| 1 | package Heap::Fibonacci; |
| 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 | # common names |
| 21 | # h - heap head |
| 22 | # el - linkable element, contains user-provided value |
| 23 | # v - user-provided value |
| 24 | |
| 25 | ################################################# debugging control |
| 26 | |
| 27 | my $debug = 0; |
| 28 | my $validate = 0; |
| 29 | |
| 30 | # enable/disable debugging output |
| 31 | sub debug { |
| 32 | @_ ? ($debug = shift) : $debug; |
| 33 | } |
| 34 | |
| 35 | # enable/disable validation checks on values |
| 36 | sub validate { |
| 37 | @_ ? ($validate = shift) : $validate; |
| 38 | } |
| 39 | |
| 40 | my $width = 3; |
| 41 | my $bar = ' | '; |
| 42 | my $corner = ' +-'; |
| 43 | my $vfmt = "%3d"; |
| 44 | |
| 45 | sub set_width { |
| 46 | $width = shift; |
| 47 | $width = 2 if $width < 2; |
| 48 | |
| 49 | $vfmt = "%${width}d"; |
| 50 | $bar = $corner = ' ' x $width; |
| 51 | substr($bar,-2,1) = '|'; |
| 52 | substr($corner,-2,2) = '+-'; |
| 53 | } |
| 54 | |
| 55 | sub hdump; |
| 56 | |
| 57 | sub hdump { |
| 58 | my $el = shift; |
| 59 | my $l1 = shift; |
| 60 | my $b = shift; |
| 61 | |
| 62 | my $ch; |
| 63 | my $ch1; |
| 64 | |
| 65 | unless( $el ) { |
| 66 | print $l1, "\n"; |
| 67 | return; |
| 68 | } |
| 69 | |
| 70 | hdump $ch1 = $el->{child}, |
| 71 | $l1 . sprintf( $vfmt, $el->{val}->val), |
| 72 | $b . $bar; |
| 73 | |
| 74 | if( $ch1 ) { |
| 75 | for( $ch = $ch1->{right}; $ch != $ch1; $ch = $ch->{right} ) { |
| 76 | hdump $ch, $b . $corner, $b . $bar; |
| 77 | } |
| 78 | } |
| 79 | } |
| 80 | |
| 81 | sub heapdump { |
| 82 | my $h; |
| 83 | |
| 84 | while( $h = shift ) { |
| 85 | my $top = $$h or last; |
| 86 | my $el = $top; |
| 87 | |
| 88 | do { |
| 89 | hdump $el, sprintf( "%02d: ", $el->{degree}), ' '; |
| 90 | $el = $el->{right}; |
| 91 | } until $el == $top; |
| 92 | print "\n"; |
| 93 | } |
| 94 | } |
| 95 | |
| 96 | sub bhcheck; |
| 97 | |
| 98 | sub bhcheck { |
| 99 | my $el = shift; |
| 100 | my $p = shift; |
| 101 | |
| 102 | my $cur = $el; |
| 103 | my $prev; |
| 104 | my $ch; |
| 105 | do { |
| 106 | $prev = $cur; |
| 107 | $cur = $cur->{right}; |
| 108 | die "bad back link" unless $cur->{left} == $prev; |
| 109 | die "bad parent link" |
| 110 | unless (defined $p && defined $cur->{p} && $cur->{p} == $p) |
| 111 | || (!defined $p && !defined $cur->{p}); |
| 112 | die "bad degree( $cur->{degree} > $p->{degree} )" |
| 113 | if $p && $p->{degree} <= $cur->{degree}; |
| 114 | die "not heap ordered" |
| 115 | if $p && $p->{val}->cmp($cur->{val}) > 0; |
| 116 | $ch = $cur->{child} and bhcheck $ch, $cur; |
| 117 | } until $cur == $el; |
| 118 | } |
| 119 | |
| 120 | |
| 121 | sub heapcheck { |
| 122 | my $h; |
| 123 | my $el; |
| 124 | while( $h = shift ) { |
| 125 | heapdump $h if $validate >= 2; |
| 126 | $el = $$h and bhcheck $el, undef; |
| 127 | } |
| 128 | } |
| 129 | |
| 130 | |
| 131 | ################################################# forward declarations |
| 132 | |
| 133 | sub ascending_cut; |
| 134 | sub elem; |
| 135 | sub elem_DESTROY; |
| 136 | sub link_to_left_of; |
| 137 | |
| 138 | ################################################# heap methods |
| 139 | |
| 140 | # Cormen et al. use two values for the heap, a pointer to an element in the |
| 141 | # list at the top, and a count of the number of elements. The count is only |
| 142 | # used to determine the size of array required to hold log(count) pointers, |
| 143 | # but perl can set array sizes as needed and doesn't need to know their size |
| 144 | # when they are created, so we're not maintaining that field. |
| 145 | sub new { |
| 146 | my $self = shift; |
| 147 | my $class = ref($self) || $self; |
| 148 | my $h = undef; |
| 149 | bless \$h, $class; |
| 150 | } |
| 151 | |
| 152 | sub DESTROY { |
| 153 | my $h = shift; |
| 154 | |
| 155 | elem_DESTROY $$h; |
| 156 | } |
| 157 | |
| 158 | sub add { |
| 159 | my $h = shift; |
| 160 | my $v = shift; |
| 161 | $validate && do { |
| 162 | die "Method 'heap' required for element on heap" |
| 163 | unless $v->can('heap'); |
| 164 | die "Method 'cmp' required for element on heap" |
| 165 | unless $v->can('cmp'); |
| 166 | }; |
| 167 | my $el = elem $v; |
| 168 | my $top; |
| 169 | if( !($top = $$h) ) { |
| 170 | $$h = $el; |
| 171 | } else { |
| 172 | link_to_left_of $top->{left}, $el ; |
| 173 | link_to_left_of $el,$top; |
| 174 | $$h = $el if $v->cmp($top->{val}) < 0; |
| 175 | } |
| 176 | } |
| 177 | |
| 178 | sub top { |
| 179 | my $h = shift; |
| 180 | $$h && $$h->{val}; |
| 181 | } |
| 182 | |
| 183 | *minimum = \⊤ |
| 184 | |
| 185 | sub extract_top { |
| 186 | my $h = shift; |
| 187 | my $el = $$h or return undef; |
| 188 | my $ltop = $el->{left}; |
| 189 | my $cur; |
| 190 | my $next; |
| 191 | |
| 192 | # $el is the heap with the lowest value on it |
| 193 | # move all of $el's children (if any) to the top list (between |
| 194 | # $ltop and $el) |
| 195 | if( $cur = $el->{child} ) { |
| 196 | # remember the beginning of the list of children |
| 197 | my $first = $cur; |
| 198 | do { |
| 199 | # the children are moving to the top, clear the p |
| 200 | # pointer for all of them |
| 201 | $cur->{p} = undef; |
| 202 | } until ($cur = $cur->{right}) == $first; |
| 203 | |
| 204 | # remember the end of the list |
| 205 | $cur = $cur->{left}; |
| 206 | link_to_left_of $ltop, $first; |
| 207 | link_to_left_of $cur, $el; |
| 208 | } |
| 209 | |
| 210 | if( $el->{right} == $el ) { |
| 211 | # $el had no siblings or children, the top only contains $el |
| 212 | # and $el is being removed |
| 213 | $$h = undef; |
| 214 | } else { |
| 215 | link_to_left_of $el->{left}, $$h = $el->{right}; |
| 216 | # now all those loose ends have to be merged together as we |
| 217 | # search for the |
| 218 | # new smallest element |
| 219 | $h->consolidate; |
| 220 | } |
| 221 | |
| 222 | # extract the actual value and return that, $el is no longer used |
| 223 | # but break all of its links so that it won't be pointed to... |
| 224 | my $top = $el->{val}; |
| 225 | $top->heap(undef); |
| 226 | $el->{left} = $el->{right} = $el->{p} = $el->{child} = $el->{val} = |
| 227 | undef; |
| 228 | $top; |
| 229 | } |
| 230 | |
| 231 | *extract_minimum = \&extract_top; |
| 232 | |
| 233 | sub absorb { |
| 234 | my $h = shift; |
| 235 | my $h2 = shift; |
| 236 | |
| 237 | my $el = $$h; |
| 238 | unless( $el ) { |
| 239 | $$h = $$h2; |
| 240 | $$h2 = undef; |
| 241 | return $h; |
| 242 | } |
| 243 | |
| 244 | my $el2 = $$h2 or return $h; |
| 245 | |
| 246 | # add $el2 and its siblings to the head list for $h |
| 247 | # at start, $ell -> $el -> ... -> $ell is on $h (where $ell is |
| 248 | # $el->{left}) |
| 249 | # $el2l -> $el2 -> ... -> $el2l are on $h2 |
| 250 | # at end, $ell -> $el2l -> ... -> $el2 -> $el -> ... -> $ell are |
| 251 | # all on $h |
| 252 | my $el2l = $el2->{left}; |
| 253 | link_to_left_of $el->{left}, $el2; |
| 254 | link_to_left_of $el2l, $el; |
| 255 | |
| 256 | # change the top link if needed |
| 257 | $$h = $el2 if $el->{val}->cmp( $el2->{val} ) > 0; |
| 258 | |
| 259 | # clean out $h2 |
| 260 | $$h2 = undef; |
| 261 | |
| 262 | # return the heap |
| 263 | $h; |
| 264 | } |
| 265 | |
| 266 | # a key has been decreased, it may have to percolate up in its heap |
| 267 | sub decrease_key { |
| 268 | my $h = shift; |
| 269 | my $top = $$h; |
| 270 | my $v = shift; |
| 271 | my $el = $v->heap or return undef; |
| 272 | my $p; |
| 273 | |
| 274 | # first, link $h to $el if it is now the smallest (we will |
| 275 | # soon link $el to $top to properly put it up to the top list, |
| 276 | # if it isn't already there) |
| 277 | $$h = $el if $top->{val}->cmp( $v ) > 0; |
| 278 | |
| 279 | if( $p = $el->{p} and $v->cmp($p->{val}) < 0 ) { |
| 280 | # remove $el from its parent's list - it is now smaller |
| 281 | |
| 282 | ascending_cut $top, $p, $el; |
| 283 | } |
| 284 | |
| 285 | $v; |
| 286 | } |
| 287 | |
| 288 | |
| 289 | # to delete an item, we bubble it to the top of its heap (as if its key |
| 290 | # had been decreased to -infinity), and then remove it (as in extract_top) |
| 291 | sub delete { |
| 292 | my $h = shift; |
| 293 | my $v = shift; |
| 294 | my $el = $v->heap or return undef; |
| 295 | |
| 296 | # if there is a parent, cut $el to the top (as if it had just had its |
| 297 | # key decreased to a smaller value than $p's value |
| 298 | my $p; |
| 299 | $p = $el->{p} and ascending_cut $$h, $p, $el; |
| 300 | |
| 301 | # $el is in the top list now, make it look like the smallest and |
| 302 | # remove it |
| 303 | $$h = $el; |
| 304 | $h->extract_top; |
| 305 | } |
| 306 | |
| 307 | |
| 308 | ################################################# internal utility functions |
| 309 | |
| 310 | sub elem { |
| 311 | my $v = shift; |
| 312 | my $el = undef; |
| 313 | $el = { |
| 314 | p => undef, |
| 315 | degree => 0, |
| 316 | mark => 0, |
| 317 | child => undef, |
| 318 | val => $v, |
| 319 | left => undef, |
| 320 | right => undef, |
| 321 | }; |
| 322 | $el->{left} = $el->{right} = $el; |
| 323 | $v->heap($el); |
| 324 | $el; |
| 325 | } |
| 326 | |
| 327 | sub elem_DESTROY { |
| 328 | my $el = shift; |
| 329 | my $ch; |
| 330 | my $next; |
| 331 | |
| 332 | while( $el ) { |
| 333 | $ch = $el->{child} and elem_DESTROY $ch; |
| 334 | $next = $el->{right}; |
| 335 | |
| 336 | $el->{val}->heap(undef); |
| 337 | $el->{child} = $el->{right} = $el->{left} = $el->{p} = $el->{val} |
| 338 | = undef; |
| 339 | $el = $next; |
| 340 | } |
| 341 | } |
| 342 | |
| 343 | sub link_to_left_of { |
| 344 | my $l = shift; |
| 345 | my $r = shift; |
| 346 | |
| 347 | $l->{right} = $r; |
| 348 | $r->{left} = $l; |
| 349 | } |
| 350 | |
| 351 | sub link_as_parent_of { |
| 352 | my $p = shift; |
| 353 | my $c = shift; |
| 354 | |
| 355 | my $pc; |
| 356 | |
| 357 | if( $pc = $p->{child} ) { |
| 358 | link_to_left_of $pc->{left}, $c; |
| 359 | link_to_left_of $c, $pc; |
| 360 | } else { |
| 361 | link_to_left_of $c, $c; |
| 362 | } |
| 363 | $p->{child} = $c; |
| 364 | $c->{p} = $p; |
| 365 | $p->{degree}++; |
| 366 | $c->{mark} = 0; |
| 367 | $p; |
| 368 | } |
| 369 | |
| 370 | sub consolidate { |
| 371 | my $h = shift; |
| 372 | |
| 373 | my $cur; |
| 374 | my $this; |
| 375 | my $next = $$h; |
| 376 | my $last = $next->{left}; |
| 377 | my @a; |
| 378 | do { |
| 379 | # examine next item on top list |
| 380 | $this = $cur = $next; |
| 381 | $next = $cur->{right}; |
| 382 | my $d = $cur->{degree}; |
| 383 | my $alt; |
| 384 | while( $alt = $a[$d] ) { |
| 385 | # we already saw another item of the same degree, |
| 386 | # put the larger valued one under the smaller valued |
| 387 | # one - switch $cur and $alt if necessary so that $cur |
| 388 | # is the smaller |
| 389 | ($cur,$alt) = ($alt,$cur) |
| 390 | if $cur->{val}->cmp( $alt->{val} ) > 0; |
| 391 | # remove $alt from the top list |
| 392 | link_to_left_of $alt->{left}, $alt->{right}; |
| 393 | # and put it under $cur |
| 394 | link_as_parent_of $cur, $alt; |
| 395 | # make sure that $h still points to a node at the top |
| 396 | $$h = $cur; |
| 397 | # we've removed the old $d degree entry |
| 398 | $a[$d] = undef; |
| 399 | # and we now have a $d+1 degree entry to try to insert |
| 400 | # into @a |
| 401 | ++$d; |
| 402 | } |
| 403 | # found a previously unused degree |
| 404 | $a[$d] = $cur; |
| 405 | } until $this == $last; |
| 406 | $cur = $$h; |
| 407 | for $cur (grep defined, @a) { |
| 408 | $$h = $cur if $$h->{val}->cmp( $cur->{val} ) > 0; |
| 409 | } |
| 410 | } |
| 411 | |
| 412 | sub ascending_cut { |
| 413 | my $top = shift; |
| 414 | my $p = shift; |
| 415 | my $el = shift; |
| 416 | |
| 417 | while( 1 ) { |
| 418 | if( --$p->{degree} ) { |
| 419 | # there are still other children below $p |
| 420 | my $l = $el->{left}; |
| 421 | $p->{child} = $l; |
| 422 | link_to_left_of $l, $el->{right}; |
| 423 | } else { |
| 424 | # $el was the only child of $p |
| 425 | $p->{child} = undef; |
| 426 | } |
| 427 | link_to_left_of $top->{left}, $el; |
| 428 | link_to_left_of $el, $top; |
| 429 | $el->{p} = undef; |
| 430 | $el->{mark} = 0; |
| 431 | |
| 432 | # propagate up the list |
| 433 | $el = $p; |
| 434 | |
| 435 | # quit at the top |
| 436 | last unless $p = $el->{p}; |
| 437 | |
| 438 | # quit if we can mark $el |
| 439 | $el->{mark} = 1, last unless $el->{mark}; |
| 440 | } |
| 441 | } |
| 442 | |
| 443 | |
| 444 | 1; |
| 445 | |
| 446 | __END__ |
| 447 | |
| 448 | =head1 NAME |
| 449 | |
| 450 | Heap::Fibonacci - a Perl extension for keeping data partially sorted |
| 451 | |
| 452 | =head1 SYNOPSIS |
| 453 | |
| 454 | use Heap::Fibonacci; |
| 455 | |
| 456 | $heap = Heap::Fibonacci->new; |
| 457 | # see Heap(3) for usage |
| 458 | |
| 459 | =head1 DESCRIPTION |
| 460 | |
| 461 | Keeps elements in heap order using a linked list of Fibonacci trees. |
| 462 | The I<heap> method of an element is used to store a reference to |
| 463 | the node in the list that refers to the element. |
| 464 | |
| 465 | See L<Heap> for details on using this module. |
| 466 | |
| 467 | =head1 AUTHOR |
| 468 | |
| 469 | John Macdonald, jmm@perlwolf.com |
| 470 | |
| 471 | =head1 COPYRIGHT |
| 472 | |
| 473 | Copyright 1998-2003, O'Reilly & Associates. |
| 474 | |
| 475 | This code is distributed under the same copyright terms as perl itself. |
| 476 | |
| 477 | =head1 SEE ALSO |
| 478 | |
| 479 | Heap(3), Heap::Elem(3). |
| 480 | |
| 481 | =cut |