
|
for (my $i = 0; $i < @C; $i++) {
|
|
for my $v (@{ $C[ $i ]}) {
|
|
$V2BC{ $v }{ $i }++;
|
|
delete $T{ $v };
|
|
}
|
|
}
|
|
|
|
for (my $i = 0; $i < @C; $i++) {
|
|
if (@{ $C[ $i ] } == 2) {
|
|
push @BR, $C[ $i ];
|
|
} else {
|
|
push @BC, $C[ $i ];
|
|
}
|
|
}
|
|
|
|
if (keys %T) {
|
|
$r = $v = each %T;
|
|
}
|
|
}
|
|
|
|
return [ [values %AP], \@BC, \@BR, \%V2BC ];
|
|
}
|
|
|
|
sub biconnectivity {
|
|
my $g = shift;
|
|
$g->expect_undirected;
|
|
my $bcc = _check_cache($g, 'biconnectivity',
|
|
\&_biconnectivity_compute, @_);
|
|
return defined $bcc ? @$bcc : ( );
|
|
}
|
|
|
|
sub is_biconnected {
|
|
my $g = shift;
|
|
my ($ap, $bc) = ($g->biconnectivity(@_))[0, 1];
|
|
return defined $ap ? @$ap == 0 && $g->vertices >= 3 : undef;
|
|
}
|
|
|
|
sub is_edge_connected {
|
|
my $g = shift;
|
|
my ($br) = ($g->biconnectivity(@_))[2];
|
|
return defined $br ? @$br == 0 && $g->edges : undef;
|
|
}
|
|
|
|
sub is_edge_separable {
|
|
my $g = shift;
|
|
my $c = $g->is_edge_connected;
|
|
defined $c ? !$c && $g->edges : undef;
|
|
}
|
|
|
|
sub articulation_points {
|
|
my $g = shift;
|
|
my ($ap) = ($g->biconnectivity(@_))[0];
|
|
return defined $ap ? @$ap : ();
|
|
}
|
|
|
|
*cut_vertices = \&articulation_points;
|
|
|
|
sub biconnected_components {
|
|
my $g = shift;
|
|
my ($bc) = ($g->biconnectivity(@_))[1];
|
|
return defined $bc ? @$bc : ();
|
|
}
|
|
|
|
sub biconnected_component_by_index {
|
|
my $g = shift;
|
|
my $i = shift;
|
|
my ($bc) = ($g->biconnectivity(@_))[1];
|
|
return defined $bc ? $bc->[ $i ] : undef;
|
|
}
|
|
|
|
sub biconnected_component_by_vertex {
|
|
my $g = shift;
|
|
my $v = shift;
|
|
my ($v2bc) = ($g->biconnectivity(@_))[3];
|
|
return defined $v2bc->{ $v } ? keys %{ $v2bc->{ $v } } : ();
|
|
}
|
|
|
|
sub same_biconnected_components {
|
|
my $g = shift;
|
|
my $u = shift;
|
|
my @u = $g->biconnected_component_by_vertex($u, @_);
|
|
return 0 unless @u;
|
|
my %ubc; @ubc{ @u } = ();
|
|
while (@_) {
|
|
my $v = shift;
|
|
my @v = $g->biconnected_component_by_vertex($v);
|
|
if (@v) {
|
|
my %vbc; @vbc{ @v } = ();
|
|
my $vi;
|
|
for my $ui (keys %ubc) {
|
|
if (exists $vbc{ $ui }) {
|
|
$vi = $ui;
|
|
last;
|
|
}
|
|
}
|
|
return 0 unless defined $vi;
|
|
}
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
sub biconnected_graph {
|
|
my ($g, %opt) = @_;
|
|
my ($bc, $v2bc) = ($g->biconnectivity, %opt)[1, 3];
|
|
my $bcg = Graph::Undirected->new;
|
|
my $sc_cb =
|
|
exists $opt{super_component} ?
|
|
$opt{super_component} : $super_component;
|
|
for my $c (@$bc) {
|
|
$bcg->add_vertex(my $s = $sc_cb->(@$c));
|
|
$bcg->set_vertex_attribute($s, 'subvertices', [ @$c ]);
|
|
}
|
|
my %k;
|
|
for my $i (0..$#$bc) {
|
|
my @u = @{ $bc->[ $i ] };
|
|
my %i; @i{ @u } = ();
|
|
for my $j (0..$#$bc) {
|
|
if ($i > $j) {
|
|
my @v = @{ $bc->[ $j ] };
|
|
my %j; @j{ @v } = ();
|
|
for my $u (@u) {
|
|
if (exists $j{ $u }) {
|
|
unless ($k{ $i }{ $j }++) {
|
|
$bcg->add_edge($sc_cb->(@{$bc->[$i]}),
|
|
$sc_cb->(@{$bc->[$j]}));
|
|
}
|
|
last;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
return $bcg;
|
|
}
|
|
|
|
sub bridges {
|
|
my $g = shift;
|
|
my ($br) = ($g->biconnectivity(@_))[2];
|
|
return defined $br ? @$br : ();
|
|
}
|
|
|
|
###
|
|
# SPT.
|
|
#
|
|
|
|
sub _SPT_add {
|
|
my ($g, $h, $HF, $r, $attr, $unseen, $etc) = @_;
|
|
my $etc_r = $etc->{ $r } || 0;
|
|
for my $s ( grep { exists $unseen->{ $_ } } $g->successors( $r ) ) {
|
|
my $t = $g->get_edge_attribute( $r, $s, $attr );
|
|
$t = 1 unless defined $t;
|
|
if ($t < 0) {
|
|
require Carp;
|
|
Carp::croak("Graph::SPT_Dijkstra: edge $r-$s is negative ($t)");
|
|
}
|
|
if (!defined($etc->{ $s }) || ($etc_r + $t) < $etc->{ $s }) {
|
|
my $etc_s = $etc->{ $s } || 0;
|
|
$etc->{ $s } = $etc_r + $t;
|
|
# print "$r - $s : setting $s to $etc->{ $s } ($etc_r, $etc_s)\n";
|
|
$h->set_vertex_attribute( $s, $attr, $etc->{ $s });
|
|
$h->set_vertex_attribute( $s, 'p', $r );
|
|
$HF->add( Graph::SPTHeapElem->new($r, $s, $etc->{ $s }) );
|
|
}
|
|
}
|
|
}
|
|
|
|
sub _SPT_Dijkstra_compute {
|
|
}
|
|
|
|
sub SPT_Dijkstra {
|
|
my $g = shift;
|
|
my %opt = @_ == 1 ? (first_root => $_[0]) : @_;
|
|
my $first_root = $opt{ first_root };
|
|
unless (defined $first_root) {
|
|
$opt{ first_root } = $first_root = $g->random_vertex();
|
|
}
|
|
my $spt_di = $g->get_graph_attribute('_spt_di');
|
|
unless (defined $spt_di && exists $spt_di->{ $first_root } && $spt_di->{ $first_root }->[ 0 ] == $g->[ _G ]) {
|
|
my %etc;
|
|
my $sptg = $g->_heap_walk($g->new, \&_SPT_add, \%etc, %opt);
|
|
$spt_di->{ $first_root } = [ $g->[ _G ], $sptg ];
|
|
$g->set_graph_attribute('_spt_di', $spt_di);
|
|
}
|
|
|
|
my $spt = $spt_di->{ $first_root }->[ 1 ];
|
|
|
|
$spt->set_graph_attribute('SPT_Dijkstra_root', $first_root);
|
|
|
|
return $spt;
|
|
}
|
|
|
|
*SSSP_Dijkstra = \&SPT_Dijkstra;
|
|
|
|
*single_source_shortest_paths = \&SPT_Dijkstra;
|
|
|
|
sub SP_Dijkstra {
|
|
my ($g, $u, $v) = @_;
|
|
my $sptg = $g->SPT_Dijkstra(first_root => $u);
|
|
my @path = ($v);
|
|
my %seen;
|
|
my $V = $g->vertices;
|
|
my $p;
|
|
while (defined($p = $sptg->get_vertex_attribute($v, 'p'))) {
|
|
last if exists $seen{$p};
|
|
push @path, $p;
|
|
$v = $p;
|
|
$seen{$p}++;
|
|
last if keys %seen == $V || $u eq $v;
|
|
}
|
|
@path = () if @path && $path[-1] ne $u;
|
|
return reverse @path;
|
|
}
|
|
|
|
sub __SPT_Bellman_Ford {
|
|
my ($g, $u, $v, $attr, $d, $p, $c0, $c1) = @_;
|
|
return unless $c0->{ $u };
|
|
my $w = $g->get_edge_attribute($u, $v, $attr);
|
|
$w = 1 unless defined $w;
|
|
if (defined $d->{ $v }) {
|
|
if (defined $d->{ $u }) {
|
|
if ($d->{ $v } > $d->{ $u } + $w) {
|
|
$d->{ $v } = $d->{ $u } + $w;
|
|
$p->{ $v } = $u;
|
|
$c1->{ $v }++;
|
|
}
|
|
} # else !defined $d->{ $u } && defined $d->{ $v }
|
|
} else {
|
|
if (defined $d->{ $u }) {
|
|
# defined $d->{ $u } && !defined $d->{ $v }
|
|
$d->{ $v } = $d->{ $u } + $w;
|
|
$p->{ $v } = $u;
|
|
$c1->{ $v }++;
|
|
} # else !defined $d->{ $u } && !defined $d->{ $v }
|
|
}
|
|
}
|
|
|
|
sub _SPT_Bellman_Ford {
|
|
my ($g, $opt, $unseenh, $unseena, $r, $next, $code, $attr) = @_;
|
|
my %d;
|
|
return unless defined $r;
|
|
$d{ $r } = 0;
|
|
my %p;
|
|
my $V = $g->vertices;
|
|
my %c0; # Changed during the last iteration?
|
|
$c0{ $r }++;
|
|
for (my $i = 0; $i < $V; $i++) {
|
|
my %c1;
|
|
for my $e ($g->edges) {
|
|
my ($u, $v) = @$e;
|
|
__SPT_Bellman_Ford($g, $u, $v, $attr, \%d, \%p, \%c0, \%c1);
|
|
if ($g->undirected) {
|
|
__SPT_Bellman_Ford($g, $v, $u, $attr, \%d, \%p, \%c0, \%c1);
|
|
}
|
|
}
|
|
%c0 = %c1 unless $i == $V - 1;
|
|
}
|
|
|
|
for my $e ($g->edges) {
|
|
my ($u, $v) = @$e;
|
|
if (defined $d{ $u } && defined $d{ $v }) {
|
|
my $d = $g->get_edge_attribute($u, $v, $attr);
|
|
if (defined $d && $d{ $v } > $d{ $u } + $d) {
|
|
require Carp;
|
|
Carp::croak("Graph::SPT_Bellman_Ford: negative cycle exists");
|
|
}
|
|
}
|
|
}
|
|
|
|
return (\%p, \%d);
|
|
}
|
|
|
|
sub _SPT_Bellman_Ford_compute {
|
|
}
|
|
|
|
sub SPT_Bellman_Ford {
|
|
my $g = shift;
|
|
|
|
my ($opt, $unseenh, $unseena, $r, $next, $code, $attr) = $g->_root_opt(@_);
|
|
|
|
unless (defined $r) {
|
|
$r = $g->random_vertex();
|
|
return unless defined $r;
|
|
}
|
|
|
|
my $spt_bf = $g->get_graph_attribute('_spt_bf');
|
|
unless (defined $spt_bf &&
|
|
exists $spt_bf->{ $r } && $spt_bf->{ $r }->[ 0 ] == $g->[ _G ]) {
|
|
my ($p, $d) =
|
|
$g->_SPT_Bellman_Ford($opt, $unseenh, $unseena,
|
|
$r, $next, $code, $attr);
|
|
my $h = $g->new;
|
|
for my $v (keys %$p) {
|
|
my $u = $p->{ $v };
|
|
$h->add_edge( $u, $v );
|
|
$h->set_edge_attribute( $u, $v, $attr,
|
|
$g->get_edge_attribute($u, $v, $attr));
|
|
$h->set_vertex_attribute( $v, $attr, $d->{ $v } );
|
|
$h->set_vertex_attribute( $v, 'p', $u );
|
|
}
|
|
$spt_bf->{ $r } = [ $g->[ _G ], $h ];
|
|
$g->set_graph_attribute('_spt_bf', $spt_bf);
|
|
}
|
|
|
|
my $spt = $spt_bf->{ $r }->[ 1 ];
|
|
|
|
$spt->set_graph_attribute('SPT_Bellman_Ford_root', $r);
|
|
|
|
return $spt;
|
|
}
|
|
|
|
*SSSP_Bellman_Ford = \&SPT_Bellman_Ford;
|
|
|
|
sub SP_Bellman_Ford {
|
|
my ($g, $u, $v) = @_;
|
|
my $sptg = $g->SPT_Bellman_Ford(first_root => $u);
|
|
my @path = ($v);
|
|
my %seen;
|
|
my $V = $g->vertices;
|
|
my $p;
|
|
while (defined($p = $sptg->get_vertex_attribute($v, 'p'))) {
|
|
last if exists $seen{$p};
|
|
push @path, $p;
|
|
$v = $p;
|
|
$seen{$p}++;
|
|
last if keys %seen == $V;
|
|
}
|
|
# @path = () if @path && "$path[-1]" ne "$u";
|
|
return reverse @path;
|
|
}
|
|
|
|
###
|
|
# Transitive Closure.
|
|
#
|
|
|
|
sub TransitiveClosure_Floyd_Warshall {
|
|
my $self = shift;
|
|
my $class = ref $self || $self;
|
|
$self = shift unless ref $self;
|
|
bless Graph::TransitiveClosure->new($self, @_), $class;
|
|
}
|
|
|
|
*transitive_closure = \&TransitiveClosure_Floyd_Warshall;
|
|
|
|
sub APSP_Floyd_Warshall {
|
|
my $self = shift;
|
|
my $class = ref $self || $self;
|
|
$self = shift unless ref $self;
|
|
bless Graph::TransitiveClosure->new($self, path => 1, @_), $class;
|
|
}
|
|
|
|
*all_pairs_shortest_paths = \&APSP_Floyd_Warshall;
|
|
|
|
sub _transitive_closure_matrix_compute {
|
|
}
|
|
|
|
sub transitive_closure_matrix {
|
|
my $g = shift;
|
|
my $tcm = $g->get_graph_attribute('_tcm');
|
|
if (defined $tcm) {
|
|
if (ref $tcm eq 'ARRAY') { # YECHHH!
|
|
if ($tcm->[ 0 ] == $g->[ _G ]) {
|
|
$tcm = $tcm->[ 1 ];
|
|
} else {
|
|
undef $tcm;
|
|
}
|
|
}
|
|
}
|
|
unless (defined $tcm) {
|
|
my $apsp = $g->APSP_Floyd_Warshall(@_);
|
|
$tcm = $apsp->get_graph_attribute('_tcm');
|
|
$g->set_graph_attribute('_tcm', [ $g->[ _G ], $tcm ]);
|
|
}
|
|
|
|
return $tcm;
|
|
}
|
|
|
|
sub path_length {
|
|
my $g = shift;
|
|
my $tcm = $g->transitive_closure_matrix;
|
|
$tcm->path_length(@_);
|
|
}
|
|
|
|
sub path_predecessor {
|
|
my $g = shift;
|
|
my $tcm = $g->transitive_closure_matrix;
|
|
$tcm->path_predecessor(@_);
|
|
}
|
|
|
|
sub path_vertices {
|
|
my $g = shift;
|
|
my $tcm = $g->transitive_closure_matrix;
|
|
$tcm->path_vertices(@_);
|
|
}
|
|
|
|
sub is_reachable {
|
|
my $g = shift;
|
|
my $tcm = $g->transitive_closure_matrix;
|
|
$tcm->is_reachable(@_);
|
|
}
|
|
|
|
sub for_shortest_paths {
|
|
my $g = shift;
|
|
my $c = shift;
|
|
my $t = $g->transitive_closure_matrix;
|
|
my @v = $g->vertices;
|
|
my $n = 0;
|
|
for my $u (@v) {
|
|
for my $v (@v) {
|
|
next unless $t->is_reachable($u, $v);
|
|
$n++;
|
|
$c->($t, $u, $v, $n);
|
|
}
|
|
}
|
|
return $n;
|
|
}
|
|
|
|
sub _minmax_path {
|
|
my $g = shift;
|
|
my $min;
|
|
my $max;
|
|
my $minp;
|
|
my $maxp;
|
|
$g->for_shortest_paths(sub {
|
|
my ($t, $u, $v, $n) = @_;
|
|
my $l = $t->path_length($u, $v);
|
|
return unless defined $l;
|
|
my $p;
|
|
if ($u ne $v && (!defined $max || $l > $max)) {
|
|
$max = $l;
|
|
$maxp = $p = [ $t->path_vertices($u, $v) ];
|
|
}
|
|
if ($u ne $v && (!defined $min || $l < $min)) {
|
|
$min = $l;
|
|
$minp = $p || [ $t->path_vertices($u, $v) ];
|
|
}
|
|
});
|
|
return ($min, $max, $minp, $maxp);
|
|
}
|
|
|
|
sub diameter {
|
|
my $g = shift;
|
|
my ($min, $max, $minp, $maxp) = $g->_minmax_path(@_);
|
|
return defined $maxp ? (wantarray ? @$maxp : $max) : undef;
|
|
}
|
|
|
|
*graph_diameter = \&diameter;
|
|
|
|
sub longest_path {
|
|
my ($g, $u, $v) = @_;
|
|
my $t = $g->transitive_closure_matrix;
|
|
if (defined $u) {
|
|
if (defined $v) {
|
|
return wantarray ?
|
|
$t->path_vertices($u, $v) : $t->path_length($u, $v);
|
|
} else {
|
|
my $max;
|
|
my @max;
|
|
for my $v ($g->vertices) {
|
|
next if $u eq $v;
|
|
my $l = $t->path_length($u, $v);
|
|
if (defined $l && (!defined $max || $l > $max)) {
|
|
$max = $l;
|
|
@max = $t->path_vertices($u, $v);
|
|
}
|
|
}
|
|
return wantarray ? @max : $max;
|
|
}
|
|
} else {
|
|
if (defined $v) {
|
|
my $max;
|
|
my @max;
|
|
for my $u ($g->vertices) {
|
|
next if $u eq $v;
|
|
my $l = $t->path_length($u, $v);
|
|
if (defined $l && (!defined $max || $l > $max)) {
|
|
$max = $l;
|
|
@max = $t->path_vertices($u, $v);
|
|
}
|
|
}
|
|
return wantarray ? @max : @max - 1;
|
|
} else {
|
|
my ($min, $max, $minp, $maxp) = $g->_minmax_path(@_);
|
|
return defined $maxp ? (wantarray ? @$maxp : $max) : undef;
|
|
}
|
|
}
|
|
}
|
|
|
|
sub vertex_eccentricity {
|
|
my ($g, $u) = @_;
|
|
$g->expect_undirected;
|
|
if ($g->is_connected) {
|
|
my $max;
|
|
for my $v ($g->vertices) {
|
|
next if $u eq $v;
|
|
my $l = $g->path_length($u, $v);
|
|
if (defined $l && (!defined $max || $l > $max)) {
|
|
$max = $l;
|
|
}
|
|
}
|
|
return $max;
|
|
} else {
|
|
return Infinity();
|
|
}
|
|
}
|
|
|
|
sub shortest_path {
|
|
my ($g, $u, $v) = @_;
|
|
$g->expect_undirected;
|
|
my $t = $g->transitive_closure_matrix;
|
|
if (defined $u) {
|
|
if (defined $v) {
|
|
return wantarray ?
|
|
$t->path_vertices($u, $v) : $t->path_length($u, $v);
|
|
} else {
|
|
my $min;
|
|
my @min;
|
|
for my $v ($g->vertices) {
|
|
next if $u eq $v;
|
|
my $l = $t->path_length($u, $v);
|
|
if (defined $l && (!defined $min || $l < $min)) {
|
|
$min = $l;
|
|
@min = $t->path_vertices($u, $v);
|
|
}
|
|
}
|
|
return wantarray ? @min : $min;
|
|
}
|
|
} else {
|
|
if (defined $v) {
|
|
my $min;
|
|
my @min;
|
|
for my $u ($g->vertices) {
|
|
next if $u eq $v;
|
|
my $l = $t->path_length($u, $v);
|
|
if (defined $l && (!defined $min || $l < $min)) {
|
|
$min = $l;
|
|
@min = $t->path_vertices($u, $v);
|
|
}
|
|
}
|
|
return wantarray ? @min : $min;
|
|
} else {
|
|
my ($min, $max, $minp, $maxp) = $g->_minmax_path(@_);
|
|
return defined $minp ? (wantarray ? @$minp : $min) : undef;
|
|
}
|
|
}
|
|
}
|
|
|
|
sub radius {
|
|
my $g = shift;
|
|
$g->expect_undirected;
|
|
my ($center, $radius) = (undef, Infinity());
|
|
for my $v ($g->vertices) {
|
|
my $x = $g->vertex_eccentricity($v);
|
|
($center, $radius) = ($v, $x) if defined $x && $x < $radius;
|
|
}
|
|
return $radius;
|
|
}
|
|
|
|
sub center_vertices {
|
|
my ($g, $delta) = @_;
|
|
$g->expect_undirected;
|
|
$delta = 0 unless defined $delta;
|
|
$delta = abs($delta);
|
|
my @c;
|
|
my $r = $g->radius;
|
|
if (defined $r) {
|
|
for my $v ($g->vertices) {
|
|
my $e = $g->vertex_eccentricity($v);
|
|
next unless defined $e;
|
|
push @c, $v if abs($e - $r) <= $delta;
|
|
}
|
|
}
|
|
return @c;
|
|
}
|
|
|
|
*centre_vertices = \¢er_vertices;
|
|
|
|
sub average_path_length {
|
|
my $g = shift;
|
|
my @A = @_;
|
|
my $d = 0;
|
|
my $m = 0;
|
|
my $n = $g->for_shortest_paths(sub {
|
|
my ($t, $u, $v, $n) = @_;
|
|
my $l = $t->path_length($u, $v);
|
|
if ($l) {
|
|
my $c = @A == 0 ||
|
|
(@A == 1 && $u eq $A[0]) ||
|
|
((@A == 2) &&
|
|
(defined $A[0] &&
|
|
$u eq $A[0]) ||
|
|
(defined $A[1] &&
|
|
$v eq $A[1]));
|
|
if ($c) {
|
|
$d += $l;
|
|
$m++;
|
|
}
|
|
}
|
|
});
|
|
return $m ? $d / $m : undef;
|
|
}
|
|
|
|
###
|
|
# Simple tests.
|
|
#
|
|
|
|
sub is_multi_graph {
|
|
my $g = shift;
|
|
return 0 unless $g->is_multiedged || $g->is_countedged;
|
|
my $multiedges = 0;
|
|
for my $e ($g->edges05) {
|
|
my ($u, @v) = @$e;
|
|
for my $v (@v) {
|
|
return 0 if $u eq $v;
|
|
}
|
|
$multiedges++ if $g->get_edge_count(@$e) > 1;
|
|
}
|
|
return $multiedges;
|
|
}
|
|
|
|
sub is_simple_graph {
|
|
my $g = shift;
|
|
return 1 unless $g->is_countedged || $g->is_multiedged;
|
|
for my $e ($g->edges05) {
|
|
return 0 if $g->get_edge_count(@$e) > 1;
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
sub is_pseudo_graph {
|
|
my $g = shift;
|
|
my $m = $g->is_countedged || $g->is_multiedged;
|
|
for my $e ($g->edges05) {
|
|
my ($u, @v) = @$e;
|
|
for my $v (@v) {
|
|
return 1 if $u eq $v;
|
|
}
|
|
return 1 if $m && $g->get_edge_count($u, @v) > 1;
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
###
|
|
# Rough isomorphism guess.
|
|
#
|
|
|
|
my %_factorial = (0 => 1, 1 => 1);
|
|
|
|
sub __factorial {
|
|
my $n = shift;
|
|
for (my $i = 2; $i <= $n; $i++) {
|
|
next if exists $_factorial{$i};
|
|
$_factorial{$i} = $i * $_factorial{$i - 1};
|
|
}
|
|
$_factorial{$n};
|
|
}
|
|
|
|
sub _factorial {
|
|
my $n = int(shift);
|
|
if ($n < 0) {
|
|
require Carp;
|
|
Carp::croak("factorial of a negative number");
|
|
}
|
|
__factorial($n) unless exists $_factorial{$n};
|
|
return $_factorial{$n};
|
|
}
|
|
|
|
sub could_be_isomorphic {
|
|
my ($g0, $g1) = @_;
|
|
return 0 unless $g0->vertices == $g1->vertices;
|
|
return 0 unless $g0->edges05 == $g1->edges05;
|
|
my %d0;
|
|
for my $v0 ($g0->vertices) {
|
|
$d0{ $g0->in_degree($v0) }{ $g0->out_degree($v0) }++
|
|
}
|
|
my %d1;
|
|
for my $v1 ($g1->vertices) {
|
|
$d1{ $g1->in_degree($v1) }{ $g1->out_degree($v1) }++
|
|
}
|
|
return 0 unless keys %d0 == keys %d1;
|
|
for my $da (keys %d0) {
|
|
return 0
|
|
unless exists $d1{$da} &&
|
|
keys %{ $d0{$da} } == keys %{ $d1{$da} };
|
|
for my $db (keys %{ $d0{$da} }) {
|
|
return 0
|
|
unless exists $d1{$da}{$db} &&
|
|
$d0{$da}{$db} == $d1{$da}{$db};
|
|
}
|
|
}
|
|
for my $da (keys %d0) {
|
|
for my $db (keys %{ $d0{$da} }) {
|
|
return 0 unless $d1{$da}{$db} == $d0{$da}{$db};
|
|
}
|
|
delete $d1{$da};
|
|
}
|
|
return 0 unless keys %d1 == 0;
|
|
my $f = 1;
|
|
for my $da (keys %d0) {
|
|
for my $db (keys %{ $d0{$da} }) {
|
|
$f *= _factorial(abs($d0{$da}{$db}));
|
|
}
|
|
}
|
|
return $f;
|
|
}
|
|
|
|
###
|
|
# Debugging.
|
|
#
|
|
|
|
sub _dump {
|
|
require Data::Dumper;
|
|
my $d = Data::Dumper->new([$_[0]],[ref $_[0]]);
|
|
defined wantarray ? $d->Dump : print $d->Dump;
|
|
}
|
|
|
|
1;
|