WikiDiff3.php

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<?php
class WikiDiff3 {

    // Input variables
    private $from;
    private $to;
    private $m;
    private $n;

    private $tooLong;
    private $powLimit;

    // State variables
    private $maxDifferences;
    private $lcsLengthCorrectedForHeuristic = false;

    // Output variables
    public $length;
    public $removed;
    public $added;
    public $heuristicUsed;

    function __construct( $tooLong = 2000000, $powLimit = 1.45 ) {
        $this->tooLong = $tooLong;
        $this->powLimit = $powLimit;
    }

    public function diff( /*array*/ $from, /*array*/ $to ) {
        // remember initial lengths
        $m = count( $from );
        $n = count( $to );

        $this->heuristicUsed = false;

        // output
        $removed = $m > 0 ? array_fill( 0, $m, true ) : array();
        $added = $n > 0 ? array_fill( 0, $n, true ) : array();

        // reduce the complexity for the next step (intentionally done twice)
        // remove common tokens at the start
        $i = 0;
        while ( $i < $m && $i < $n && $from[$i] === $to[$i] ) {
            $removed[$i] = $added[$i] = false;
            unset( $from[$i], $to[$i] );
            ++$i;
        }

        // remove common tokens at the end
        $j = 1;
        while ( $i + $j <= $m && $i + $j <= $n && $from[$m - $j] === $to[$n - $j] ) {
            $removed[$m - $j] = $added[$n - $j] = false;
            unset( $from[$m - $j], $to[$n - $j] );
            ++$j;
        }

        $this->from = $newFromIndex = $this->to = $newToIndex = array();

        // remove tokens not in both sequences
        $shared = array();
        foreach ( $from as $key ) {
            $shared[$key] = false;
        }

        foreach ( $to as $index => &$el ) {
            if ( array_key_exists( $el, $shared ) ) {
                // keep it
                $this->to[] = $el;
                $shared[$el] = true;
                $newToIndex[] = $index;
            }
        }
        foreach ( $from as $index => &$el ) {
            if ( $shared[$el] ) {
                // keep it
                $this->from[] = $el;
                $newFromIndex[] = $index;
            }
        }

        unset( $shared, $from, $to );

        $this->m = count( $this->from );
        $this->n = count( $this->to );

        $this->removed = $this->m > 0 ? array_fill( 0, $this->m, true ) : array();
        $this->added = $this->n > 0 ? array_fill( 0, $this->n, true ) : array();

        if ( $this->m == 0 || $this->n == 0 ) {
            $this->length = 0;
        } else {
            $this->maxDifferences = ceil( ( $this->m + $this->n ) / 2.0 );
            if ( $this->m * $this->n > $this->tooLong ) {
                // limit complexity to D^POW_LIMIT for long sequences
                $this->maxDifferences = floor( pow( $this->maxDifferences, $this->powLimit - 1.0 ) );
                wfDebug( "Limiting max number of differences to $this->maxDifferences\n" );
            }

            /*
             * The common prefixes and suffixes are always part of some LCS, include
             * them now to reduce our search space
             */
            $max = min( $this->m, $this->n );
            for ( $forwardBound = 0; $forwardBound < $max
                && $this->from[$forwardBound] === $this->to[$forwardBound];
                ++$forwardBound
            ) {
                $this->removed[$forwardBound] = $this->added[$forwardBound] = false;
            }

            $backBoundL1 = $this->m - 1;
            $backBoundL2 = $this->n - 1;

            while ( $backBoundL1 >= $forwardBound && $backBoundL2 >= $forwardBound
                && $this->from[$backBoundL1] === $this->to[$backBoundL2]
            ) {
                $this->removed[$backBoundL1--] = $this->added[$backBoundL2--] = false;
            }

            $temp = array_fill( 0, $this->m + $this->n + 1, 0 );
            $V = array( $temp, $temp );
            $snake = array( 0, 0, 0 );

            $this->length = $forwardBound + $this->m - $backBoundL1 - 1
                + $this->lcs_rec(
                    $forwardBound,
                    $backBoundL1,
                    $forwardBound,
                    $backBoundL2,
                    $V,
                    $snake
            );
        }

        $this->m = $m;
        $this->n = $n;

        $this->length += $i + $j - 1;

        foreach ( $this->removed as $key => &$removed_elem ) {
            if ( !$removed_elem ) {
                $removed[$newFromIndex[$key]] = false;
            }
        }
        foreach ( $this->added as $key => &$added_elem ) {
            if ( !$added_elem ) {
                $added[$newToIndex[$key]] = false;
            }
        }
        $this->removed = $removed;
        $this->added = $added;
    }

    function diff_range( $from_lines, $to_lines ) {
        // Diff and store locally
        $this->diff( $from_lines, $to_lines );
        unset( $from_lines, $to_lines );

        $ranges = array();
        $xi = $yi = 0;
        while ( $xi < $this->m || $yi < $this->n ) {
            // Matching "snake".
            while ( $xi < $this->m && $yi < $this->n
                && !$this->removed[$xi]
                && !$this->added[$yi]
            ) {
                ++$xi;
                ++$yi;
            }
            // Find deletes & adds.
            $xstart = $xi;
            while ( $xi < $this->m && $this->removed[$xi] ) {
                ++$xi;
            }

            $ystart = $yi;
            while ( $yi < $this->n && $this->added[$yi] ) {
                ++$yi;
            }

            if ( $xi > $xstart || $yi > $ystart ) {
                $ranges[] = new RangeDifference( $xstart, $xi, $ystart, $yi );
            }
        }

        return $ranges;
    }

    private function lcs_rec( $bottoml1, $topl1, $bottoml2, $topl2, &$V, &$snake ) {
        // check that both sequences are non-empty
        if ( $bottoml1 > $topl1 || $bottoml2 > $topl2 ) {
            return 0;
        }

        $d = $this->find_middle_snake( $bottoml1, $topl1, $bottoml2,
            $topl2, $V, $snake );

        // need to store these so we don't lose them when they're
        // overwritten by the recursion
        $len = $snake[2];
        $startx = $snake[0];
        $starty = $snake[1];

        // the middle snake is part of the LCS, store it
        for ( $i = 0; $i < $len; ++$i ) {
            $this->removed[$startx + $i] = $this->added[$starty + $i] = false;
        }

        if ( $d > 1 ) {
            return $len
            + $this->lcs_rec( $bottoml1, $startx - 1, $bottoml2,
                $starty - 1, $V, $snake )
            + $this->lcs_rec( $startx + $len, $topl1, $starty + $len,
                $topl2, $V, $snake );
        } elseif ( $d == 1 ) {
            /*
             * In this case the sequences differ by exactly 1 line. We have
             * already saved all the lines after the difference in the for loop
             * above, now we need to save all the lines before the difference.
             */
            $max = min( $startx - $bottoml1, $starty - $bottoml2 );
            for ( $i = 0; $i < $max; ++$i ) {
                $this->removed[$bottoml1 + $i] =
                    $this->added[$bottoml2 + $i] = false;
            }

            return $max + $len;
        }

        return $len;
    }

    private function find_middle_snake( $bottoml1, $topl1, $bottoml2, $topl2, &$V, &$snake ) {
        $from = &$this->from;
        $to = &$this->to;
        $V0 = &$V[0];
        $V1 = &$V[1];
        $snake0 = &$snake[0];
        $snake1 = &$snake[1];
        $snake2 = &$snake[2];
        $bottoml1_min_1 = $bottoml1 - 1;
        $bottoml2_min_1 = $bottoml2 - 1;
        $N = $topl1 - $bottoml1_min_1;
        $M = $topl2 - $bottoml2_min_1;
        $delta = $N - $M;
        $maxabsx = $N + $bottoml1;
        $maxabsy = $M + $bottoml2;
        $limit = min( $this->maxDifferences, ceil( ( $N + $M ) / 2 ) );

        // value_to_add_forward: a 0 or 1 that we add to the start
        // offset to make it odd/even
        if ( ( $M & 1 ) == 1 ) {
            $value_to_add_forward = 1;
        } else {
            $value_to_add_forward = 0;
        }

        if ( ( $N & 1 ) == 1 ) {
            $value_to_add_backward = 1;
        } else {
            $value_to_add_backward = 0;
        }

        $start_forward = -$M;
        $end_forward = $N;
        $start_backward = -$N;
        $end_backward = $M;

        $limit_min_1 = $limit - 1;
        $limit_plus_1 = $limit + 1;

        $V0[$limit_plus_1] = 0;
        $V1[$limit_min_1] = $N;
        $limit = min( $this->maxDifferences, ceil( ( $N + $M ) / 2 ) );

        if ( ( $delta & 1 ) == 1 ) {
            for ( $d = 0; $d <= $limit; ++$d ) {
                $start_diag = max( $value_to_add_forward + $start_forward, -$d );
                $end_diag = min( $end_forward, $d );
                $value_to_add_forward = 1 - $value_to_add_forward;

                // compute forward furthest reaching paths
                for ( $k = $start_diag; $k <= $end_diag; $k += 2 ) {
                    if ( $k == -$d || ( $k < $d
                            && $V0[$limit_min_1 + $k] < $V0[$limit_plus_1 + $k] )
                    ) {
                        $x = $V0[$limit_plus_1 + $k];
                    } else {
                        $x = $V0[$limit_min_1 + $k] + 1;
                    }

                    $absx = $snake0 = $x + $bottoml1;
                    $absy = $snake1 = $x - $k + $bottoml2;

                    while ( $absx < $maxabsx && $absy < $maxabsy && $from[$absx] === $to[$absy] ) {
                        ++$absx;
                        ++$absy;
                    }
                    $x = $absx - $bottoml1;

                    $snake2 = $absx - $snake0;
                    $V0[$limit + $k] = $x;
                    if ( $k >= $delta - $d + 1 && $k <= $delta + $d - 1
                        && $x >= $V1[$limit + $k - $delta]
                    ) {
                        return 2 * $d - 1;
                    }

                    // check to see if we can cut down the diagonal range
                    if ( $x >= $N && $end_forward > $k - 1 ) {
                        $end_forward = $k - 1;
                    } elseif ( $absy - $bottoml2 >= $M ) {
                        $start_forward = $k + 1;
                        $value_to_add_forward = 0;
                    }
                }

                $start_diag = max( $value_to_add_backward + $start_backward, -$d );
                $end_diag = min( $end_backward, $d );
                $value_to_add_backward = 1 - $value_to_add_backward;

                // compute backward furthest reaching paths
                for ( $k = $start_diag; $k <= $end_diag; $k += 2 ) {
                    if ( $k == $d
                        || ( $k != -$d && $V1[$limit_min_1 + $k] < $V1[$limit_plus_1 + $k] )
                    ) {
                        $x = $V1[$limit_min_1 + $k];
                    } else {
                        $x = $V1[$limit_plus_1 + $k] - 1;
                    }

                    $y = $x - $k - $delta;

                    $snake2 = 0;
                    while ( $x > 0 && $y > 0
                        && $from[$x + $bottoml1_min_1] === $to[$y + $bottoml2_min_1]
                    ) {
                        --$x;
                        --$y;
                        ++$snake2;
                    }
                    $V1[$limit + $k] = $x;

                    // check to see if we can cut down our diagonal range
                    if ( $x <= 0 ) {
                        $start_backward = $k + 1;
                        $value_to_add_backward = 0;
                    } elseif ( $y <= 0 && $end_backward > $k - 1 ) {
                        $end_backward = $k - 1;
                    }
                }
            }
        } else {
            for ( $d = 0; $d <= $limit; ++$d ) {
                $start_diag = max( $value_to_add_forward + $start_forward, -$d );
                $end_diag = min( $end_forward, $d );
                $value_to_add_forward = 1 - $value_to_add_forward;

                // compute forward furthest reaching paths
                for ( $k = $start_diag; $k <= $end_diag; $k += 2 ) {
                    if ( $k == -$d
                        || ( $k < $d && $V0[$limit_min_1 + $k] < $V0[$limit_plus_1 + $k] )
                    ) {
                        $x = $V0[$limit_plus_1 + $k];
                    } else {
                        $x = $V0[$limit_min_1 + $k] + 1;
                    }

                    $absx = $snake0 = $x + $bottoml1;
                    $absy = $snake1 = $x - $k + $bottoml2;

                    while ( $absx < $maxabsx && $absy < $maxabsy && $from[$absx] === $to[$absy] ) {
                        ++$absx;
                        ++$absy;
                    }
                    $x = $absx - $bottoml1;
                    $snake2 = $absx - $snake0;
                    $V0[$limit + $k] = $x;

                    // check to see if we can cut down the diagonal range
                    if ( $x >= $N && $end_forward > $k - 1 ) {
                        $end_forward = $k - 1;
                    } elseif ( $absy - $bottoml2 >= $M ) {
                        $start_forward = $k + 1;
                        $value_to_add_forward = 0;
                    }
                }

                $start_diag = max( $value_to_add_backward + $start_backward, -$d );
                $end_diag = min( $end_backward, $d );
                $value_to_add_backward = 1 - $value_to_add_backward;

                // compute backward furthest reaching paths
                for ( $k = $start_diag; $k <= $end_diag; $k += 2 ) {
                    if ( $k == $d
                        || ( $k != -$d && $V1[$limit_min_1 + $k] < $V1[$limit_plus_1 + $k] )
                    ) {
                        $x = $V1[$limit_min_1 + $k];
                    } else {
                        $x = $V1[$limit_plus_1 + $k] - 1;
                    }

                    $y = $x - $k - $delta;

                    $snake2 = 0;
                    while ( $x > 0 && $y > 0
                        && $from[$x + $bottoml1_min_1] === $to[$y + $bottoml2_min_1]
                    ) {
                        --$x;
                        --$y;
                        ++$snake2;
                    }
                    $V1[$limit + $k] = $x;

                    if ( $k >= -$delta - $d && $k <= $d - $delta
                        && $x <= $V0[$limit + $k + $delta]
                    ) {
                        $snake0 = $bottoml1 + $x;
                        $snake1 = $bottoml2 + $y;

                        return 2 * $d;
                    }

                    // check to see if we can cut down our diagonal range
                    if ( $x <= 0 ) {
                        $start_backward = $k + 1;
                        $value_to_add_backward = 0;
                    } elseif ( $y <= 0 && $end_backward > $k - 1 ) {
                        $end_backward = $k - 1;
                    }
                }
            }
        }
        /*
         * computing the true LCS is too expensive, instead find the diagonal
         * with the most progress and pretend a midle snake of length 0 occurs
         * there.
         */

        $most_progress = self::findMostProgress( $M, $N, $limit, $V );

        $snake0 = $bottoml1 + $most_progress[0];
        $snake1 = $bottoml2 + $most_progress[1];
        $snake2 = 0;
        wfDebug( "Computing the LCS is too expensive. Using a heuristic.\n" );
        $this->heuristicUsed = true;

        return 5; /*
        * HACK: since we didn't really finish the LCS computation
        * we don't really know the length of the SES. We don't do
        * anything with the result anyway, unless it's <=1. We know
        * for a fact SES > 1 so 5 is as good a number as any to
        * return here
        */
    }

    private static function findMostProgress( $M, $N, $limit, $V ) {
        $delta = $N - $M;

        if ( ( $M & 1 ) == ( $limit & 1 ) ) {
            $forward_start_diag = max( -$M, -$limit );
        } else {
            $forward_start_diag = max( 1 - $M, -$limit );
        }

        $forward_end_diag = min( $N, $limit );

        if ( ( $N & 1 ) == ( $limit & 1 ) ) {
            $backward_start_diag = max( -$N, -$limit );
        } else {
            $backward_start_diag = max( 1 - $N, -$limit );
        }

        $backward_end_diag = -min( $M, $limit );

        $temp = array( 0, 0, 0 );

        $max_progress = array_fill( 0, ceil( max( $forward_end_diag - $forward_start_diag,
                $backward_end_diag - $backward_start_diag ) / 2 ), $temp );
        $num_progress = 0; // the 1st entry is current, it is initialized
        // with 0s

        // first search the forward diagonals
        for ( $k = $forward_start_diag; $k <= $forward_end_diag; $k += 2 ) {
            $x = $V[0][$limit + $k];
            $y = $x - $k;
            if ( $x > $N || $y > $M ) {
                continue;
            }

            $progress = $x + $y;
            if ( $progress > $max_progress[0][2] ) {
                $num_progress = 0;
                $max_progress[0][0] = $x;
                $max_progress[0][1] = $y;
                $max_progress[0][2] = $progress;
            } elseif ( $progress == $max_progress[0][2] ) {
                ++$num_progress;
                $max_progress[$num_progress][0] = $x;
                $max_progress[$num_progress][1] = $y;
                $max_progress[$num_progress][2] = $progress;
            }
        }

        $max_progress_forward = true; // initially the maximum
        // progress is in the forward
        // direction

        // now search the backward diagonals
        for ( $k = $backward_start_diag; $k <= $backward_end_diag; $k += 2 ) {
            $x = $V[1][$limit + $k];
            $y = $x - $k - $delta;
            if ( $x < 0 || $y < 0 ) {
                continue;
            }

            $progress = $N - $x + $M - $y;
            if ( $progress > $max_progress[0][2] ) {
                $num_progress = 0;
                $max_progress_forward = false;
                $max_progress[0][0] = $x;
                $max_progress[0][1] = $y;
                $max_progress[0][2] = $progress;
            } elseif ( $progress == $max_progress[0][2] && !$max_progress_forward ) {
                ++$num_progress;
                $max_progress[$num_progress][0] = $x;
                $max_progress[$num_progress][1] = $y;
                $max_progress[$num_progress][2] = $progress;
            }
        }

        // return the middle diagonal with maximal progress.
        return $max_progress[(int)floor( $num_progress / 2 )];
    }

    public function getLcsLength() {
        if ( $this->heuristicUsed && !$this->lcsLengthCorrectedForHeuristic ) {
            $this->lcsLengthCorrectedForHeuristic = true;
            $this->length = $this->m - array_sum( $this->added );
        }

        return $this->length;
    }

}

class RangeDifference {

    public $leftstart;

    public $leftend;

    public $leftlength;

    public $rightstart;

    public $rightend;

    public $rightlength;

    function __construct( $leftstart, $leftend, $rightstart, $rightend ) {
        $this->leftstart = $leftstart;
        $this->leftend = $leftend;
        $this->leftlength = $leftend - $leftstart;
        $this->rightstart = $rightstart;
        $this->rightend = $rightend;
        $this->rightlength = $rightend - $rightstart;
    }

}