EXPORT

  combine
  derange
  multiset
  permute
  string
  factorial

combine()

 Usage   : my @combinations = combine($k,@n);
 Function: implements nCk (n choose k), or n!/(k!*(n-k!)).
           returns all unique unorderd combinations of k items from set n.
           items in n are assumed to be character data, and are
           copied into the return data structure (see "Returns" below).
 Example : my @n = qw(a b c);
           my @c = combine(2,@n);
           print join "\n", map { join " ", @$_ } @c;
           # prints:
           # b c
           # a c
           # a b
 Returns : a list of arrays, where each array contains a unique combination
           of k items from n
 Args    : a list of items to be combined
 Notes   : data is internally assumed to be alphanumeric.  this is necessary
           to efficiently generate combinations of large sets.  if you need
           combinations of non-alphanumeric data, or on data
           C<sort {$a cmp $b}> would not be appropriate, use the
           object-oriented API.  See L</new()> and the B<compare> option.

           Identical items are assumed to be non-unique.  That is, calling
           C<combine(1,'a','a') yields two sets: {a}, and {a}.  See
           L</next_multiset() if this is not the desired behavior.

derange()

 Usage   : my @deranges = derange(@n);
 Function: implements !n, a derangement of n items in which none of the
           items appear in their originally ordered place.
 Example : my @n = qw(a b c);
           my @d = derange(@n);
           print join "\n", map { join " ", @$_ } @d;
           # prints:
           # a c b
           # b a c
           # b c a
           # c a b
           # c b a
 Returns : a list of arrays, where each array contains a derangement of
           k items from n (where k == n).
 Args    : a list of items to be deranged.
 Note    : k should really be parameterizable.  this will happen
           in a later version of the module.  send me a patch to
           make that version come out sooner.
 Notes   : data is internally assumed to be alphanumeric.  this is necessary
           to efficiently generate combinations of large sets.  if you need
           combinations of non-alphanumeric data, or on data
           C<sort {$a cmp $b}> would not be appropriate, use the
           object-oriented API.  See L</new()>, and the B<compare> option.

next_derangement()

 Usage   : my @derangement = $c->next_derangement();
 Function: get derangements for @data.
 Returns : returns a permutation of items from @data (see L</new()>),
           where none of the items appear in their natural order.  repeated calls
           retrieve all unique derangements of @data elements.  a returned empty
           list signifies all derangements have been iterated.
 Args    : none.

factorial()

 Usage   : my $f = factorial(4); #returns 24, or 4*3*2*1
 Function: calculates n! (n factorial).
 Returns : undef if n is non-integer or n < 0
 Args    : a positive, non-zero integer
 Note    : this function is used internally by combine() and permute()

permute()

 Usage   : my @permutations = permute(@n);
 Function: implements nPk (n permute k) (where k == n), or n!/(n-k)!
            returns all unique permutations of k items from set n
           (where n == k, see "Note" below).  items in n are assumed to
           be character data, and are copied into the return data
           structure.
 Example : my @n = qw(a b c);
           my @p = permute(@n);
           print join "\n", map { join " ", @$_ } @p;
           # prints:
           # b a c
           # b c a
           # c b a
           # c a b
           # a c b
           # a b c
 Returns : a list of arrays, where each array contains a permutation of
           k items from n (where k == n).
 Args    : a list of items to be permuted.
 Note    : k should really be parameterizable.  this will happen
           in a later version of the module.  send me a patch to
           make that version come out sooner.
 Notes   : data is internally assumed to be alphanumeric.  this is necessary
           to efficiently generate combinations of large sets.  if you need
           combinations of non-alphanumeric data, or on data
           C<sort {$a cmp $b}> would not be appropriate, use the
           object-oriented API.  See L</new()>, and the B<compare> option.

           Identical items are assumed to be non-unique.  That is, calling
           C<permute('a','a') yields two sets: {a,a}, and {a,a}.  See
           L</next_string() if this is not the desired behavior.

new()

 Usage   : my $c = Math::Combinatorics->new( count => 2,       #treated as int
                                             data => [1,2,3,4] #arrayref or anonymous array
                                           );
 Function: build a new Math::Combinatorics object.
 Returns : a Math::Combinatorics object
 Args    : count     - required for combinatoric functions/methods.  number of elements to be
                       present in returned set(s).
           data      - required for combinatoric B<AND> permutagenic functions/methods.  this is the
                       set elements are chosen from.  B<NOTE>: this array is modified in place; make
                       a copy of your array if the order matters in the caller's space.
           frequency - optional vector of data frequencies.  must be the same length as the B<data>
                       constructor argument.  These two constructor calls here are equivalent:

                         $a = 'a';
                         $b = 'b';

                         Math::Combinatorics->new( count=>2, data=>[\$a,\$a,\$a,\$a,\$a,\$b,\$b] );
                         Math::Combinatorics->new( count=>2, data=>[\$a,\$b], frequency=>[5,2] );

                       so why use this?  sometimes it's useful to have multiple identical entities in
                       a set (in set theory jargon, this is called a "bag", See L<Set::Bag>).
           compare   - optional subroutine reference used in sorting elements of the set.  examples:

                       #appropriate for character elements
                       compare => sub { $_[0] cmp $_[1] }
                       #appropriate for numeric elements
                       compare => sub { $_[0] <=> $_[1] }
                       #appropriate for object elements, perhaps
                       compare => sub { $_[0]->value <=> $_[1]->value }

                     The default sort mechanism is based on references, and cannot be predicted.
                     Improvements for a more flexible compare() mechanism are most welcome.

next_combination()

 Usage   : my @combo = $c->next_combination();
 Function: get combinations of size $count from @data.
 Returns : returns a combination of $count items from @data (see L</new()>).
           repeated calls retrieve all unique combinations of $count elements.
           a returned empty list signifies all combinations have been iterated.
 Note    : this method may only be used if a B<frequency> argument is B<NOT>
           given to L</new()>, otherwise use L</next_multiset()>.
 Args    : none.

next_multiset()

 Usage   : my @multiset = $c->next_multiset();
 Function: get multisets for @data.
 Returns : returns a multiset of items from @data (see L</new()>).
           a multiset is a special type of combination where the set from which
           combinations are drawn contains items that are indistinguishable.  use
           L</next_multiset()> when a B<frequency> argument is passed to L</new()>.
           repeated calls retrieve all unique multisets of @data elements.  a
           returned empty list signifies all multisets have been iterated.
 Note    : this method may only be used if a B<frequency> argument is given to
           L</new()>, otherwise use L</next_combination()>.
 Args    : none.

next_permutation()

 Usage   : my @permu = $c->next_permutation();
 Function: get permutations of elements in @data.
 Returns : returns a permutation of items from @data (see L</new()>).
           repeated calls retrieve all unique permutations of @data elements.
           a returned empty list signifies all permutations have been iterated.
 Note    : this method may only be used if a B<frequency> argument is B<NOT>
           given to L</new()>, otherwise use L</next_string()>.
 Args    : none.

next_string()

 Usage   : my @string = $c->next_string();
 Function: get strings for @data.
 Returns : returns a multiset of items from @data (see L</new()>).
           a multiset is a special type of permutation where the set from which
           combinations are drawn contains items that are indistinguishable.  use
           L</next_permutation()> when a B<frequency> argument is passed to L</new()>.
           repeated calls retrieve all unique multisets of @data elements.  a
           returned empty list signifies all strings have been iterated.
 Note    : this method may only be used if a B<frequency> argument is given to
           L</new()>, otherwise use L</next_permutation()>.
 Args    : none.

sum()

 Usage   : my $sum = sum(1,2,3); # returns 6
 Function: sums a list of integers.  non-integer list elements are ignored
 Returns : sum of integer items in arguments passed in
 Args    : a list of integers
 Note    : this function is used internally by combine()

compare()

 Usage   : $obj->compare()
 Function: internal, undocumented.  holds a comparison coderef.
 Returns : value of compare (a coderef)

count()

 Usage   : $obj->count()
 Function: internal, undocumented.  holds the "k" in nCk or nPk.
 Returns : value of count (an int)

data()

 Usage   : $obj->data()
 Function: internal, undocumented.  holds the set "n" in nCk or nPk.
 Returns : value of data (an arrayref)

swap()

reverse()

rotate()

upper_bound()

lower_bound()

_permutation_cursor()

 Usage   : $obj->_permutation_cursor()
 Function: internal method.  cursor on permutation iterator order.
 Returns : value of _permutation_cursor (an arrayref)
 Args    : none