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