[ '+',  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