| Filename | /Users/ap13/perl5/lib/perl5/Graph/TransitiveClosure/Matrix.pm |
| Statements | Executed 7 statements in 1.51ms |
| Calls | P | F | Exclusive Time |
Inclusive Time |
Subroutine |
|---|---|---|---|---|---|
| 1 | 1 | 1 | 745µs | 2.66ms | Graph::TransitiveClosure::Matrix::BEGIN@5 |
| 1 | 1 | 1 | 12µs | 25µs | Graph::TransitiveClosure::Matrix::BEGIN@3 |
| 1 | 1 | 1 | 7µs | 7µs | Graph::TransitiveClosure::Matrix::BEGIN@6 |
| 0 | 0 | 0 | 0s | 0s | Graph::TransitiveClosure::Matrix::_new |
| 0 | 0 | 0 | 0s | 0s | Graph::TransitiveClosure::Matrix::has_vertices |
| 0 | 0 | 0 | 0s | 0s | Graph::TransitiveClosure::Matrix::is_reachable |
| 0 | 0 | 0 | 0s | 0s | Graph::TransitiveClosure::Matrix::is_transitive |
| 0 | 0 | 0 | 0s | 0s | Graph::TransitiveClosure::Matrix::new |
| 0 | 0 | 0 | 0s | 0s | Graph::TransitiveClosure::Matrix::path_length |
| 0 | 0 | 0 | 0s | 0s | Graph::TransitiveClosure::Matrix::path_predecessor |
| 0 | 0 | 0 | 0s | 0s | Graph::TransitiveClosure::Matrix::path_vertices |
| 0 | 0 | 0 | 0s | 0s | Graph::TransitiveClosure::Matrix::vertices |
| Line | State ments |
Time on line |
Calls | Time in subs |
Code |
|---|---|---|---|---|---|
| 1 | package Graph::TransitiveClosure::Matrix; | ||||
| 2 | |||||
| 3 | 2 | 23µs | 2 | 37µs | # spent 25µs (12+12) within Graph::TransitiveClosure::Matrix::BEGIN@3 which was called:
# once (12µs+12µs) by Graph::TransitiveClosure::BEGIN@10 at line 3 # spent 25µs making 1 call to Graph::TransitiveClosure::Matrix::BEGIN@3
# spent 12µs making 1 call to strict::import |
| 4 | |||||
| 5 | 2 | 112µs | 1 | 2.66ms | # spent 2.66ms (745µs+1.91) within Graph::TransitiveClosure::Matrix::BEGIN@5 which was called:
# once (745µs+1.91ms) by Graph::TransitiveClosure::BEGIN@10 at line 5 # spent 2.66ms making 1 call to Graph::TransitiveClosure::Matrix::BEGIN@5 |
| 6 | 2 | 1.37ms | 1 | 7µs | # spent 7µs within Graph::TransitiveClosure::Matrix::BEGIN@6 which was called:
# once (7µs+0s) by Graph::TransitiveClosure::BEGIN@10 at line 6 # spent 7µs making 1 call to Graph::TransitiveClosure::Matrix::BEGIN@6 |
| 7 | |||||
| 8 | sub _new { | ||||
| 9 | my ($g, $class, $opt, $want_transitive, $want_reflexive, $want_path, $want_path_vertices) = @_; | ||||
| 10 | my $m = Graph::AdjacencyMatrix->new($g, %$opt); | ||||
| 11 | my @V = $g->vertices; | ||||
| 12 | my $am = $m->adjacency_matrix; | ||||
| 13 | my $dm; # The distance matrix. | ||||
| 14 | my $pm; # The predecessor matrix. | ||||
| 15 | my @di; | ||||
| 16 | my %di; @di{ @V } = 0..$#V; | ||||
| 17 | my @ai = @{ $am->[0] }; | ||||
| 18 | my %ai = %{ $am->[1] }; | ||||
| 19 | my @pi; | ||||
| 20 | my %pi; | ||||
| 21 | unless ($want_transitive) { | ||||
| 22 | $dm = $m->distance_matrix; | ||||
| 23 | @di = @{ $dm->[0] }; | ||||
| 24 | %di = %{ $dm->[1] }; | ||||
| 25 | $pm = Graph::Matrix->new($g); | ||||
| 26 | @pi = @{ $pm->[0] }; | ||||
| 27 | %pi = %{ $pm->[1] }; | ||||
| 28 | for my $u (@V) { | ||||
| 29 | my $diu = $di{$u}; | ||||
| 30 | my $aiu = $ai{$u}; | ||||
| 31 | for my $v (@V) { | ||||
| 32 | my $div = $di{$v}; | ||||
| 33 | my $aiv = $ai{$v}; | ||||
| 34 | next unless | ||||
| 35 | # $am->get($u, $v) | ||||
| 36 | vec($ai[$aiu], $aiv, 1) | ||||
| 37 | ; | ||||
| 38 | # $dm->set($u, $v, $u eq $v ? 0 : 1) | ||||
| 39 | $di[$diu]->[$div] = $u eq $v ? 0 : 1 | ||||
| 40 | unless | ||||
| 41 | defined | ||||
| 42 | # $dm->get($u, $v) | ||||
| 43 | $di[$diu]->[$div] | ||||
| 44 | ; | ||||
| 45 | $pi[$diu]->[$div] = $v unless $u eq $v; | ||||
| 46 | } | ||||
| 47 | } | ||||
| 48 | } | ||||
| 49 | # XXX (see the bits below): sometimes, being nice and clean is the | ||||
| 50 | # wrong thing to do. In this case, using the public API for graph | ||||
| 51 | # transitive matrices and bitmatrices makes things awfully slow. | ||||
| 52 | # Instead, we go straight for the jugular of the data structures. | ||||
| 53 | for my $u (@V) { | ||||
| 54 | my $diu = $di{$u}; | ||||
| 55 | my $aiu = $ai{$u}; | ||||
| 56 | my $didiu = $di[$diu]; | ||||
| 57 | my $aiaiu = $ai[$aiu]; | ||||
| 58 | for my $v (@V) { | ||||
| 59 | my $div = $di{$v}; | ||||
| 60 | my $aiv = $ai{$v}; | ||||
| 61 | my $didiv = $di[$div]; | ||||
| 62 | my $aiaiv = $ai[$aiv]; | ||||
| 63 | if ( | ||||
| 64 | # $am->get($v, $u) | ||||
| 65 | vec($aiaiv, $aiu, 1) | ||||
| 66 | || ($want_reflexive && $u eq $v)) { | ||||
| 67 | my $aivivo = $aiaiv; | ||||
| 68 | if ($want_transitive) { | ||||
| 69 | if ($want_reflexive) { | ||||
| 70 | for my $w (@V) { | ||||
| 71 | next if $w eq $u; | ||||
| 72 | my $aiw = $ai{$w}; | ||||
| 73 | return 0 | ||||
| 74 | if vec($aiaiu, $aiw, 1) && | ||||
| 75 | !vec($aiaiv, $aiw, 1); | ||||
| 76 | } | ||||
| 77 | # See XXX above. | ||||
| 78 | # for my $w (@V) { | ||||
| 79 | # my $aiw = $ai{$w}; | ||||
| 80 | # if ( | ||||
| 81 | # # $am->get($u, $w) | ||||
| 82 | # vec($aiaiu, $aiw, 1) | ||||
| 83 | # || ($u eq $w)) { | ||||
| 84 | # return 0 | ||||
| 85 | # if $u ne $w && | ||||
| 86 | # # !$am->get($v, $w) | ||||
| 87 | # !vec($aiaiv, $aiw, 1) | ||||
| 88 | # ; | ||||
| 89 | # # $am->set($v, $w) | ||||
| 90 | # vec($aiaiv, $aiw, 1) = 1 | ||||
| 91 | # ; | ||||
| 92 | # } | ||||
| 93 | # } | ||||
| 94 | } else { | ||||
| 95 | # See XXX above. | ||||
| 96 | # for my $w (@V) { | ||||
| 97 | # my $aiw = $ai{$w}; | ||||
| 98 | # if ( | ||||
| 99 | # # $am->get($u, $w) | ||||
| 100 | # vec($aiaiu, $aiw, 1) | ||||
| 101 | # ) { | ||||
| 102 | # return 0 | ||||
| 103 | # if $u ne $w && | ||||
| 104 | # # !$am->get($v, $w) | ||||
| 105 | # !vec($aiaiv, $aiw, 1) | ||||
| 106 | # ; | ||||
| 107 | # # $am->set($v, $w) | ||||
| 108 | # vec($aiaiv, $aiw, 1) = 1 | ||||
| 109 | # ; | ||||
| 110 | # } | ||||
| 111 | # } | ||||
| 112 | $aiaiv |= $aiaiu; | ||||
| 113 | } | ||||
| 114 | } else { | ||||
| 115 | if ($want_reflexive) { | ||||
| 116 | $aiaiv |= $aiaiu; | ||||
| 117 | vec($aiaiv, $aiu, 1) = 1; | ||||
| 118 | # See XXX above. | ||||
| 119 | # for my $w (@V) { | ||||
| 120 | # my $aiw = $ai{$w}; | ||||
| 121 | # if ( | ||||
| 122 | # # $am->get($u, $w) | ||||
| 123 | # vec($aiaiu, $aiw, 1) | ||||
| 124 | # || ($u eq $w)) { | ||||
| 125 | # # $am->set($v, $w) | ||||
| 126 | # vec($aiaiv, $aiw, 1) = 1 | ||||
| 127 | # ; | ||||
| 128 | # } | ||||
| 129 | # } | ||||
| 130 | } else { | ||||
| 131 | $aiaiv |= $aiaiu; | ||||
| 132 | # See XXX above. | ||||
| 133 | # for my $w (@V) { | ||||
| 134 | # my $aiw = $ai{$w}; | ||||
| 135 | # if ( | ||||
| 136 | # # $am->get($u, $w) | ||||
| 137 | # vec($aiaiu, $aiw, 1) | ||||
| 138 | # ) { | ||||
| 139 | # # $am->set($v, $w) | ||||
| 140 | # vec($aiaiv, $aiw, 1) = 1 | ||||
| 141 | # ; | ||||
| 142 | # } | ||||
| 143 | # } | ||||
| 144 | } | ||||
| 145 | } | ||||
| 146 | if ($aiaiv ne $aivivo) { | ||||
| 147 | $ai[$aiv] = $aiaiv; | ||||
| 148 | $aiaiu = $aiaiv if $u eq $v; | ||||
| 149 | } | ||||
| 150 | } | ||||
| 151 | if ($want_path && !$want_transitive) { | ||||
| 152 | for my $w (@V) { | ||||
| 153 | my $aiw = $ai{$w}; | ||||
| 154 | next unless | ||||
| 155 | # See XXX above. | ||||
| 156 | # $am->get($v, $u) | ||||
| 157 | vec($aiaiv, $aiu, 1) | ||||
| 158 | && | ||||
| 159 | # See XXX above. | ||||
| 160 | # $am->get($u, $w) | ||||
| 161 | vec($aiaiu, $aiw, 1) | ||||
| 162 | ; | ||||
| 163 | my $diw = $di{$w}; | ||||
| 164 | my ($d0, $d1a, $d1b); | ||||
| 165 | if (defined $dm) { | ||||
| 166 | # See XXX above. | ||||
| 167 | # $d0 = $dm->get($v, $w); | ||||
| 168 | # $d1a = $dm->get($v, $u) || 1; | ||||
| 169 | # $d1b = $dm->get($u, $w) || 1; | ||||
| 170 | $d0 = $didiv->[$diw]; | ||||
| 171 | $d1a = $didiv->[$diu] || 1; | ||||
| 172 | $d1b = $didiu->[$diw] || 1; | ||||
| 173 | } else { | ||||
| 174 | $d1a = 1; | ||||
| 175 | $d1b = 1; | ||||
| 176 | } | ||||
| 177 | my $d1 = $d1a + $d1b; | ||||
| 178 | if (!defined $d0 || ($d1 < $d0)) { | ||||
| 179 | # print "d1 = $d1a ($v, $u) + $d1b ($u, $w) = $d1 ($v, $w) (".(defined$d0?$d0:"-").")\n"; | ||||
| 180 | # See XXX above. | ||||
| 181 | # $dm->set($v, $w, $d1); | ||||
| 182 | $didiv->[$diw] = $d1; | ||||
| 183 | $pi[$div]->[$diw] = $pi[$div]->[$diu] | ||||
| 184 | if $want_path_vertices; | ||||
| 185 | } | ||||
| 186 | } | ||||
| 187 | # $dm->set($u, $v, 1) | ||||
| 188 | $didiu->[$div] = 1 | ||||
| 189 | if $u ne $v && | ||||
| 190 | # $am->get($u, $v) | ||||
| 191 | vec($aiaiu, $aiv, 1) | ||||
| 192 | && | ||||
| 193 | # !defined $dm->get($u, $v); | ||||
| 194 | !defined $didiu->[$div]; | ||||
| 195 | } | ||||
| 196 | } | ||||
| 197 | } | ||||
| 198 | return 1 if $want_transitive; | ||||
| 199 | my %V; @V{ @V } = @V; | ||||
| 200 | $am->[0] = \@ai; | ||||
| 201 | $am->[1] = \%ai; | ||||
| 202 | if (defined $dm) { | ||||
| 203 | $dm->[0] = \@di; | ||||
| 204 | $dm->[1] = \%di; | ||||
| 205 | } | ||||
| 206 | if (defined $pm) { | ||||
| 207 | $pm->[0] = \@pi; | ||||
| 208 | $pm->[1] = \%pi; | ||||
| 209 | } | ||||
| 210 | bless [ $am, $dm, $pm, \%V ], $class; | ||||
| 211 | } | ||||
| 212 | |||||
| 213 | sub new { | ||||
| 214 | my ($class, $g, %opt) = @_; | ||||
| 215 | my %am_opt = (distance_matrix => 1); | ||||
| 216 | if (exists $opt{attribute_name}) { | ||||
| 217 | $am_opt{attribute_name} = $opt{attribute_name}; | ||||
| 218 | delete $opt{attribute_name}; | ||||
| 219 | } | ||||
| 220 | if ($opt{distance_matrix}) { | ||||
| 221 | $am_opt{distance_matrix} = $opt{distance_matrix}; | ||||
| 222 | } | ||||
| 223 | delete $opt{distance_matrix}; | ||||
| 224 | if (exists $opt{path}) { | ||||
| 225 | $opt{path_length} = $opt{path}; | ||||
| 226 | $opt{path_vertices} = $opt{path}; | ||||
| 227 | delete $opt{path}; | ||||
| 228 | } | ||||
| 229 | my $want_path_length; | ||||
| 230 | if (exists $opt{path_length}) { | ||||
| 231 | $want_path_length = $opt{path_length}; | ||||
| 232 | delete $opt{path_length}; | ||||
| 233 | } | ||||
| 234 | my $want_path_vertices; | ||||
| 235 | if (exists $opt{path_vertices}) { | ||||
| 236 | $want_path_vertices = $opt{path_vertices}; | ||||
| 237 | delete $opt{path_vertices}; | ||||
| 238 | } | ||||
| 239 | my $want_reflexive; | ||||
| 240 | if (exists $opt{reflexive}) { | ||||
| 241 | $want_reflexive = $opt{reflexive}; | ||||
| 242 | delete $opt{reflexive}; | ||||
| 243 | } | ||||
| 244 | my $want_transitive; | ||||
| 245 | if (exists $opt{is_transitive}) { | ||||
| 246 | $want_transitive = $opt{is_transitive}; | ||||
| 247 | $am_opt{is_transitive} = $want_transitive; | ||||
| 248 | delete $opt{is_transitive}; | ||||
| 249 | } | ||||
| 250 | die "Graph::TransitiveClosure::Matrix::new: Unknown options: @{[map { qq['$_' => $opt{$_}]} keys %opt]}" | ||||
| 251 | if keys %opt; | ||||
| 252 | $want_reflexive = 1 unless defined $want_reflexive; | ||||
| 253 | my $want_path = $want_path_length || $want_path_vertices; | ||||
| 254 | # $g->expect_dag if $want_path; | ||||
| 255 | _new($g, $class, | ||||
| 256 | \%am_opt, | ||||
| 257 | $want_transitive, $want_reflexive, | ||||
| 258 | $want_path, $want_path_vertices); | ||||
| 259 | } | ||||
| 260 | |||||
| 261 | sub has_vertices { | ||||
| 262 | my $tc = shift; | ||||
| 263 | for my $v (@_) { | ||||
| 264 | return 0 unless exists $tc->[3]->{ $v }; | ||||
| 265 | } | ||||
| 266 | return 1; | ||||
| 267 | } | ||||
| 268 | |||||
| 269 | sub is_reachable { | ||||
| 270 | my ($tc, $u, $v) = @_; | ||||
| 271 | return undef unless $tc->has_vertices($u, $v); | ||||
| 272 | return 1 if $u eq $v; | ||||
| 273 | $tc->[0]->get($u, $v); | ||||
| 274 | } | ||||
| 275 | |||||
| 276 | sub is_transitive { | ||||
| 277 | if (@_ == 1) { # Any graph. | ||||
| 278 | __PACKAGE__->new($_[0], is_transitive => 1); # Scary. | ||||
| 279 | } else { # A TC graph. | ||||
| 280 | my ($tc, $u, $v) = @_; | ||||
| 281 | return undef unless $tc->has_vertices($u, $v); | ||||
| 282 | $tc->[0]->get($u, $v); | ||||
| 283 | } | ||||
| 284 | } | ||||
| 285 | |||||
| 286 | sub vertices { | ||||
| 287 | my $tc = shift; | ||||
| 288 | values %{ $tc->[3] }; | ||||
| 289 | } | ||||
| 290 | |||||
| 291 | sub path_length { | ||||
| 292 | my ($tc, $u, $v) = @_; | ||||
| 293 | return undef unless $tc->has_vertices($u, $v); | ||||
| 294 | return 0 if $u eq $v; | ||||
| 295 | $tc->[1]->get($u, $v); | ||||
| 296 | } | ||||
| 297 | |||||
| 298 | sub path_predecessor { | ||||
| 299 | my ($tc, $u, $v) = @_; | ||||
| 300 | return undef if $u eq $v; | ||||
| 301 | return undef unless $tc->has_vertices($u, $v); | ||||
| 302 | $tc->[2]->get($u, $v); | ||||
| 303 | } | ||||
| 304 | |||||
| 305 | sub path_vertices { | ||||
| 306 | my ($tc, $u, $v) = @_; | ||||
| 307 | return unless $tc->is_reachable($u, $v); | ||||
| 308 | return wantarray ? () : 0 if $u eq $v; | ||||
| 309 | my @v = ( $u ); | ||||
| 310 | while ($u ne $v) { | ||||
| 311 | last unless defined($u = $tc->path_predecessor($u, $v)); | ||||
| 312 | push @v, $u; | ||||
| 313 | } | ||||
| 314 | $tc->[2]->set($u, $v, [ @v ]) if @v; | ||||
| 315 | return @v; | ||||
| 316 | } | ||||
| 317 | |||||
| 318 | 1 | 4µs | 1; | ||
| 319 | __END__ |