OS/pintos-env/pintos/tests/Algorithm/Diff.pm

package Algorithm::Diff;
# Skip to first "=head" line for documentation.
use strict;

use integer;    # see below in _replaceNextLargerWith() for mod to make
                # if you don't use this
use vars qw( $VERSION @EXPORT_OK );
$VERSION = 1.19_01;
#          ^ ^^ ^^-- Incremented at will
#          | \+----- Incremented for non-trivial changes to features
#          \-------- Incremented for fundamental changes
require Exporter;
*import    = \&Exporter::import;
@EXPORT_OK = qw(
    prepare LCS LCDidx LCS_length
    diff sdiff compact_diff
    traverse_sequences traverse_balanced
);

# McIlroy-Hunt diff algorithm
# Adapted from the Smalltalk code of Mario I. Wolczko, <mario@wolczko.com>
# by Ned Konz, perl@bike-nomad.com
# Updates by Tye McQueen, http://perlmonks.org/?node=tye

# Create a hash that maps each element of $aCollection to the set of
# positions it occupies in $aCollection, restricted to the elements
# within the range of indexes specified by $start and $end.
# The fourth parameter is a subroutine reference that will be called to
# generate a string to use as a key.
# Additional parameters, if any, will be passed to this subroutine.
#
# my $hashRef = _withPositionsOfInInterval( \@array, $start, $end, $keyGen );

sub _withPositionsOfInInterval
{
    my $aCollection = shift;    # array ref
    my $start       = shift;
    my $end         = shift;
    my $keyGen      = shift;
    my %d;
    my $index;
    for ( $index = $start ; $index <= $end ; $index++ )
    {
        my $element = $aCollection->[$index];
        my $key = &$keyGen( $element, @_ );
        if ( exists( $d{$key} ) )
        {
            unshift ( @{ $d{$key} }, $index );
        }
        else
        {
            $d{$key} = [$index];
        }
    }
    return wantarray ? %d : \%d;
}

# Find the place at which aValue would normally be inserted into the
# array. If that place is already occupied by aValue, do nothing, and
# return undef. If the place does not exist (i.e., it is off the end of
# the array), add it to the end, otherwise replace the element at that
# point with aValue.  It is assumed that the array's values are numeric.
# This is where the bulk (75%) of the time is spent in this module, so
# try to make it fast!

sub _replaceNextLargerWith
{
    my ( $array, $aValue, $high ) = @_;
    $high ||= $#$array;

    # off the end?
    if ( $high == -1 || $aValue > $array->[-1] )
    {
        push ( @$array, $aValue );
        return $high + 1;
    }

    # binary search for insertion point...
    my $low = 0;
    my $index;
    my $found;
    while ( $low <= $high )
    {
        $index = ( $high + $low ) / 2;

        # $index = int(( $high + $low ) / 2);  # without 'use integer'
        $found = $array->[$index];

        if ( $aValue == $found )
        {
            return undef;
        }
        elsif ( $aValue > $found )
        {
            $low = $index + 1;
        }
        else
        {
            $high = $index - 1;
        }
    }

    # now insertion point is in $low.
    $array->[$low] = $aValue;    # overwrite next larger
    return $low;
}

# This method computes the longest common subsequence in $a and $b.

# Result is array or ref, whose contents is such that
#   $a->[ $i ] == $b->[ $result[ $i ] ]
# foreach $i in ( 0 .. $#result ) if $result[ $i ] is defined.

# An additional argument may be passed; this is a hash or key generating
# function that should return a string that uniquely identifies the given
# element.  It should be the case that if the key is the same, the elements
# will compare the same. If this parameter is undef or missing, the key
# will be the element as a string.

# By default, comparisons will use "eq" and elements will be turned into keys
# using the default stringizing operator '""'.

# Additional parameters, if any, will be passed to the key generation
# routine.

sub _longestCommonSubsequence
{
    my $a        = shift;    # array ref or hash ref
    my $b        = shift;    # array ref or hash ref
    my $counting = shift;    # scalar
    my $keyGen   = shift;    # code ref
    my $compare;             # code ref

    if ( ref($a) eq 'HASH' )
    {                        # prepared hash must be in $b
        my $tmp = $b;
        $b = $a;
        $a = $tmp;
    }

    # Check for bogus (non-ref) argument values
    if ( !ref($a) || !ref($b) )
    {
        my @callerInfo = caller(1);
        die 'error: must pass array or hash references to ' . $callerInfo[3];
    }

    # set up code refs
    # Note that these are optimized.
    if ( !defined($keyGen) )    # optimize for strings
    {
        $keyGen = sub { $_[0] };
        $compare = sub { my ( $a, $b ) = @_; $a eq $b };
    }
    else
    {
        $compare = sub {
            my $a = shift;
            my $b = shift;
            &$keyGen( $a, @_ ) eq &$keyGen( $b, @_ );
        };
    }

    my ( $aStart, $aFinish, $matchVector ) = ( 0, $#$a, [] );
    my ( $prunedCount, $bMatches ) = ( 0, {} );

    if ( ref($b) eq 'HASH' )    # was $bMatches prepared for us?
    {
        $bMatches = $b;
    }
    else
    {
        my ( $bStart, $bFinish ) = ( 0, $#$b );

        # First we prune off any common elements at the beginning
        while ( $aStart <= $aFinish
            and $bStart <= $bFinish
            and &$compare( $a->[$aStart], $b->[$bStart], @_ ) )
        {
            $matchVector->[ $aStart++ ] = $bStart++;
            $prunedCount++;
        }

        # now the end
        while ( $aStart <= $aFinish
            and $bStart <= $bFinish
            and &$compare( $a->[$aFinish], $b->[$bFinish], @_ ) )
        {
            $matchVector->[ $aFinish-- ] = $bFinish--;
            $prunedCount++;
        }

        # Now compute the equivalence classes of positions of elements
        $bMatches =
          _withPositionsOfInInterval( $b, $bStart, $bFinish, $keyGen, @_ );
    }
    my $thresh = [];
    my $links  = [];

    my ( $i, $ai, $j, $k );
    for ( $i = $aStart ; $i <= $aFinish ; $i++ )
    {
        $ai = &$keyGen( $a->[$i], @_ );
        if ( exists( $bMatches->{$ai} ) )
        {
            $k = 0;
            for $j ( @{ $bMatches->{$ai} } )
            {

                # optimization: most of the time this will be true
                if ( $k and $thresh->[$k] > $j and $thresh->[ $k - 1 ] < $j )
                {
                    $thresh->[$k] = $j;
                }
                else
                {
                    $k = _replaceNextLargerWith( $thresh, $j, $k );
                }

                # oddly, it's faster to always test this (CPU cache?).
                if ( defined($k) )
                {
                    $links->[$k] =
                      [ ( $k ? $links->[ $k - 1 ] : undef ), $i, $j ];
                }
            }
        }
    }

    if (@$thresh)
    {
        return $prunedCount + @$thresh if $counting;
        for ( my $link = $links->[$#$thresh] ; $link ; $link = $link->[0] )
        {
            $matchVector->[ $link->[1] ] = $link->[2];
        }
    }
    elsif ($counting)
    {
        return $prunedCount;
    }

    return wantarray ? @$matchVector : $matchVector;
}

sub traverse_sequences
{
    my $a                 = shift;          # array ref
    my $b                 = shift;          # array ref
    my $callbacks         = shift || {};
    my $keyGen            = shift;
    my $matchCallback     = $callbacks->{'MATCH'} || sub { };
    my $discardACallback  = $callbacks->{'DISCARD_A'} || sub { };
    my $finishedACallback = $callbacks->{'A_FINISHED'};
    my $discardBCallback  = $callbacks->{'DISCARD_B'} || sub { };
    my $finishedBCallback = $callbacks->{'B_FINISHED'};
    my $matchVector = _longestCommonSubsequence( $a, $b, 0, $keyGen, @_ );

    # Process all the lines in @$matchVector
    my $lastA = $#$a;
    my $lastB = $#$b;
    my $bi    = 0;
    my $ai;

    for ( $ai = 0 ; $ai <= $#$matchVector ; $ai++ )
    {
        my $bLine = $matchVector->[$ai];
        if ( defined($bLine) )    # matched
        {
            &$discardBCallback( $ai, $bi++, @_ ) while $bi < $bLine;
            &$matchCallback( $ai,    $bi++, @_ );
        }
        else
        {
            &$discardACallback( $ai, $bi, @_ );
        }
    }

    # The last entry (if any) processed was a match.
    # $ai and $bi point just past the last matching lines in their sequences.

    while ( $ai <= $lastA or $bi <= $lastB )
    {

        # last A?
        if ( $ai == $lastA + 1 and $bi <= $lastB )
        {
            if ( defined($finishedACallback) )
            {
                &$finishedACallback( $lastA, @_ );
                $finishedACallback = undef;
            }
            else
            {
                &$discardBCallback( $ai, $bi++, @_ ) while $bi <= $lastB;
            }
        }

        # last B?
        if ( $bi == $lastB + 1 and $ai <= $lastA )
        {
            if ( defined($finishedBCallback) )
            {
                &$finishedBCallback( $lastB, @_ );
                $finishedBCallback = undef;
            }
            else
            {
                &$discardACallback( $ai++, $bi, @_ ) while $ai <= $lastA;
            }
        }

        &$discardACallback( $ai++, $bi, @_ ) if $ai <= $lastA;
        &$discardBCallback( $ai, $bi++, @_ ) if $bi <= $lastB;
    }

    return 1;
}

sub traverse_balanced
{
    my $a                 = shift;              # array ref
    my $b                 = shift;              # array ref
    my $callbacks         = shift || {};
    my $keyGen            = shift;
    my $matchCallback     = $callbacks->{'MATCH'} || sub { };
    my $discardACallback  = $callbacks->{'DISCARD_A'} || sub { };
    my $discardBCallback  = $callbacks->{'DISCARD_B'} || sub { };
    my $changeCallback    = $callbacks->{'CHANGE'};
    my $matchVector = _longestCommonSubsequence( $a, $b, 0, $keyGen, @_ );

    # Process all the lines in match vector
    my $lastA = $#$a;
    my $lastB = $#$b;
    my $bi    = 0;
    my $ai    = 0;
    my $ma    = -1;
    my $mb;

    while (1)
    {

        # Find next match indices $ma and $mb
        do {
            $ma++;
        } while(
                $ma <= $#$matchVector
            &&  !defined $matchVector->[$ma]
        );

        last if $ma > $#$matchVector;    # end of matchVector?
        $mb = $matchVector->[$ma];

        # Proceed with discard a/b or change events until
        # next match
        while ( $ai < $ma || $bi < $mb )
        {

            if ( $ai < $ma && $bi < $mb )
            {

                # Change
                if ( defined $changeCallback )
                {
                    &$changeCallback( $ai++, $bi++, @_ );
                }
                else
                {
                    &$discardACallback( $ai++, $bi, @_ );
                    &$discardBCallback( $ai, $bi++, @_ );
                }
            }
            elsif ( $ai < $ma )
            {
                &$discardACallback( $ai++, $bi, @_ );
            }
            else
            {

                # $bi < $mb
                &$discardBCallback( $ai, $bi++, @_ );
            }
        }

        # Match
        &$matchCallback( $ai++, $bi++, @_ );
    }

    while ( $ai <= $lastA || $bi <= $lastB )
    {
        if ( $ai <= $lastA && $bi <= $lastB )
        {

            # Change
            if ( defined $changeCallback )
            {
                &$changeCallback( $ai++, $bi++, @_ );
            }
            else
            {
                &$discardACallback( $ai++, $bi, @_ );
                &$discardBCallback( $ai, $bi++, @_ );
            }
        }
        elsif ( $ai <= $lastA )
        {
            &$discardACallback( $ai++, $bi, @_ );
        }
        else
        {

            # $bi <= $lastB
            &$discardBCallback( $ai, $bi++, @_ );
        }
    }

    return 1;
}

sub prepare
{
    my $a       = shift;    # array ref
    my $keyGen  = shift;    # code ref

    # set up code ref
    $keyGen = sub { $_[0] } unless defined($keyGen);

    return scalar _withPositionsOfInInterval( $a, 0, $#$a, $keyGen, @_ );
}

sub LCS
{
    my $a = shift;                  # array ref
    my $b = shift;                  # array ref or hash ref
    my $matchVector = _longestCommonSubsequence( $a, $b, 0, @_ );
    my @retval;
    my $i;
    for ( $i = 0 ; $i <= $#$matchVector ; $i++ )
    {
        if ( defined( $matchVector->[$i] ) )
        {
            push ( @retval, $a->[$i] );
        }
    }
    return wantarray ? @retval : \@retval;
}

sub LCS_length
{
    my $a = shift;                          # array ref
    my $b = shift;                          # array ref or hash ref
    return _longestCommonSubsequence( $a, $b, 1, @_ );
}

sub LCSidx
{
    my $a= shift @_;
    my $b= shift @_;
    my $match= _longestCommonSubsequence( $a, $b, 0, @_ );
    my @am= grep defined $match->[$_], 0..$#$match;
    my @bm= @{$match}[@am];
    return \@am, \@bm;
}

sub compact_diff
{
    my $a= shift @_;
    my $b= shift @_;
    my( $am, $bm )= LCSidx( $a, $b, @_ );
    my @cdiff;
    my( $ai, $bi )= ( 0, 0 );
    push @cdiff, $ai, $bi;
    while( 1 ) {
        while(  @$am  &&  $ai == $am->[0]  &&  $bi == $bm->[0]  ) {
            shift @$am;
            shift @$bm;
            ++$ai, ++$bi;
        }
        push @cdiff, $ai, $bi;
        last   if  ! @$am;
        $ai = $am->[0];
        $bi = $bm->[0];
        push @cdiff, $ai, $bi;
    }
    push @cdiff, 0+@$a, 0+@$b
        if  $ai < @$a || $bi < @$b;
    return wantarray ? @cdiff : \@cdiff;
}

sub diff
{
    my $a      = shift;    # array ref
    my $b      = shift;    # array ref
    my $retval = [];
    my $hunk   = [];
    my $discard = sub {
        push @$hunk, [ '-', $_[0], $a->[ $_[0] ] ];
    };
    my $add = sub {
        push @$hunk, [ '+', $_[1], $b->[ $_[1] ] ];
    };
    my $match = sub {
        push @$retval, $hunk
            if 0 < @$hunk;
        $hunk = []
    };
    traverse_sequences( $a, $b,
        { MATCH => $match, DISCARD_A => $discard, DISCARD_B => $add }, @_ );
    &$match();
    return wantarray ? @$retval : $retval;
}

sub sdiff
{
    my $a      = shift;    # array ref
    my $b      = shift;    # array ref
    my $retval = [];
    my $discard = sub { push ( @$retval, [ '-', $a->[ $_[0] ], "" ] ) };
    my $add = sub { push ( @$retval, [ '+', "", $b->[ $_[1] ] ] ) };
    my $change = sub {
        push ( @$retval, [ 'c', $a->[ $_[0] ], $b->[ $_[1] ] ] );
    };
    my $match = sub {
        push ( @$retval, [ 'u', $a->[ $_[0] ], $b->[ $_[1] ] ] );
    };
    traverse_balanced(
        $a,
        $b,
        {
            MATCH     => $match,
            DISCARD_A => $discard,
            DISCARD_B => $add,
            CHANGE    => $change,
        },
        @_
    );
    return wantarray ? @$retval : $retval;
}

########################################
my $Root= __PACKAGE__;
package Algorithm::Diff::_impl;
use strict;

sub _Idx()  { 0 } # $me->[_Idx]: Ref to array of hunk indices
            # 1   # $me->[1]: Ref to first sequence
            # 2   # $me->[2]: Ref to second sequence
sub _End()  { 3 } # $me->[_End]: Diff between forward and reverse pos
sub _Same() { 4 } # $me->[_Same]: 1 if pos 1 contains unchanged items
sub _Base() { 5 } # $me->[_Base]: Added to range's min and max
sub _Pos()  { 6 } # $me->[_Pos]: Which hunk is currently selected
sub _Off()  { 7 } # $me->[_Off]: Offset into _Idx for current position
sub _Min() { -2 } # Added to _Off to get min instead of max+1

sub Die
{
    require Carp;
    Carp::confess( @_ );
}

sub _ChkPos
{
    my( $me )= @_;
    return   if  $me->[_Pos];
    my $meth= ( caller(1) )[3];
    Die( "Called $meth on 'reset' object" );
}

sub _ChkSeq
{
    my( $me, $seq )= @_;
    return $seq + $me->[_Off]
        if  1 == $seq  ||  2 == $seq;
    my $meth= ( caller(1) )[3];
    Die( "$meth: Invalid sequence number ($seq); must be 1 or 2" );
}

sub getObjPkg
{
    my( $us )= @_;
    return ref $us   if  ref $us;
    return $us . "::_obj";
}

sub new
{
    my( $us, $seq1, $seq2, $opts ) = @_;
    my @args;
    for( $opts->{keyGen} ) {
        push @args, $_   if  $_;
    }
    for( $opts->{keyGenArgs} ) {
        push @args, @$_   if  $_;
    }
    my $cdif= Algorithm::Diff::compact_diff( $seq1, $seq2, @args );
    my $same= 1;
    if(  0 == $cdif->[2]  &&  0 == $cdif->[3]  ) {
        $same= 0;
        splice @$cdif, 0, 2;
    }
    my @obj= ( $cdif, $seq1, $seq2 );
    $obj[_End] = (1+@$cdif)/2;
    $obj[_Same] = $same;
    $obj[_Base] = 0;
    my $me = bless \@obj, $us->getObjPkg();
    $me->Reset( 0 );
    return $me;
}

sub Reset
{
    my( $me, $pos )= @_;
    $pos= int( $pos || 0 );
    $pos += $me->[_End]
        if  $pos < 0;
    $pos= 0
        if  $pos < 0  ||  $me->[_End] <= $pos;
    $me->[_Pos]= $pos || !1;
    $me->[_Off]= 2*$pos - 1;
    return $me;
}

sub Base
{
    my( $me, $base )= @_;
    my $oldBase= $me->[_Base];
    $me->[_Base]= 0+$base   if  defined $base;
    return $oldBase;
}

sub Copy
{
    my( $me, $pos, $base )= @_;
    my @obj= @$me;
    my $you= bless \@obj, ref($me);
    $you->Reset( $pos )   if  defined $pos;
    $you->Base( $base );
    return $you;
}

sub Next {
    my( $me, $steps )= @_;
    $steps= 1   if  ! defined $steps;
    if( $steps ) {
        my $pos= $me->[_Pos];
        my $new= $pos + $steps;
        $new= 0   if  $pos  &&  $new < 0;
        $me->Reset( $new )
    }
    return $me->[_Pos];
}

sub Prev {
    my( $me, $steps )= @_;
    $steps= 1   if  ! defined $steps;
    my $pos= $me->Next(-$steps);
    $pos -= $me->[_End]   if  $pos;
    return $pos;
}

sub Diff {
    my( $me )= @_;
    $me->_ChkPos();
    return 0   if  $me->[_Same] == ( 1 & $me->[_Pos] );
    my $ret= 0;
    my $off= $me->[_Off];
    for my $seq ( 1, 2 ) {
        $ret |= $seq
            if  $me->[_Idx][ $off + $seq + _Min ]
            <   $me->[_Idx][ $off + $seq ];
    }
    return $ret;
}

sub Min {
    my( $me, $seq, $base )= @_;
    $me->_ChkPos();
    my $off= $me->_ChkSeq($seq);
    $base= $me->[_Base] if !defined $base;
    return $base + $me->[_Idx][ $off + _Min ];
}

sub Max {
    my( $me, $seq, $base )= @_;
    $me->_ChkPos();
    my $off= $me->_ChkSeq($seq);
    $base= $me->[_Base] if !defined $base;
    return $base + $me->[_Idx][ $off ] -1;
}

sub Range {
    my( $me, $seq, $base )= @_;
    $me->_ChkPos();
    my $off = $me->_ChkSeq($seq);
    if( !wantarray ) {
        return  $me->[_Idx][ $off ]
            -   $me->[_Idx][ $off + _Min ];
    }
    $base= $me->[_Base] if !defined $base;
    return  ( $base + $me->[_Idx][ $off + _Min ] )
        ..  ( $base + $me->[_Idx][ $off ] - 1 );
}

sub Items {
    my( $me, $seq )= @_;
    $me->_ChkPos();
    my $off = $me->_ChkSeq($seq);
    if( !wantarray ) {
        return  $me->[_Idx][ $off ]
            -   $me->[_Idx][ $off + _Min ];
    }
    return
        @{$me->[$seq]}[
                $me->[_Idx][ $off + _Min ]
            ..  ( $me->[_Idx][ $off ] - 1 )
        ];
}

sub Same {
    my( $me )= @_;
    $me->_ChkPos();
    return wantarray ? () : 0
        if  $me->[_Same] != ( 1 & $me->[_Pos] );
    return $me->Items(1);
}

my %getName;
BEGIN {
    %getName= (
        same => \&Same,
        diff => \&Diff,
        base => \&Base,
        min  => \&Min,
        max  => \&Max,
        range=> \&Range,
        items=> \&Items, # same thing
    );
}

sub Get
{
    my $me= shift @_;
    $me->_ChkPos();
    my @value;
    for my $arg (  @_  ) {
        for my $word (  split ' ', $arg  ) {
            my $meth;
            if(     $word !~ /^(-?\d+)?([a-zA-Z]+)([12])?$/
                ||  not  $meth= $getName{ lc $2 }
            ) {
                Die( $Root, ", Get: Invalid request ($word)" );
            }
            my( $base, $name, $seq )= ( $1, $2, $3 );
            push @value, scalar(
                4 == length($name)
                    ? $meth->( $me )
                    : $meth->( $me, $seq, $base )
            );
        }
    }
    if(  wantarray  ) {
        return @value;
    } elsif(  1 == @value  ) {
        return $value[0];
    }
    Die( 0+@value, " values requested from ",
        $Root, "'s Get in scalar context" );
}


my $Obj= getObjPkg($Root);
no strict 'refs';

for my $meth (  qw( new getObjPkg )  ) {
    *{$Root."::".$meth} = \&{$meth};
    *{$Obj ."::".$meth} = \&{$meth};
}
for my $meth (  qw(
    Next Prev Reset Copy Base Diff
    Same Items Range Min Max Get
    _ChkPos _ChkSeq
)  ) {
    *{$Obj."::".$meth} = \&{$meth};
}

1;
__END__

=head1 NAME

Algorithm::Diff - Compute `intelligent' differences between two files / lists

=head1 SYNOPSIS

    require Algorithm::Diff;

    # This example produces traditional 'diff' output:

    my $diff = Algorithm::Diff->new( \@seq1, \@seq2 );

    $diff->Base( 1 );   # Return line numbers, not indices
    while(  $diff->Next()  ) {
        next   if  $diff->Same();
        my $sep = '';
        if(  ! $diff->Items(2)  ) {
            sprintf "%d,%dd%d\n",
                $diff->Get(qw( Min1 Max1 Max2 ));
        } elsif(  ! $diff->Items(1)  ) {
            sprint "%da%d,%d\n",
                $diff->Get(qw( Max1 Min2 Max2 ));
        } else {
            $sep = "---\n";
            sprintf "%d,%dc%d,%d\n",
                $diff->Get(qw( Min1 Max1 Min2 Max2 ));
        }
        print "< $_"   for  $diff->Items(1);
        print $sep;
        print "> $_"   for  $diff->Items(2);
    }


    # Alternate interfaces:

    use Algorithm::Diff qw(
        LCS LCS_length LCSidx
        diff sdiff compact_diff
        traverse_sequences traverse_balanced );

    @lcs    = LCS( \@seq1, \@seq2 );
    $lcsref = LCS( \@seq1, \@seq2 );
    $count  = LCS_length( \@seq1, \@seq2 );

    ( $seq1idxref, $seq2idxref ) = LCSidx( \@seq1, \@seq2 );


    # Complicated interfaces:

    @diffs  = diff( \@seq1, \@seq2 );

    @sdiffs = sdiff( \@seq1, \@seq2 );

    @cdiffs = compact_diff( \@seq1, \@seq2 );

    traverse_sequences(
        \@seq1,
        \@seq2,
        {   MATCH     => \&callback1,
            DISCARD_A => \&callback2,
            DISCARD_B => \&callback3,
        },
        \&key_generator,
        @extra_args,
    );

    traverse_balanced(
        \@seq1,
        \@seq2,
        {   MATCH     => \&callback1,
            DISCARD_A => \&callback2,
            DISCARD_B => \&callback3,
            CHANGE    => \&callback4,
        },
        \&key_generator,
        @extra_args,
    );


=head1 INTRODUCTION

(by Mark-Jason Dominus)

I once read an article written by the authors of C<diff>; they said
that they worked very hard on the algorithm until they found the
right one.

I think what they ended up using (and I hope someone will correct me,
because I am not very confident about this) was the `longest common
subsequence' method.  In the LCS problem, you have two sequences of
items:

    a b c d f g h j q z

    a b c d e f g i j k r x y z

and you want to find the longest sequence of items that is present in
both original sequences in the same order.  That is, you want to find
a new sequence I<S> which can be obtained from the first sequence by
deleting some items, and from the secend sequence by deleting other
items.  You also want I<S> to be as long as possible.  In this case I<S>
is

    a b c d f g j z

From there it's only a small step to get diff-like output:

    e   h i   k   q r x y
    +   - +   +   - + + +

This module solves the LCS problem.  It also includes a canned function
to generate C<diff>-like output.

It might seem from the example above that the LCS of two sequences is
always pretty obvious, but that's not always the case, especially when
the two sequences have many repeated elements.  For example, consider

    a x b y c z p d q
    a b c a x b y c z

A naive approach might start by matching up the C<a> and C<b> that
appear at the beginning of each sequence, like this:

    a x b y c         z p d q
    a   b   c a b y c z

This finds the common subsequence C<a b c z>.  But actually, the LCS
is C<a x b y c z>:

          a x b y c z p d q
    a b c a x b y c z

or

    a       x b y c z p d q
    a b c a x b y c z

=head1 USAGE

(See also the README file and several example
scripts include with this module.)

This module now provides an object-oriented interface that uses less
memory and is easier to use than most of the previous procedural
interfaces.  It also still provides several exportable functions.  We'll
deal with these in ascending order of difficulty:  C<LCS>,
C<LCS_length>, C<LCSidx>, OO interface, C<prepare>, C<diff>, C<sdiff>,
C<traverse_sequences>, and C<traverse_balanced>.

=head2 C<LCS>

Given references to two lists of items, LCS returns an array containing
their longest common subsequence.  In scalar context, it returns a
reference to such a list.

    @lcs    = LCS( \@seq1, \@seq2 );
    $lcsref = LCS( \@seq1, \@seq2 );

C<LCS> may be passed an optional third parameter; this is a CODE
reference to a key generation function.  See L</KEY GENERATION
FUNCTIONS>.

    @lcs    = LCS( \@seq1, \@seq2, \&keyGen, @args );
    $lcsref = LCS( \@seq1, \@seq2, \&keyGen, @args );

Additional parameters, if any, will be passed to the key generation
routine.

=head2 C<LCS_length>

This is just like C<LCS> except it only returns the length of the
longest common subsequence.  This provides a performance gain of about
9% compared to C<LCS>.

=head2 C<LCSidx>

Like C<LCS> except it returns references to two arrays.  The first array
contains the indices into @seq1 where the LCS items are located.  The
second array contains the indices into @seq2 where the LCS items are located.

Therefore, the following three lists will contain the same values:

    my( $idx1, $idx2 ) = LCSidx( \@seq1, \@seq2 );
    my @list1 = @seq1[ @$idx1 ];
    my @list2 = @seq2[ @$idx2 ];
    my @list3 = LCS( \@seq1, \@seq2 );

=head2 C<new>

    $diff = Algorithm::Diffs->new( \@seq1, \@seq2 );
    $diff = Algorithm::Diffs->new( \@seq1, \@seq2, \%opts );

C<new> computes the smallest set of additions and deletions necessary
to turn the first sequence into the second and compactly records them
in the object.

You use the object to iterate over I<hunks>, where each hunk represents
a contiguous section of items which should be added, deleted, replaced,
or left unchanged.

=over 4

The following summary of all of the methods looks a lot like Perl code
but some of the symbols have different meanings:

    [ ]     Encloses optional arguments
    :       Is followed by the default value for an optional argument
    |       Separates alternate return results

Method summary:

    $obj        = Algorithm::Diff->new( \@seq1, \@seq2, [ \%opts ] );
    $pos        = $obj->Next(  [ $count : 1 ] );
    $revPos     = $obj->Prev(  [ $count : 1 ] );
    $obj        = $obj->Reset( [ $pos : 0 ] );
    $copy       = $obj->Copy(  [ $pos, [ $newBase ] ] );
    $oldBase    = $obj->Base(  [ $newBase ] );

Note that all of the following methods C<die> if used on an object that
is "reset" (not currently pointing at any hunk).

    $bits       = $obj->Diff(  );
    @items|$cnt = $obj->Same(  );
    @items|$cnt = $obj->Items( $seqNum );
    @idxs |$cnt = $obj->Range( $seqNum, [ $base ] );
    $minIdx     = $obj->Min(   $seqNum, [ $base ] );
    $maxIdx     = $obj->Max(   $seqNum, [ $base ] );
    @values     = $obj->Get(   @names );

Passing in C<undef> for an optional argument is always treated the same
as if no argument were passed in.

=item C<Next>

    $pos = $diff->Next();    # Move forward 1 hunk
    $pos = $diff->Next( 2 ); # Move forward 2 hunks
    $pos = $diff->Next(-5);  # Move backward 5 hunks

C<Next> moves the object to point at the next hunk.  The object starts
out "reset", which means it isn't pointing at any hunk.  If the object
is reset, then C<Next()> moves to the first hunk.

C<Next> returns a true value iff the move didn't go past the last hunk.
So C<Next(0)> will return true iff the object is not reset.

Actually, C<Next> returns the object's new position, which is a number
between 1 and the number of hunks (inclusive), or returns a false value.

=item C<Prev>

C<Prev($N)> is almost identical to C<Next(-$N)>; it moves to the $Nth
previous hunk.  On a 'reset' object, C<Prev()> [and C<Next(-1)>] move
to the last hunk.

The position returned by C<Prev> is relative to the I<end> of the
hunks; -1 for the last hunk, -2 for the second-to-last, etc.

=item C<Reset>

    $diff->Reset();     # Reset the object's position
    $diff->Reset($pos); # Move to the specified hunk
    $diff->Reset(1);    # Move to the first hunk
    $diff->Reset(-1);   # Move to the last hunk

C<Reset> returns the object, so, for example, you could use
C<< $diff->Reset()->Next(-1) >> to get the number of hunks.

=item C<Copy>

    $copy = $diff->Copy( $newPos, $newBase );

C<Copy> returns a copy of the object.  The copy and the orignal object
share most of their data, so making copies takes very little memory.
The copy maintains its own position (separate from the original), which
is the main purpose of copies.  It also maintains its own base.

By default, the copy's position starts out the same as the original
object's position.  But C<Copy> takes an optional first argument to set the
new position, so the following three snippets are equivalent:

    $copy = $diff->Copy($pos);

    $copy = $diff->Copy();
    $copy->Reset($pos);

    $copy = $diff->Copy()->Reset($pos);

C<Copy> takes an optional second argument to set the base for
the copy.  If you wish to change the base of the copy but leave
the position the same as in the original, here are two
equivalent ways:

    $copy = $diff->Copy();
    $copy->Base( 0 );

    $copy = $diff->Copy(undef,0);

Here are two equivalent way to get a "reset" copy:

    $copy = $diff->Copy(0);

    $copy = $diff->Copy()->Reset();

=item C<Diff>

    $bits = $obj->Diff();

C<Diff> returns a true value iff the current hunk contains items that are
different between the two sequences.  It actually returns one of the
follow 4 values:

=over 4

=item 3

C<3==(1|2)>.  This hunk contains items from @seq1 and the items
from @seq2 that should replace them.  Both sequence 1 and 2
contain changed items so both the 1 and 2 bits are set.

=item 2

This hunk only contains items from @seq2 that should be inserted (not
items from @seq1).  Only sequence 2 contains changed items so only the 2
bit is set.

=item 1

This hunk only contains items from @seq1 that should be deleted (not
items from @seq2).  Only sequence 1 contains changed items so only the 1
bit is set.

=item 0

This means that the items in this hunk are the same in both sequences.
Neither sequence 1 nor 2 contain changed items so neither the 1 nor the
2 bits are set.

=back

=item C<Same>

C<Same> returns a true value iff the current hunk contains items that
are the same in both sequences.  It actually returns the list of items
if they are the same or an emty list if they aren't.  In a scalar
context, it returns the size of the list.

=item C<Items>

    $count = $diff->Items(2);
    @items = $diff->Items($seqNum);

C<Items> returns the (number of) items from the specified sequence that
are part of the current hunk.

If the current hunk contains only insertions, then
C<< $diff->Items(1) >> will return an empty list (0 in a scalar conext).
If the current hunk contains only deletions, then C<< $diff->Items(2) >>
will return an empty list (0 in a scalar conext).

If the hunk contains replacements, then both C<< $diff->Items(1) >> and
C<< $diff->Items(2) >> will return different, non-empty lists.

Otherwise, the hunk contains identical items and all of the following
will return the same lists:

    @items = $diff->Items(1);
    @items = $diff->Items(2);
    @items = $diff->Same();

=item C<Range>

    $count = $diff->Range( $seqNum );
    @indices = $diff->Range( $seqNum );
    @indices = $diff->Range( $seqNum, $base );

C<Range> is like C<Items> except that it returns a list of I<indices> to
the items rather than the items themselves.  By default, the index of
the first item (in each sequence) is 0 but this can be changed by
calling the C<Base> method.  So, by default, the following two snippets
return the same lists:

    @list = $diff->Items(2);
    @list = @seq2[ $diff->Range(2) ];

You can also specify the base to use as the second argument.  So the
following two snippets I<always> return the same lists:

    @list = $diff->Items(1);
    @list = @seq1[ $diff->Range(1,0) ];

=item C<Base>

    $curBase = $diff->Base();
    $oldBase = $diff->Base($newBase);

C<Base> sets and/or returns the current base (usually 0 or 1) that is
used when you request range information.  The base defaults to 0 so
that range information is returned as array indices.  You can set the
base to 1 if you want to report traditional line numbers instead.

=item C<Min>

    $min1 = $diff->Min(1);
    $min = $diff->Min( $seqNum, $base );

C<Min> returns the first value that C<Range> would return (given the
same arguments) or returns C<undef> if C<Range> would return an empty
list.

=item C<Max>

C<Max> returns the last value that C<Range> would return or C<undef>.

=item C<Get>

    ( $n, $x, $r ) = $diff->Get(qw( min1 max1 range1 ));
    @values = $diff->Get(qw( 0min2 1max2 range2 same base ));

C<Get> returns one or more scalar values.  You pass in a list of the
names of the values you want returned.  Each name must match one of the
following regexes:

    /^(-?\d+)?(min|max)[12]$/i
    /^(range[12]|same|diff|base)$/i

The 1 or 2 after a name says which sequence you want the information
for (and where allowed, it is required).  The optional number before
"min" or "max" is the base to use.  So the following equalities hold:

    $diff->Get('min1') == $diff->Min(1)
    $diff->Get('0min2') == $diff->Min(2,0)

Using C<Get> in a scalar context when you've passed in more than one
name is a fatal error (C<die> is called).

=back

=head2 C<prepare>

Given a reference to a list of items, C<prepare> returns a reference
to a hash which can be used when comparing this sequence to other
sequences with C<LCS> or C<LCS_length>.

    $prep = prepare( \@seq1 );
    for $i ( 0 .. 10_000 )
    {
        @lcs = LCS( $prep, $seq[$i] );
        # do something useful with @lcs
    }

C<prepare> may be passed an optional third parameter; this is a CODE
reference to a key generation function.  See L</KEY GENERATION
FUNCTIONS>.

    $prep = prepare( \@seq1, \&keyGen );
    for $i ( 0 .. 10_000 )
    {
        @lcs = LCS( $seq[$i], $prep, \&keyGen );
        # do something useful with @lcs
    }

Using C<prepare> provides a performance gain of about 50% when calling LCS
many times compared with not preparing.

=head2 C<diff>

    @diffs     = diff( \@seq1, \@seq2 );
    $diffs_ref = diff( \@seq1, \@seq2 );

C<diff> computes the smallest set of additions and deletions necessary
to turn the first sequence into the second, and returns a description
of these changes.  The description is a list of I<hunks>; each hunk
represents a contiguous section of items which should be added,
deleted, or replaced.  (Hunks containing unchanged items are not
included.)

The return value of C<diff> is a list of hunks, or, in scalar context, a
reference to such a list.  If there are no differences, the list will be
empty.

Here is an example.  Calling C<diff> for the following two sequences:

    a b c e h j l m n p
    b c d e f j k l m r s t

would produce the following list:

    (
      [ [ '-', 0, 'a' ] ],

      [ [ '+', 2, 'd' ] ],

      [ [ '-', 4, 'h' ],
        [ '+', 4, 'f' ] ],

      [ [ '+', 6, 'k' ] ],

      [ [ '-',  8, 'n' ],
        [ '-',  9, 'p' ],
        [ '+',  9, 'r' ],
        [ '+', 10, 's' ],
        [ '+', 11, 't' ] ],
    )

There are five hunks here.  The first hunk says that the C<a> at
position 0 of the first sequence should be deleted (C<->).  The second
hunk says that the C<d> at position 2 of the second sequence should
be inserted (C<+>).  The third hunk says that the C<h> at position 4
of the first sequence should be removed and replaced with the C<f>
from position 4 of the second sequence.  And so on.

C<diff> may be passed an optional third parameter; this is a CODE
reference to a key generation function.  See L</KEY GENERATION
FUNCTIONS>.

Additional parameters, if any, will be passed to the key generation
routine.

=head2 C<sdiff>

    @sdiffs     = sdiff( \@seq1, \@seq2 );
    $sdiffs_ref = sdiff( \@seq1, \@seq2 );

C<sdiff> computes all necessary components to show two sequences
and their minimized differences side by side, just like the
Unix-utility I<sdiff> does:

    same             same
    before     |     after
    old        <     -
    -          >     new

It returns a list of array refs, each pointing to an array of
display instructions. In scalar context it returns a reference
to such a list. If there are no differences, the list will have one
entry per item, each indicating that the item was unchanged.

Display instructions consist of three elements: A modifier indicator
(C<+>: Element added, C<->: Element removed, C<u>: Element unmodified,
C<c>: Element changed) and the value of the old and new elements, to
be displayed side-by-side.

An C<sdiff> of the following two sequences:

    a b c e h j l m n p
    b c d e f j k l m r s t

results in

    ( [ '-', 'a', ''  ],
      [ 'u', 'b', 'b' ],
      [ 'u', 'c', 'c' ],
      [ '+', '',  'd' ],
      [ 'u', 'e', 'e' ],
      [ 'c', 'h', 'f' ],
      [ 'u', 'j', 'j' ],
      [ '+', '',  'k' ],
      [ 'u', 'l', 'l' ],
      [ 'u', 'm', 'm' ],
      [ 'c', 'n', 'r' ],
      [ 'c', 'p', 's' ],
      [ '+', '',  't' ],
    )

C<sdiff> may be passed an optional third parameter; this is a CODE
reference to a key generation function.  See L</KEY GENERATION
FUNCTIONS>.

Additional parameters, if any, will be passed to the key generation
routine.

=head2 C<compact_diff>

C<compact_diff> is much like C<sdiff> except it returns a much more
compact description consisting of just one flat list of indices.  An
example helps explain the format:

    my @a = qw( a b c   e  h j   l m n p      );
    my @b = qw(   b c d e f  j k l m    r s t );
    @cdiff = compact_diff( \@a, \@b );
    # Returns:
    #   @a      @b       @a       @b
    #  start   start   values   values
    (    0,      0,   #       =
         0,      0,   #    a  !
         1,      0,   #  b c  =  b c
         3,      2,   #       !  d
         3,      3,   #    e  =  e
         4,      4,   #    f  !  h
         5,      5,   #    j  =  j
         6,      6,   #       !  k
         6,      7,   #  l m  =  l m
         8,      9,   #  n p  !  r s t
        10,     12,   #
    );

The 0th, 2nd, 4th, etc. entries are all indices into @seq1 (@a in the
above example) indicating where a hunk begins.  The 1st, 3rd, 5th, etc.
entries are all indices into @seq2 (@b in the above example) indicating
where the same hunk begins.

So each pair of indices (except the last pair) describes where a hunk
begins (in each sequence).  Since each hunk must end at the item just
before the item that starts the next hunk, the next pair of indices can
be used to determine where the hunk ends.

So, the first 4 entries (0..3) describe the first hunk.  Entries 0 and 1
describe where the first hunk begins (and so are always both 0).
Entries 2 and 3 describe where the next hunk begins, so subtracting 1
from each tells us where the first hunk ends.  That is, the first hunk
contains items C<$diff[0]> through C<$diff[2] - 1> of the first sequence
and contains items C<$diff[1]> through C<$diff[3] - 1> of the second
sequence.

In other words, the first hunk consists of the following two lists of items:

               #  1st pair     2nd pair
               # of indices   of indices
    @list1 = @a[ $cdiff[0] .. $cdiff[2]-1 ];
    @list2 = @b[ $cdiff[1] .. $cdiff[3]-1 ];
               # Hunk start   Hunk end

Note that the hunks will always alternate between those that are part of
the LCS (those that contain unchanged items) and those that contain
changes.  This means that all we need to be told is whether the first
hunk is a 'same' or 'diff' hunk and we can determine which of the other
hunks contain 'same' items or 'diff' items.

By convention, we always make the first hunk contain unchanged items.
So the 1st, 3rd, 5th, etc. hunks (all odd-numbered hunks if you start
counting from 1) all contain unchanged items.  And the 2nd, 4th, 6th,
etc. hunks (all even-numbered hunks if you start counting from 1) all
contain changed items.

Since @a and @b don't begin with the same value, the first hunk in our
example is empty (otherwise we'd violate the above convention).  Note
that the first 4 index values in our example are all zero.  Plug these
values into our previous code block and we get:

    @hunk1a = @a[ 0 .. 0-1 ];
    @hunk1b = @b[ 0 .. 0-1 ];

And C<0..-1> returns the empty list.

Move down one pair of indices (2..5) and we get the offset ranges for
the second hunk, which contains changed items.

Since C<@diff[2..5]> contains (0,0,1,0) in our example, the second hunk
consists of these two lists of items:

        @hunk2a = @a[ $cdiff[2] .. $cdiff[4]-1 ];
        @hunk2b = @b[ $cdiff[3] .. $cdiff[5]-1 ];
    # or
        @hunk2a = @a[ 0 .. 1-1 ];
        @hunk2b = @b[ 0 .. 0-1 ];
    # or
        @hunk2a = @a[ 0 .. 0 ];
        @hunk2b = @b[ 0 .. -1 ];
    # or
        @hunk2a = ( 'a' );
        @hunk2b = ( );

That is, we would delete item 0 ('a') from @a.

Since C<@diff[4..7]> contains (1,0,3,2) in our example, the third hunk
consists of these two lists of items:

        @hunk3a = @a[ $cdiff[4] .. $cdiff[6]-1 ];
        @hunk3a = @b[ $cdiff[5] .. $cdiff[7]-1 ];
    # or
        @hunk3a = @a[ 1 .. 3-1 ];
        @hunk3a = @b[ 0 .. 2-1 ];
    # or
        @hunk3a = @a[ 1 .. 2 ];
        @hunk3a = @b[ 0 .. 1 ];
    # or
        @hunk3a = qw( b c );
        @hunk3a = qw( b c );

Note that this third hunk contains unchanged items as our convention demands.

You can continue this process until you reach the last two indices,
which will always be the number of items in each sequence.  This is
required so that subtracting one from each will give you the indices to
the last items in each sequence.

=head2 C<traverse_sequences>

C<traverse_sequences> used to be the most general facility provided by
this module (the new OO interface is more powerful and much easier to
use).

Imagine that there are two arrows.  Arrow A points to an element of
sequence A, and arrow B points to an element of the sequence B. 
Initially, the arrows point to the first elements of the respective
sequences.  C<traverse_sequences> will advance the arrows through the
sequences one element at a time, calling an appropriate user-specified
callback function before each advance.  It willadvance the arrows in
such a way that if there are equal elements C<$A[$i]> and C<$B[$j]>
which are equal and which are part of the LCS, there will be some moment
during the execution of C<traverse_sequences> when arrow A is pointing
to C<$A[$i]> and arrow B is pointing to C<$B[$j]>.  When this happens,
C<traverse_sequences> will call the C<MATCH> callback function and then
it will advance both arrows.

Otherwise, one of the arrows is pointing to an element of its sequence
that is not part of the LCS.  C<traverse_sequences> will advance that
arrow and will call the C<DISCARD_A> or the C<DISCARD_B> callback,
depending on which arrow it advanced.  If both arrows point to elements
that are not part of the LCS, then C<traverse_sequences> will advance
one of them and call the appropriate callback, but it is not specified
which it will call.

The arguments to C<traverse_sequences> are the two sequences to
traverse, and a hash which specifies the callback functions, like this:

    traverse_sequences(
        \@seq1, \@seq2,
        {   MATCH => $callback_1,
            DISCARD_A => $callback_2,
            DISCARD_B => $callback_3,
        }
    );

Callbacks for MATCH, DISCARD_A, and DISCARD_B are invoked with at least
the indices of the two arrows as their arguments.  They are not expected
to return any values.  If a callback is omitted from the table, it is
not called.

Callbacks for A_FINISHED and B_FINISHED are invoked with at least the
corresponding index in A or B.

If arrow A reaches the end of its sequence, before arrow B does,
C<traverse_sequences> will call the C<A_FINISHED> callback when it
advances arrow B, if there is such a function; if not it will call
C<DISCARD_B> instead.  Similarly if arrow B finishes first. 
C<traverse_sequences> returns when both arrows are at the ends of their
respective sequences.  It returns true on success and false on failure. 
At present there is no way to fail.

C<traverse_sequences> may be passed an optional fourth parameter; this
is a CODE reference to a key generation function.  See L</KEY GENERATION
FUNCTIONS>.

Additional parameters, if any, will be passed to the key generation function.

If you want to pass additional parameters to your callbacks, but don't
need a custom key generation function, you can get the default by
passing undef:

    traverse_sequences(
        \@seq1, \@seq2,
        {   MATCH => $callback_1,
            DISCARD_A => $callback_2,
            DISCARD_B => $callback_3,
        },
        undef,     # default key-gen
        $myArgument1,
        $myArgument2,
        $myArgument3,
    );

C<traverse_sequences> does not have a useful return value; you are
expected to plug in the appropriate behavior with the callback
functions.

=head2 C<traverse_balanced>

C<traverse_balanced> is an alternative to C<traverse_sequences>. It
uses a different algorithm to iterate through the entries in the
computed LCS. Instead of sticking to one side and showing element changes
as insertions and deletions only, it will jump back and forth between
the two sequences and report I<changes> occurring as deletions on one
side followed immediatly by an insertion on the other side.

In addition to the C<DISCARD_A>, C<DISCARD_B>, and C<MATCH> callbacks
supported by C<traverse_sequences>, C<traverse_balanced> supports
a C<CHANGE> callback indicating that one element got C<replaced> by another:

    traverse_balanced(
        \@seq1, \@seq2,
        {   MATCH => $callback_1,
            DISCARD_A => $callback_2,
            DISCARD_B => $callback_3,
            CHANGE    => $callback_4,
        }
    );

If no C<CHANGE> callback is specified, C<traverse_balanced>
will map C<CHANGE> events to C<DISCARD_A> and C<DISCARD_B> actions,
therefore resulting in a similar behaviour as C<traverse_sequences>
with different order of events.

C<traverse_balanced> might be a bit slower than C<traverse_sequences>,
noticable only while processing huge amounts of data.

The C<sdiff> function of this module 
is implemented as call to C<traverse_balanced>.

C<traverse_balanced> does not have a useful return value; you are expected to
plug in the appropriate behavior with the callback functions.

=head1 KEY GENERATION FUNCTIONS

Most of the functions accept an optional extra parameter.  This is a
CODE reference to a key generating (hashing) function that should return
a string that uniquely identifies a given element.  It should be the
case that if two elements are to be considered equal, their keys should
be the same (and the other way around).  If no key generation function
is provided, the key will be the element as a string.

By default, comparisons will use "eq" and elements will be turned into keys
using the default stringizing operator '""'.

Where this is important is when you're comparing something other than
strings.  If it is the case that you have multiple different objects
that should be considered to be equal, you should supply a key
generation function. Otherwise, you have to make sure that your arrays
contain unique references.

For instance, consider this example:

    package Person;

    sub new
    {
        my $package = shift;
        return bless { name => '', ssn => '', @_ }, $package;
    }

    sub clone
    {
        my $old = shift;
        my $new = bless { %$old }, ref($old);
    }

    sub hash
    {
        return shift()->{'ssn'};
    }

    my $person1 = Person->new( name => 'Joe', ssn => '123-45-6789' );
    my $person2 = Person->new( name => 'Mary', ssn => '123-47-0000' );
    my $person3 = Person->new( name => 'Pete', ssn => '999-45-2222' );
    my $person4 = Person->new( name => 'Peggy', ssn => '123-45-9999' );
    my $person5 = Person->new( name => 'Frank', ssn => '000-45-9999' );

If you did this:

    my $array1 = [ $person1, $person2, $person4 ];
    my $array2 = [ $person1, $person3, $person4, $person5 ];
    Algorithm::Diff::diff( $array1, $array2 );

everything would work out OK (each of the objects would be converted
into a string like "Person=HASH(0x82425b0)" for comparison).

But if you did this:

    my $array1 = [ $person1, $person2, $person4 ];
    my $array2 = [ $person1, $person3, $person4->clone(), $person5 ];
    Algorithm::Diff::diff( $array1, $array2 );

$person4 and $person4->clone() (which have the same name and SSN)
would be seen as different objects. If you wanted them to be considered
equivalent, you would have to pass in a key generation function:

    my $array1 = [ $person1, $person2, $person4 ];
    my $array2 = [ $person1, $person3, $person4->clone(), $person5 ];
    Algorithm::Diff::diff( $array1, $array2, \&Person::hash );

This would use the 'ssn' field in each Person as a comparison key, and
so would consider $person4 and $person4->clone() as equal.

You may also pass additional parameters to the key generation function
if you wish.

=head1 ERROR CHECKING

If you pass these routines a non-reference and they expect a reference,
they will die with a message.

=head1 AUTHOR

This version released by Tye McQueen (http://perlmonks.org/?node=tye).

=head1 LICENSE

Parts Copyright (c) 2000-2004 Ned Konz.  All rights reserved.
Parts by Tye McQueen.

This program is free software; you can redistribute it and/or modify it
under the same terms as Perl.

=head1 MAILING LIST

Mark-Jason still maintains a mailing list.  To join a low-volume mailing
list for announcements related to diff and Algorithm::Diff, send an
empty mail message to mjd-perl-diff-request@plover.com.

=head1 CREDITS

Versions through 0.59 (and much of this documentation) were written by:

Mark-Jason Dominus, mjd-perl-diff@plover.com

This version borrows some documentation and routine names from
Mark-Jason's, but Diff.pm's code was completely replaced.

This code was adapted from the Smalltalk code of Mario Wolczko
<mario@wolczko.com>, which is available at
ftp://st.cs.uiuc.edu/pub/Smalltalk/MANCHESTER/manchester/4.0/diff.st

C<sdiff> and C<traverse_balanced> were written by Mike Schilli
<m@perlmeister.com>.

The algorithm is that described in
I<A Fast Algorithm for Computing Longest Common Subsequences>,
CACM, vol.20, no.5, pp.350-353, May 1977, with a few
minor improvements to improve the speed.

Much work was done by Ned Konz (perl@bike-nomad.com).

The OO interface and some other changes are by Tye McQueen.

=cut