includes/diff/DiffEngine.php

   1 <?php
   2 /**
   3  * New version of the difference engine
   4  *
   5  * Copyright © 2008 Guy Van den Broeck <guy@guyvdb.eu>
   6  *
   7  * This program is free software; you can redistribute it and/or modify
   8  * it under the terms of the GNU General Public License as published by
   9  * the Free Software Foundation; either version 2 of the License, or
  10  * (at your option) any later version.
  11  *
  12  * This program is distributed in the hope that it will be useful,
  13  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  14  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15  * GNU General Public License for more details.
  16  *
  17  * You should have received a copy of the GNU General Public License
  18  * along with this program; if not, write to the Free Software
  19  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
  20  * http://www.gnu.org/copyleft/gpl.html
  21  *
  22  * @file
  23  * @ingroup DifferenceEngine
  24  */
  25 use MediaWiki\Diff\ComplexityException;
  26
  27 // FIXME: Don't use assert() in this file
  28 // phpcs:disable MediaWiki.Usage.ForbiddenFunctions.assert
  29
  30 /**
  31  * This diff implementation is mainly lifted from the LCS algorithm of the Eclipse project which
  32  * in turn is based on Myers' "An O(ND) difference algorithm and its variations"
  33  * (http://citeseer.ist.psu.edu/myers86ond.html) with range compression (see Wu et al.'s
  34  * "An O(NP) Sequence Comparison Algorithm").
  35  *
  36  * This implementation supports an upper bound on the execution time.
  37  *
  38  * Some ideas (and a bit of code) are from analyze.c, from GNU
  39  * diffutils-2.7, which can be found at:
  40  *     ftp://gnudist.gnu.org/pub/gnu/diffutils/diffutils-2.7.tar.gz
  41  *
  42  * Complexity: O((M + N)D) worst case time, O(M + N + D^2) expected time, O(M + N) space
  43  *
  44  * @author Guy Van den Broeck, Geoffrey T. Dairiki, Tim Starling
  45  * @ingroup DifferenceEngine
  46  */
  47 class DiffEngine {
  48
  49         // Input variables
  50         /** @var string[] */
  51         private $from;
  52         /** @var string[] */
  53         private $to;
  54         private $m;
  55         private $n;
  56
  57         private $tooLong;
  58         private $powLimit;
  59
  60         protected $bailoutComplexity = 0;
  61
  62         // State variables
  63         private $maxDifferences;
  64         private $lcsLengthCorrectedForHeuristic = false;
  65
  66         // Output variables
  67         public $length;
  68         public $removed;
  69         public $added;
  70         public $heuristicUsed;
  71
  72         function __construct( $tooLong = 2000000, $powLimit = 1.45 ) {
  73                 $this->tooLong = $tooLong;
  74                 $this->powLimit = $powLimit;
  75         }
  76
  77         /**
  78          * Performs diff
  79          *
  80          * @param string[] $from_lines
  81          * @param string[] $to_lines
  82          * @throws ComplexityException
  83          *
  84          * @return DiffOp[]
  85          */
  86         public function diff( $from_lines, $to_lines ) {
  87                 // Diff and store locally
  88                 $this->diffInternal( $from_lines, $to_lines );
  89
  90                 // Merge edits when possible
  91                 $this->shiftBoundaries( $from_lines, $this->removed, $this->added );
  92                 $this->shiftBoundaries( $to_lines, $this->added, $this->removed );
  93
  94                 // Compute the edit operations.
  95                 $n_from = count( $from_lines );
  96                 $n_to = count( $to_lines );
  97
  98                 $edits = [];
  99                 $xi = $yi = 0;
 100                 while ( $xi < $n_from || $yi < $n_to ) {
 101                         assert( $yi < $n_to || $this->removed[$xi] );
 102                         assert( $xi < $n_from || $this->added[$yi] );
 103
 104                         // Skip matching "snake".
 105                         $copy = [];
 106                         while ( $xi < $n_from && $yi < $n_to
 107                                         && !$this->removed[$xi] && !$this->added[$yi]
 108                         ) {
 109                                 $copy[] = $from_lines[$xi++];
 110                                 ++$yi;
 111                         }
 112                         if ( $copy ) {
 113                                 $edits[] = new DiffOpCopy( $copy );
 114                         }
 115
 116                         // Find deletes & adds.
 117                         $delete = [];
 118                         while ( $xi < $n_from && $this->removed[$xi] ) {
 119                                 $delete[] = $from_lines[$xi++];
 120                         }
 121
 122                         $add = [];
 123                         while ( $yi < $n_to && $this->added[$yi] ) {
 124                                 $add[] = $to_lines[$yi++];
 125                         }
 126
 127                         if ( $delete && $add ) {
 128                                 $edits[] = new DiffOpChange( $delete, $add );
 129                         } elseif ( $delete ) {
 130                                 $edits[] = new DiffOpDelete( $delete );
 131                         } elseif ( $add ) {
 132                                 $edits[] = new DiffOpAdd( $add );
 133                         }
 134                 }
 135
 136                 return $edits;
 137         }
 138
 139         /**
 140          * Sets the complexity (in comparison operations) that can't be exceeded
 141          * @param int $value
 142          */
 143         public function setBailoutComplexity( $value ) {
 144                 $this->bailoutComplexity = $value;
 145         }
 146
 147         /**
 148          * Adjust inserts/deletes of identical lines to join changes
 149          * as much as possible.
 150          *
 151          * We do something when a run of changed lines include a
 152          * line at one end and has an excluded, identical line at the other.
 153          * We are free to choose which identical line is included.
 154          * `compareseq' usually chooses the one at the beginning,
 155          * but usually it is cleaner to consider the following identical line
 156          * to be the "change".
 157          *
 158          * This is extracted verbatim from analyze.c (GNU diffutils-2.7).
 159          *
 160          * @param string[] $lines
 161          * @param string[] $changed
 162          * @param string[] $other_changed
 163          */
 164         private function shiftBoundaries( array $lines, array &$changed, array $other_changed ) {
 165                 $i = 0;
 166                 $j = 0;
 167
 168                 assert( count( $lines ) == count( $changed ) );
 169                 $len = count( $lines );
 170                 $other_len = count( $other_changed );
 171
 172                 while ( 1 ) {
 173                         /*
 174                          * Scan forwards to find beginning of another run of changes.
 175                          * Also keep track of the corresponding point in the other file.
 176                          *
 177                          * Throughout this code, $i and $j are adjusted together so that
 178                          * the first $i elements of $changed and the first $j elements
 179                          * of $other_changed both contain the same number of zeros
 180                          * (unchanged lines).
 181                          * Furthermore, $j is always kept so that $j == $other_len or
 182                          * $other_changed[$j] == false.
 183                          */
 184                         while ( $j < $other_len && $other_changed[$j] ) {
 185                                 $j++;
 186                         }
 187
 188                         while ( $i < $len && !$changed[$i] ) {
 189                                 assert( $j < $other_len && !$other_changed[$j] );
 190                                 $i++;
 191                                 $j++;
 192                                 while ( $j < $other_len && $other_changed[$j] ) {
 193                                         $j++;
 194                                 }
 195                         }
 196
 197                         if ( $i == $len ) {
 198                                 break;
 199                         }
 200
 201                         $start = $i;
 202
 203                         // Find the end of this run of changes.
 204                         while ( ++$i < $len && $changed[$i] ) {
 205                                 continue;
 206                         }
 207
 208                         do {
 209                                 /*
 210                                  * Record the length of this run of changes, so that
 211                                  * we can later determine whether the run has grown.
 212                                  */
 213                                 $runlength = $i - $start;
 214
 215                                 /*
 216                                  * Move the changed region back, so long as the
 217                                  * previous unchanged line matches the last changed one.
 218                                  * This merges with previous changed regions.
 219                                  */
 220                                 while ( $start > 0 && $lines[$start - 1] == $lines[$i - 1] ) {
 221                                         $changed[--$start] = 1;
 222                                         $changed[--$i] = false;
 223                                         while ( $start > 0 && $changed[$start - 1] ) {
 224                                                 $start--;
 225                                         }
 226                                         assert( $j > 0 );
 227                                         while ( $other_changed[--$j] ) {
 228                                                 continue;
 229                                         }
 230                                         assert( $j >= 0 && !$other_changed[$j] );
 231                                 }
 232
 233                                 /*
 234                                  * Set CORRESPONDING to the end of the changed run, at the last
 235                                  * point where it corresponds to a changed run in the other file.
 236                                  * CORRESPONDING == LEN means no such point has been found.
 237                                  */
 238                                 $corresponding = $j < $other_len ? $i : $len;
 239
 240                                 /*
 241                                  * Move the changed region forward, so long as the
 242                                  * first changed line matches the following unchanged one.
 243                                  * This merges with following changed regions.
 244                                  * Do this second, so that if there are no merges,
 245                                  * the changed region is moved forward as far as possible.
 246                                  */
 247                                 while ( $i < $len && $lines[$start] == $lines[$i] ) {
 248                                         $changed[$start++] = false;
 249                                         $changed[$i++] = 1;
 250                                         while ( $i < $len && $changed[$i] ) {
 251                                                 $i++;
 252                                         }
 253
 254                                         assert( $j < $other_len && !$other_changed[$j] );
 255                                         $j++;
 256                                         if ( $j < $other_len && $other_changed[$j] ) {
 257                                                 $corresponding = $i;
 258                                                 while ( $j < $other_len && $other_changed[$j] ) {
 259                                                         $j++;
 260                                                 }
 261                                         }
 262                                 }
 263                         } while ( $runlength != $i - $start );
 264
 265                         /*
 266                          * If possible, move the fully-merged run of changes
 267                          * back to a corresponding run in the other file.
 268                          */
 269                         while ( $corresponding < $i ) {
 270                                 $changed[--$start] = 1;
 271                                 $changed[--$i] = 0;
 272                                 assert( $j > 0 );
 273                                 while ( $other_changed[--$j] ) {
 274                                         continue;
 275                                 }
 276                                 assert( $j >= 0 && !$other_changed[$j] );
 277                         }
 278                 }
 279         }
 280
 281         /**
 282          * @param string[] $from
 283          * @param string[] $to
 284          * @throws ComplexityException
 285          */
 286         protected function diffInternal( array $from, array $to ) {
 287                 // remember initial lengths
 288                 $m = count( $from );
 289                 $n = count( $to );
 290
 291                 $this->heuristicUsed = false;
 292
 293                 // output
 294                 $removed = $m > 0 ? array_fill( 0, $m, true ) : [];
 295                 $added = $n > 0 ? array_fill( 0, $n, true ) : [];
 296
 297                 // reduce the complexity for the next step (intentionally done twice)
 298                 // remove common tokens at the start
 299                 $i = 0;
 300                 while ( $i < $m && $i < $n && $from[$i] === $to[$i] ) {
 301                         $removed[$i] = $added[$i] = false;
 302                         unset( $from[$i], $to[$i] );
 303                         ++$i;
 304                 }
 305
 306                 // remove common tokens at the end
 307                 $j = 1;
 308                 while ( $i + $j <= $m && $i + $j <= $n && $from[$m - $j] === $to[$n - $j] ) {
 309                         $removed[$m - $j] = $added[$n - $j] = false;
 310                         unset( $from[$m - $j], $to[$n - $j] );
 311                         ++$j;
 312                 }
 313
 314                 $this->from = $newFromIndex = $this->to = $newToIndex = [];
 315
 316                 // remove tokens not in both sequences
 317                 $shared = [];
 318                 foreach ( $from as $key ) {
 319                         $shared[$key] = false;
 320                 }
 321
 322                 foreach ( $to as $index => &$el ) {
 323                         if ( array_key_exists( $el, $shared ) ) {
 324                                 // keep it
 325                                 $this->to[] = $el;
 326                                 $shared[$el] = true;
 327                                 $newToIndex[] = $index;
 328                         }
 329                 }
 330                 foreach ( $from as $index => &$el ) {
 331                         if ( $shared[$el] ) {
 332                                 // keep it
 333                                 $this->from[] = $el;
 334                                 $newFromIndex[] = $index;
 335                         }
 336                 }
 337
 338                 unset( $shared, $from, $to );
 339
 340                 $this->m = count( $this->from );
 341                 $this->n = count( $this->to );
 342
 343                 if ( $this->bailoutComplexity > 0 && $this->m * $this->n > $this->bailoutComplexity ) {
 344                         throw new ComplexityException();
 345                 }
 346
 347                 $this->removed = $this->m > 0 ? array_fill( 0, $this->m, true ) : [];
 348                 $this->added = $this->n > 0 ? array_fill( 0, $this->n, true ) : [];
 349
 350                 if ( $this->m == 0 || $this->n == 0 ) {
 351                         $this->length = 0;
 352                 } else {
 353                         $this->maxDifferences = ceil( ( $this->m + $this->n ) / 2.0 );
 354                         if ( $this->m * $this->n > $this->tooLong ) {
 355                                 // limit complexity to D^POW_LIMIT for long sequences
 356                                 $this->maxDifferences = floor( $this->maxDifferences ** ( $this->powLimit - 1.0 ) );
 357                                 wfDebug( "Limiting max number of differences to $this->maxDifferences\n" );
 358                         }
 359
 360                         /*
 361                          * The common prefixes and suffixes are always part of some LCS, include
 362                          * them now to reduce our search space
 363                          */
 364                         $max = min( $this->m, $this->n );
 365                         for ( $forwardBound = 0; $forwardBound < $max
 366                                 && $this->from[$forwardBound] === $this->to[$forwardBound];
 367                                 ++$forwardBound
 368                         ) {
 369                                 $this->removed[$forwardBound] = $this->added[$forwardBound] = false;
 370                         }
 371
 372                         $backBoundL1 = $this->m - 1;
 373                         $backBoundL2 = $this->n - 1;
 374
 375                         while ( $backBoundL1 >= $forwardBound && $backBoundL2 >= $forwardBound
 376                                 && $this->from[$backBoundL1] === $this->to[$backBoundL2]
 377                         ) {
 378                                 $this->removed[$backBoundL1--] = $this->added[$backBoundL2--] = false;
 379                         }
 380
 381                         $temp = array_fill( 0, $this->m + $this->n + 1, 0 );
 382                         $V = [ $temp, $temp ];
 383                         $snake = [ 0, 0, 0 ];
 384
 385                         $this->length = $forwardBound + $this->m - $backBoundL1 - 1
 386                                 + $this->lcs_rec(
 387                                         $forwardBound,
 388                                         $backBoundL1,
 389                                         $forwardBound,
 390                                         $backBoundL2,
 391                                         $V,
 392                                         $snake
 393                         );
 394                 }
 395
 396                 $this->m = $m;
 397                 $this->n = $n;
 398
 399                 $this->length += $i + $j - 1;
 400
 401                 foreach ( $this->removed as $key => &$removed_elem ) {
 402                         if ( !$removed_elem ) {
 403                                 $removed[$newFromIndex[$key]] = false;
 404                         }
 405                 }
 406                 foreach ( $this->added as $key => &$added_elem ) {
 407                         if ( !$added_elem ) {
 408                                 $added[$newToIndex[$key]] = false;
 409                         }
 410                 }
 411                 $this->removed = $removed;
 412                 $this->added = $added;
 413         }
 414
 415         function diff_range( $from_lines, $to_lines ) {
 416                 // Diff and store locally
 417                 $this->diff( $from_lines, $to_lines );
 418                 unset( $from_lines, $to_lines );
 419
 420                 $ranges = [];
 421                 $xi = $yi = 0;
 422                 while ( $xi < $this->m || $yi < $this->n ) {
 423                         // Matching "snake".
 424                         while ( $xi < $this->m && $yi < $this->n
 425                                 && !$this->removed[$xi]
 426                                 && !$this->added[$yi]
 427                         ) {
 428                                 ++$xi;
 429                                 ++$yi;
 430                         }
 431                         // Find deletes & adds.
 432                         $xstart = $xi;
 433                         while ( $xi < $this->m && $this->removed[$xi] ) {
 434                                 ++$xi;
 435                         }
 436
 437                         $ystart = $yi;
 438                         while ( $yi < $this->n && $this->added[$yi] ) {
 439                                 ++$yi;
 440                         }
 441
 442                         if ( $xi > $xstart || $yi > $ystart ) {
 443                                 $ranges[] = new RangeDifference( $xstart, $xi, $ystart, $yi );
 444                         }
 445                 }
 446
 447                 return $ranges;
 448         }
 449
 450         private function lcs_rec( $bottoml1, $topl1, $bottoml2, $topl2, &$V, &$snake ) {
 451                 // check that both sequences are non-empty
 452                 if ( $bottoml1 > $topl1 || $bottoml2 > $topl2 ) {
 453                         return 0;
 454                 }
 455
 456                 $d = $this->find_middle_snake( $bottoml1, $topl1, $bottoml2,
 457                         $topl2, $V, $snake );
 458
 459                 // need to store these so we don't lose them when they're
 460                 // overwritten by the recursion
 461                 list( $startx, $starty, $len ) = $snake;
 462
 463                 // the middle snake is part of the LCS, store it
 464                 for ( $i = 0; $i < $len; ++$i ) {
 465                         $this->removed[$startx + $i] = $this->added[$starty + $i] = false;
 466                 }
 467
 468                 if ( $d > 1 ) {
 469                         return $len
 470                         + $this->lcs_rec( $bottoml1, $startx - 1, $bottoml2,
 471                                 $starty - 1, $V, $snake )
 472                         + $this->lcs_rec( $startx + $len, $topl1, $starty + $len,
 473                                 $topl2, $V, $snake );
 474                 } elseif ( $d == 1 ) {
 475                         /*
 476                          * In this case the sequences differ by exactly 1 line. We have
 477                          * already saved all the lines after the difference in the for loop
 478                          * above, now we need to save all the lines before the difference.
 479                          */
 480                         $max = min( $startx - $bottoml1, $starty - $bottoml2 );
 481                         for ( $i = 0; $i < $max; ++$i ) {
 482                                 $this->removed[$bottoml1 + $i] =
 483                                         $this->added[$bottoml2 + $i] = false;
 484                         }
 485
 486                         return $max + $len;
 487                 }
 488
 489                 return $len;
 490         }
 491
 492         private function find_middle_snake( $bottoml1, $topl1, $bottoml2, $topl2, &$V, &$snake ) {
 493                 $from = &$this->from;
 494                 $to = &$this->to;
 495                 $V0 = &$V[0];
 496                 $V1 = &$V[1];
 497                 $snake0 = &$snake[0];
 498                 $snake1 = &$snake[1];
 499                 $snake2 = &$snake[2];
 500                 $bottoml1_min_1 = $bottoml1 - 1;
 501                 $bottoml2_min_1 = $bottoml2 - 1;
 502                 $N = $topl1 - $bottoml1_min_1;
 503                 $M = $topl2 - $bottoml2_min_1;
 504                 $delta = $N - $M;
 505                 $maxabsx = $N + $bottoml1;
 506                 $maxabsy = $M + $bottoml2;
 507                 $limit = min( $this->maxDifferences, ceil( ( $N + $M ) / 2 ) );
 508
 509                 // value_to_add_forward: a 0 or 1 that we add to the start
 510                 // offset to make it odd/even
 511                 if ( $M & 1 ) {
 512                         $value_to_add_forward = 1;
 513                 } else {
 514                         $value_to_add_forward = 0;
 515                 }
 516
 517                 if ( $N & 1 ) {
 518                         $value_to_add_backward = 1;
 519                 } else {
 520                         $value_to_add_backward = 0;
 521                 }
 522
 523                 $start_forward = -$M;
 524                 $end_forward = $N;
 525                 $start_backward = -$N;
 526                 $end_backward = $M;
 527
 528                 $limit_min_1 = $limit - 1;
 529                 $limit_plus_1 = $limit + 1;
 530
 531                 $V0[$limit_plus_1] = 0;
 532                 $V1[$limit_min_1] = $N;
 533                 $limit = min( $this->maxDifferences, ceil( ( $N + $M ) / 2 ) );
 534
 535                 if ( $delta & 1 ) {
 536                         for ( $d = 0; $d <= $limit; ++$d ) {
 537                                 $start_diag = max( $value_to_add_forward + $start_forward, -$d );
 538                                 $end_diag = min( $end_forward, $d );
 539                                 $value_to_add_forward = 1 - $value_to_add_forward;
 540
 541                                 // compute forward furthest reaching paths
 542                                 for ( $k = $start_diag; $k <= $end_diag; $k += 2 ) {
 543                                         if ( $k == -$d || ( $k < $d
 544                                                         && $V0[$limit_min_1 + $k] < $V0[$limit_plus_1 + $k] )
 545                                         ) {
 546                                                 $x = $V0[$limit_plus_1 + $k];
 547                                         } else {
 548                                                 $x = $V0[$limit_min_1 + $k] + 1;
 549                                         }
 550
 551                                         $absx = $snake0 = $x + $bottoml1;
 552                                         $absy = $snake1 = $x - $k + $bottoml2;
 553
 554                                         while ( $absx < $maxabsx && $absy < $maxabsy && $from[$absx] === $to[$absy] ) {
 555                                                 ++$absx;
 556                                                 ++$absy;
 557                                         }
 558                                         $x = $absx - $bottoml1;
 559
 560                                         $snake2 = $absx - $snake0;
 561                                         $V0[$limit + $k] = $x;
 562                                         if ( $k >= $delta - $d + 1 && $k <= $delta + $d - 1
 563                                                 && $x >= $V1[$limit + $k - $delta]
 564                                         ) {
 565                                                 return 2 * $d - 1;
 566                                         }
 567
 568                                         // check to see if we can cut down the diagonal range
 569                                         if ( $x >= $N && $end_forward > $k - 1 ) {
 570                                                 $end_forward = $k - 1;
 571                                         } elseif ( $absy - $bottoml2 >= $M ) {
 572                                                 $start_forward = $k + 1;
 573                                                 $value_to_add_forward = 0;
 574                                         }
 575                                 }
 576
 577                                 $start_diag = max( $value_to_add_backward + $start_backward, -$d );
 578                                 $end_diag = min( $end_backward, $d );
 579                                 $value_to_add_backward = 1 - $value_to_add_backward;
 580
 581                                 // compute backward furthest reaching paths
 582                                 for ( $k = $start_diag; $k <= $end_diag; $k += 2 ) {
 583                                         if ( $k == $d
 584                                                 || ( $k != -$d && $V1[$limit_min_1 + $k] < $V1[$limit_plus_1 + $k] )
 585                                         ) {
 586                                                 $x = $V1[$limit_min_1 + $k];
 587                                         } else {
 588                                                 $x = $V1[$limit_plus_1 + $k] - 1;
 589                                         }
 590
 591                                         $y = $x - $k - $delta;
 592
 593                                         $snake2 = 0;
 594                                         while ( $x > 0 && $y > 0
 595                                                 && $from[$x + $bottoml1_min_1] === $to[$y + $bottoml2_min_1]
 596                                         ) {
 597                                                 --$x;
 598                                                 --$y;
 599                                                 ++$snake2;
 600                                         }
 601                                         $V1[$limit + $k] = $x;
 602
 603                                         // check to see if we can cut down our diagonal range
 604                                         if ( $x <= 0 ) {
 605                                                 $start_backward = $k + 1;
 606                                                 $value_to_add_backward = 0;
 607                                         } elseif ( $y <= 0 && $end_backward > $k - 1 ) {
 608                                                 $end_backward = $k - 1;
 609                                         }
 610                                 }
 611                         }
 612                 } else {
 613                         for ( $d = 0; $d <= $limit; ++$d ) {
 614                                 $start_diag = max( $value_to_add_forward + $start_forward, -$d );
 615                                 $end_diag = min( $end_forward, $d );
 616                                 $value_to_add_forward = 1 - $value_to_add_forward;
 617
 618                                 // compute forward furthest reaching paths
 619                                 for ( $k = $start_diag; $k <= $end_diag; $k += 2 ) {
 620                                         if ( $k == -$d
 621                                                 || ( $k < $d && $V0[$limit_min_1 + $k] < $V0[$limit_plus_1 + $k] )
 622                                         ) {
 623                                                 $x = $V0[$limit_plus_1 + $k];
 624                                         } else {
 625                                                 $x = $V0[$limit_min_1 + $k] + 1;
 626                                         }
 627
 628                                         $absx = $snake0 = $x + $bottoml1;
 629                                         $absy = $snake1 = $x - $k + $bottoml2;
 630
 631                                         while ( $absx < $maxabsx && $absy < $maxabsy && $from[$absx] === $to[$absy] ) {
 632                                                 ++$absx;
 633                                                 ++$absy;
 634                                         }
 635                                         $x = $absx - $bottoml1;
 636                                         $snake2 = $absx - $snake0;
 637                                         $V0[$limit + $k] = $x;
 638
 639                                         // check to see if we can cut down the diagonal range
 640                                         if ( $x >= $N && $end_forward > $k - 1 ) {
 641                                                 $end_forward = $k - 1;
 642                                         } elseif ( $absy - $bottoml2 >= $M ) {
 643                                                 $start_forward = $k + 1;
 644                                                 $value_to_add_forward = 0;
 645                                         }
 646                                 }
 647
 648                                 $start_diag = max( $value_to_add_backward + $start_backward, -$d );
 649                                 $end_diag = min( $end_backward, $d );
 650                                 $value_to_add_backward = 1 - $value_to_add_backward;
 651
 652                                 // compute backward furthest reaching paths
 653                                 for ( $k = $start_diag; $k <= $end_diag; $k += 2 ) {
 654                                         if ( $k == $d
 655                                                 || ( $k != -$d && $V1[$limit_min_1 + $k] < $V1[$limit_plus_1 + $k] )
 656                                         ) {
 657                                                 $x = $V1[$limit_min_1 + $k];
 658                                         } else {
 659                                                 $x = $V1[$limit_plus_1 + $k] - 1;
 660                                         }
 661
 662                                         $y = $x - $k - $delta;
 663
 664                                         $snake2 = 0;
 665                                         while ( $x > 0 && $y > 0
 666                                                 && $from[$x + $bottoml1_min_1] === $to[$y + $bottoml2_min_1]
 667                                         ) {
 668                                                 --$x;
 669                                                 --$y;
 670                                                 ++$snake2;
 671                                         }
 672                                         $V1[$limit + $k] = $x;
 673
 674                                         if ( $k >= -$delta - $d && $k <= $d - $delta
 675                                                 && $x <= $V0[$limit + $k + $delta]
 676                                         ) {
 677                                                 $snake0 = $bottoml1 + $x;
 678                                                 $snake1 = $bottoml2 + $y;
 679
 680                                                 return 2 * $d;
 681                                         }
 682
 683                                         // check to see if we can cut down our diagonal range
 684                                         if ( $x <= 0 ) {
 685                                                 $start_backward = $k + 1;
 686                                                 $value_to_add_backward = 0;
 687                                         } elseif ( $y <= 0 && $end_backward > $k - 1 ) {
 688                                                 $end_backward = $k - 1;
 689                                         }
 690                                 }
 691                         }
 692                 }
 693                 /*
 694                  * computing the true LCS is too expensive, instead find the diagonal
 695                  * with the most progress and pretend a midle snake of length 0 occurs
 696                  * there.
 697                  */
 698
 699                 $most_progress = self::findMostProgress( $M, $N, $limit, $V );
 700
 701                 $snake0 = $bottoml1 + $most_progress[0];
 702                 $snake1 = $bottoml2 + $most_progress[1];
 703                 $snake2 = 0;
 704                 wfDebug( "Computing the LCS is too expensive. Using a heuristic.\n" );
 705                 $this->heuristicUsed = true;
 706
 707                 return 5; /*
 708                 * HACK: since we didn't really finish the LCS computation
 709                 * we don't really know the length of the SES. We don't do
 710                 * anything with the result anyway, unless it's <=1. We know
 711                 * for a fact SES > 1 so 5 is as good a number as any to
 712                 * return here
 713                 */
 714         }
 715
 716         private static function findMostProgress( $M, $N, $limit, $V ) {
 717                 $delta = $N - $M;
 718
 719                 if ( ( $M & 1 ) == ( $limit & 1 ) ) {
 720                         $forward_start_diag = max( -$M, -$limit );
 721                 } else {
 722                         $forward_start_diag = max( 1 - $M, -$limit );
 723                 }
 724
 725                 $forward_end_diag = min( $N, $limit );
 726
 727                 if ( ( $N & 1 ) == ( $limit & 1 ) ) {
 728                         $backward_start_diag = max( -$N, -$limit );
 729                 } else {
 730                         $backward_start_diag = max( 1 - $N, -$limit );
 731                 }
 732
 733                 $backward_end_diag = -min( $M, $limit );
 734
 735                 $temp = [ 0, 0, 0 ];
 736
 737                 $max_progress = array_fill( 0, ceil( max( $forward_end_diag - $forward_start_diag,
 738                                 $backward_end_diag - $backward_start_diag ) / 2 ), $temp );
 739                 $num_progress = 0; // the 1st entry is current, it is initialized
 740                 // with 0s
 741
 742                 // first search the forward diagonals
 743                 for ( $k = $forward_start_diag; $k <= $forward_end_diag; $k += 2 ) {
 744                         $x = $V[0][$limit + $k];
 745                         $y = $x - $k;
 746                         if ( $x > $N || $y > $M ) {
 747                                 continue;
 748                         }
 749
 750                         $progress = $x + $y;
 751                         if ( $progress > $max_progress[0][2] ) {
 752                                 $num_progress = 0;
 753                                 $max_progress[0][0] = $x;
 754                                 $max_progress[0][1] = $y;
 755                                 $max_progress[0][2] = $progress;
 756                         } elseif ( $progress == $max_progress[0][2] ) {
 757                                 ++$num_progress;
 758                                 $max_progress[$num_progress][0] = $x;
 759                                 $max_progress[$num_progress][1] = $y;
 760                                 $max_progress[$num_progress][2] = $progress;
 761                         }
 762                 }
 763
 764                 $max_progress_forward = true; // initially the maximum
 765                 // progress is in the forward
 766                 // direction
 767
 768                 // now search the backward diagonals
 769                 for ( $k = $backward_start_diag; $k <= $backward_end_diag; $k += 2 ) {
 770                         $x = $V[1][$limit + $k];
 771                         $y = $x - $k - $delta;
 772                         if ( $x < 0 || $y < 0 ) {
 773                                 continue;
 774                         }
 775
 776                         $progress = $N - $x + $M - $y;
 777                         if ( $progress > $max_progress[0][2] ) {
 778                                 $num_progress = 0;
 779                                 $max_progress_forward = false;
 780                                 $max_progress[0][0] = $x;
 781                                 $max_progress[0][1] = $y;
 782                                 $max_progress[0][2] = $progress;
 783                         } elseif ( $progress == $max_progress[0][2] && !$max_progress_forward ) {
 784                                 ++$num_progress;
 785                                 $max_progress[$num_progress][0] = $x;
 786                                 $max_progress[$num_progress][1] = $y;
 787                                 $max_progress[$num_progress][2] = $progress;
 788                         }
 789                 }
 790
 791                 // return the middle diagonal with maximal progress.
 792                 return $max_progress[(int)floor( $num_progress / 2 )];
 793         }
 794
 795         /**
 796          * @return mixed
 797          */
 798         public function getLcsLength() {
 799                 if ( $this->heuristicUsed && !$this->lcsLengthCorrectedForHeuristic ) {
 800                         $this->lcsLengthCorrectedForHeuristic = true;
 801                         $this->length = $this->m - array_sum( $this->added );
 802                 }
 803
 804                 return $this->length;
 805         }
 806
 807 }