| 1 | package Heap::Binomial; |
| 2 | |
| 3 | use strict; |
| 4 | use vars qw($VERSION @ISA @EXPORT @EXPORT_OK); |
| 5 | |
| 6 | require Exporter; |
| 7 | require AutoLoader; |
| 8 | |
| 9 | @ISA = qw(Exporter AutoLoader); |
| 10 | |
| 11 | # No names exported. |
| 12 | # No names available for export. |
| 13 | @EXPORT = ( ); |
| 14 | |
| 15 | $VERSION = '0.70'; |
| 16 | |
| 17 | |
| 18 | # Preloaded methods go here. |
| 19 | |
| 20 | |
| 21 | # common names |
| 22 | # h - heap head |
| 23 | # el - linkable element, contains user-provided value |
| 24 | # v - user-provided value |
| 25 | |
| 26 | ################################################# debugging control |
| 27 | |
| 28 | my $debug = 0; |
| 29 | my $validate = 0; |
| 30 | |
| 31 | # enable/disable debugging output |
| 32 | sub debug { |
| 33 | @_ ? ($debug = shift) : $debug; |
| 34 | } |
| 35 | |
| 36 | # enable/disable validation checks on values |
| 37 | sub validate { |
| 38 | @_ ? ($validate = shift) : $validate; |
| 39 | } |
| 40 | |
| 41 | my $width = 3; |
| 42 | my $bar = ' | '; |
| 43 | my $corner = ' +-'; |
| 44 | my $vfmt = "%3d"; |
| 45 | |
| 46 | sub set_width { |
| 47 | $width = shift; |
| 48 | $width = 2 if $width < 2; |
| 49 | |
| 50 | $vfmt = "%${width}d"; |
| 51 | $bar = $corner = ' ' x $width; |
| 52 | substr($bar,-2,1) = '|'; |
| 53 | substr($corner,-2,2) = '+-'; |
| 54 | } |
| 55 | |
| 56 | sub hdump { |
| 57 | my $el = shift; |
| 58 | my $l1 = shift; |
| 59 | my $b = shift; |
| 60 | |
| 61 | my $ch; |
| 62 | |
| 63 | unless( $el ) { |
| 64 | print $l1, "\n"; |
| 65 | return; |
| 66 | } |
| 67 | |
| 68 | hdump( $ch = $el->{child}, |
| 69 | $l1 . sprintf( $vfmt, $el->{val}->val), |
| 70 | $b . $bar ); |
| 71 | |
| 72 | while( $ch = $ch->{sib} ) { |
| 73 | hdump( $ch, $b . $corner, $b . $bar ); |
| 74 | } |
| 75 | } |
| 76 | |
| 77 | sub heapdump { |
| 78 | my $h; |
| 79 | |
| 80 | while( $h = shift ) { |
| 81 | my $el; |
| 82 | |
| 83 | for( $el = $$h; $el; $el = $el->{sib} ) { |
| 84 | hdump( $el, sprintf( "%02d: ", $el->{degree}), ' ' ); |
| 85 | } |
| 86 | print "\n"; |
| 87 | } |
| 88 | } |
| 89 | |
| 90 | sub bhcheck { |
| 91 | |
| 92 | my $pel = shift; |
| 93 | my $pdeg = $pel->{degree}; |
| 94 | my $pv = $pel->{val}; |
| 95 | my $cel; |
| 96 | for( $cel = $pel->{child}; $cel; $cel = $cel->{sib} ) { |
| 97 | die "degree not decreasing in heap" |
| 98 | unless --$pdeg == $cel->{degree}; |
| 99 | die "heap order not preserved" |
| 100 | unless $pv->cmp($cel->{val}) <= 0; |
| 101 | bhcheck($cel); |
| 102 | } |
| 103 | die "degree did not decrease to zero" |
| 104 | unless $pdeg == 0; |
| 105 | } |
| 106 | |
| 107 | |
| 108 | sub heapcheck { |
| 109 | my $h; |
| 110 | while( $h = shift ) { |
| 111 | heapdump $h if $validate >= 2; |
| 112 | my $el = $$h or next; |
| 113 | my $pdeg = -1; |
| 114 | for( ; $el; $el = $el->{sib} ) { |
| 115 | $el->{degree} > $pdeg |
| 116 | or die "degree not increasing in list"; |
| 117 | $pdeg = $el->{degree}; |
| 118 | bhcheck($el); |
| 119 | } |
| 120 | } |
| 121 | } |
| 122 | |
| 123 | |
| 124 | ################################################# forward declarations |
| 125 | |
| 126 | sub elem; |
| 127 | sub elem_DESTROY; |
| 128 | sub link_to; |
| 129 | sub moveto; |
| 130 | |
| 131 | ################################################# heap methods |
| 132 | |
| 133 | |
| 134 | sub new { |
| 135 | my $self = shift; |
| 136 | my $class = ref($self) || $self; |
| 137 | my $h = undef; |
| 138 | bless \$h, $class; |
| 139 | } |
| 140 | |
| 141 | sub DESTROY { |
| 142 | my $h = shift; |
| 143 | |
| 144 | elem_DESTROY $$h; |
| 145 | } |
| 146 | |
| 147 | sub add { |
| 148 | my $h = shift; |
| 149 | my $v = shift; |
| 150 | $validate && do { |
| 151 | die "Method 'heap' required for element on heap" |
| 152 | unless $v->can('heap'); |
| 153 | die "Method 'cmp' required for element on heap" |
| 154 | unless $v->can('cmp'); |
| 155 | }; |
| 156 | $$h = elem $v, $$h; |
| 157 | $h->self_union_once; |
| 158 | } |
| 159 | |
| 160 | sub top { |
| 161 | my $h = shift; |
| 162 | my $el = $$h or return undef; |
| 163 | my $top = $el->{val}; |
| 164 | while( $el = $el->{sib} ) { |
| 165 | $top = $el->{val} |
| 166 | if $top->cmp($el->{val}) > 0; |
| 167 | } |
| 168 | $top; |
| 169 | } |
| 170 | |
| 171 | *minimum = \⊤ |
| 172 | |
| 173 | sub extract_top { |
| 174 | my $h = shift; |
| 175 | my $mel = $$h or return undef; |
| 176 | my $top = $mel->{val}; |
| 177 | my $mpred = $h; |
| 178 | my $el = $mel; |
| 179 | my $pred = $h; |
| 180 | |
| 181 | # find the heap with the lowest value on it |
| 182 | while( $pred = \$el->{sib}, $el = $$pred ) { |
| 183 | if( $top->cmp($el->{val}) > 0 ) { |
| 184 | $top = $el->{val}; |
| 185 | $mel = $el; |
| 186 | $mpred = $pred; |
| 187 | } |
| 188 | } |
| 189 | |
| 190 | # found it, $mpred points to it, $mel is its container, $val is it |
| 191 | # unlink it from the chain |
| 192 | $$mpred = $mel->{sib}; |
| 193 | |
| 194 | # we're going to return the value from $mel, but all of its children |
| 195 | # must be retained in the heap. Make a second heap with the children |
| 196 | # and then merge the heaps. |
| 197 | $h->absorb_children($mel); |
| 198 | |
| 199 | # finally break all of its pointers, so that we won't leave any |
| 200 | # memory loops when we forget about the pointer to $mel |
| 201 | $mel->{p} = $mel->{child} = $mel->{sib} = $mel->{val} = undef; |
| 202 | |
| 203 | # break the back link |
| 204 | $top->heap(undef); |
| 205 | |
| 206 | # and return the value |
| 207 | $top; |
| 208 | } |
| 209 | |
| 210 | *extract_minimum = \&extract_top; |
| 211 | |
| 212 | sub absorb { |
| 213 | my $h = shift; |
| 214 | my $h2 = shift; |
| 215 | |
| 216 | my $dest_link = $h; |
| 217 | my $el1 = $$h; |
| 218 | my $el2 = $$h2; |
| 219 | my $anymerge = $el1 && $el2; |
| 220 | while( $el1 && $el2 ) { |
| 221 | if( $el1->{degree} <= $el2->{degree} ) { |
| 222 | # advance on h's list, it's already linked |
| 223 | $dest_link = \$el1->{sib}; |
| 224 | $el1 = $$dest_link; |
| 225 | } else { |
| 226 | # move next h2 elem to head of h list |
| 227 | $$dest_link = $el2; |
| 228 | $dest_link = \$el2->{sib}; |
| 229 | $el2 = $$dest_link; |
| 230 | $$dest_link = $el1; |
| 231 | } |
| 232 | } |
| 233 | |
| 234 | # if h ran out first, move rest of h2 onto end |
| 235 | if( $el2 ) { |
| 236 | $$dest_link = $el2; |
| 237 | } |
| 238 | |
| 239 | # clean out h2, all of its elements have been move to h |
| 240 | $$h2 = undef; |
| 241 | |
| 242 | # fix up h - it can have multiple items at the same degree if we |
| 243 | # actually merged two non-empty lists |
| 244 | $anymerge ? $h->self_union: $h; |
| 245 | } |
| 246 | |
| 247 | # a key has been decreased, it may have to percolate up in its heap |
| 248 | sub decrease_key { |
| 249 | my $h = shift; |
| 250 | my $v = shift; |
| 251 | my $el = $v->heap or return undef; |
| 252 | my $p; |
| 253 | |
| 254 | while( $p = $el->{p} ) { |
| 255 | last if $v->cmp($p->{val}) >= 0; |
| 256 | moveto $el, $p->{val}; |
| 257 | $el = $p; |
| 258 | } |
| 259 | |
| 260 | moveto $el, $v; |
| 261 | |
| 262 | $v; |
| 263 | } |
| 264 | |
| 265 | # to delete an item, we bubble it to the top of its heap (as if its key |
| 266 | # had been decreased to -infinity), and then remove it (as in extract_top) |
| 267 | sub delete { |
| 268 | my $h = shift; |
| 269 | my $v = shift; |
| 270 | my $el = $v->heap or return undef; |
| 271 | |
| 272 | # bubble it to the top of its heap |
| 273 | my $p; |
| 274 | while( $p = $el->{p} ) { |
| 275 | moveto $el, $p->{val}; |
| 276 | $el = $p; |
| 277 | } |
| 278 | |
| 279 | # find it on the main list, to remove it and split up the children |
| 280 | my $n; |
| 281 | for( $p = $h; ($n = $$p) && $n != $el; $p = \$n->{sib} ) { |
| 282 | ; |
| 283 | } |
| 284 | |
| 285 | # remove it from the main list |
| 286 | $$p = $el->{sib}; |
| 287 | |
| 288 | # put any children back onto the main list |
| 289 | $h->absorb_children($el); |
| 290 | |
| 291 | # remove the link to $el |
| 292 | $v->heap(undef); |
| 293 | |
| 294 | return $v; |
| 295 | } |
| 296 | |
| 297 | |
| 298 | ################################################# internal utility functions |
| 299 | |
| 300 | sub elem { |
| 301 | my $v = shift; |
| 302 | my $sib = shift; |
| 303 | my $el = { |
| 304 | p => undef, |
| 305 | degree => 0, |
| 306 | child => undef, |
| 307 | val => $v, |
| 308 | sib => $sib, |
| 309 | }; |
| 310 | $v->heap($el); |
| 311 | $el; |
| 312 | } |
| 313 | |
| 314 | sub elem_DESTROY { |
| 315 | my $el = shift; |
| 316 | my $ch; |
| 317 | my $next; |
| 318 | |
| 319 | while( $el ) { |
| 320 | $ch = $el->{child} and elem_DESTROY $ch; |
| 321 | $next = $el->{sib}; |
| 322 | |
| 323 | $el->{val}->heap(undef); |
| 324 | $el->{child} = $el->{sib} = $el->{p} = $el->{val} = undef; |
| 325 | $el = $next; |
| 326 | } |
| 327 | } |
| 328 | |
| 329 | sub link_to { |
| 330 | my $el = shift; |
| 331 | my $p = shift; |
| 332 | |
| 333 | $el->{p} = $p; |
| 334 | $el->{sib} = $p->{child}; |
| 335 | $p->{child} = $el; |
| 336 | $p->{degree}++; |
| 337 | } |
| 338 | |
| 339 | sub moveto { |
| 340 | my $el = shift; |
| 341 | my $v = shift; |
| 342 | |
| 343 | $el->{val} = $v; |
| 344 | $v->heap($el); |
| 345 | } |
| 346 | |
| 347 | # we've merged two lists in degree order. Traverse the list and link |
| 348 | # together any pairs (adding 1 + 1 to get 10 in binary) to the next |
| 349 | # higher degree. After such a merge, there may be a triple at the |
| 350 | # next degree - skip one and merge the others (adding 1 + 1 + carry |
| 351 | # of 1 to get 11 in binary). |
| 352 | sub self_union { |
| 353 | my $h = shift; |
| 354 | my $prev = $h; |
| 355 | my $cur = $$h; |
| 356 | my $next; |
| 357 | my $n2; |
| 358 | |
| 359 | while( $next = $cur->{sib} ) { |
| 360 | if( $cur->{degree} != $next->{degree} ) { |
| 361 | $prev = \$cur->{sib}; |
| 362 | $cur = $next; |
| 363 | next; |
| 364 | } |
| 365 | |
| 366 | # two or three of same degree, need to do a merge. First though, |
| 367 | # skip over the leading one of there are three (it is the result |
| 368 | # [carry] from the previous merge) |
| 369 | if( ($n2 = $next->{sib}) && $n2->{degree} == $cur->{degree} ) { |
| 370 | $prev = \$cur->{sib}; |
| 371 | $cur = $next; |
| 372 | $next = $n2; |
| 373 | } |
| 374 | |
| 375 | # and now the merge |
| 376 | if( $cur->{val}->cmp($next->{val}) <= 0 ) { |
| 377 | $cur->{sib} = $next->{sib}; |
| 378 | link_to $next, $cur; |
| 379 | } else { |
| 380 | $$prev = $next; |
| 381 | link_to $cur, $next; |
| 382 | $cur = $next; |
| 383 | } |
| 384 | } |
| 385 | $h; |
| 386 | } |
| 387 | |
| 388 | # we've added one element at the front, keep merging pairs until there isn't |
| 389 | # one of the same degree (change all the low order one bits to zero and the |
| 390 | # lowest order zero bit to one) |
| 391 | sub self_union_once { |
| 392 | my $h = shift; |
| 393 | my $cur = $$h; |
| 394 | my $next; |
| 395 | |
| 396 | while( $next = $cur->{sib} ) { |
| 397 | return if $cur->{degree} != $next->{degree}; |
| 398 | |
| 399 | # merge |
| 400 | if( $cur->{val}->cmp($next->{val}) <= 0 ) { |
| 401 | $cur->{sib} = $next->{sib}; |
| 402 | link_to $next, $cur; |
| 403 | } else { |
| 404 | $$h = $next; |
| 405 | link_to $cur, $next; |
| 406 | $cur = $next; |
| 407 | } |
| 408 | } |
| 409 | $h; |
| 410 | } |
| 411 | |
| 412 | # absorb all the children of an element into a heap |
| 413 | sub absorb_children { |
| 414 | my $h = shift; |
| 415 | my $el = shift; |
| 416 | |
| 417 | my $h2 = $h->new; |
| 418 | my $child = $el->{child}; |
| 419 | while( $child ) { |
| 420 | my $sib = $child->{sib}; |
| 421 | $child->{sib} = $$h2; |
| 422 | $child->{p} = undef; |
| 423 | $$h2 = $child; |
| 424 | $child = $sib; |
| 425 | } |
| 426 | |
| 427 | # merge them all in |
| 428 | $h->absorb($h2); |
| 429 | } |
| 430 | |
| 431 | |
| 432 | 1; |
| 433 | |
| 434 | __END__ |
| 435 | |
| 436 | =head1 NAME |
| 437 | |
| 438 | Heap::Binomial - a Perl extension for keeping data partially sorted |
| 439 | |
| 440 | =head1 SYNOPSIS |
| 441 | |
| 442 | use Heap::Binomial; |
| 443 | |
| 444 | $heap = Heap::Binomial->new; |
| 445 | # see Heap(3) for usage |
| 446 | |
| 447 | =head1 DESCRIPTION |
| 448 | |
| 449 | Keeps elements in heap order using a linked list of binomial trees. |
| 450 | The I<heap> method of an element is used to store a reference to |
| 451 | the node in the list that refers to the element. |
| 452 | |
| 453 | See L<Heap> for details on using this module. |
| 454 | |
| 455 | =head1 AUTHOR |
| 456 | |
| 457 | John Macdonald, jmm@perlwolf.com |
| 458 | |
| 459 | =head1 COPYRIGHT |
| 460 | |
| 461 | Copyright 1998-2003, O'Reilly & Associates. |
| 462 | |
| 463 | This code is distributed under the same copyright terms as perl itself. |
| 464 | |
| 465 | =head1 SEE ALSO |
| 466 | |
| 467 | Heap(3), Heap::Elem(3). |
| 468 | |
| 469 | =cut |