++ed by:

2 PAUSE users
3 non-PAUSE users.

Stephan Loyd
and 1 contributors


Algorithm::Permute - Handy and fast permutation with object oriented interface


  use Algorithm::Permute;

  # default is to create n of n objects permutation generator
  my $p = Algorithm::Permute->new(['a'..'d']);

  # but also you can create r of n objects permutation generator, where r <= n
  my $p = Algorithm::Permute->new([1..4], 3);

  while (my @res = $p->next) {
    print join(", ", @res), "\n";

  # and this one is the speed demon:
  my @array = (1..9);
  Algorithm::Permute::permute { print "@array\n" } @array;


This handy module makes performing permutation in Perl easy and fast, although perhaps its algorithm is not the fastest on the earth. It supports permutation r of n objects where 0 < r <= n.


new [@list]

Returns a permutor object for the given items.


Returns a list of the items in the next permutation. The order of the resulting permutation is the same as of the previous version of Algorithm::Permute.


Returns the list of items which will be returned by next(), but doesn't advance the sequence. Could be useful if you wished to skip over just a few unwanted permutations.


Resets the iterator to the start. May be used at any time, whether the entire set has been produced or not. Has no useful return value.


Starting with version 0.03, there is a function - not exported by default - which supports a callback style interface:


A block of code is passed, which will be executed for each permutation. The array will be changed in place, and then changed back again before permute returns. During the execution of the callback, the array is read-only and you'll get an error if you try to change its length. (You can change its elements, but the consequences are liable to confuse you and may change in future versions.)

You have to pass an array, it can't just be a list. It does work with special arrays and tied arrays, though unless you're doing something particularly abstruse you'd be better off copying the elements into a normal array first. Example:

 my @array = (1..9);
 permute { print "@array\n" } @array;

The code is run inside a pseudo block, rather than as a normal subroutine. That means you can't use return, and you can't jump out of it using goto and so on. Also, caller won't tell you anything helpful from inside the callback. Such is the price of speed.

The order in which the permutations are generated is not guaranteed, so don't rely on it.

The low-level hack behind this function makes it currently the fastest way of doing permutation among others.


I've collected some Perl routines and modules which implement permutation, and do some simple benchmark. The whole result is the following.

Permutation of eight scalars:

  Abigail's                     :  9 wallclock secs ( 8.07 usr +  0.30 sys =  8.37 CPU)
  Algorithm::Permute            :  5 wallclock secs ( 5.72 usr +  0.00 sys =  5.72 CPU)
  Algorithm::Permute qw(permute):  2 wallclock secs ( 1.65 usr +  0.00 sys =  1.65 CPU)
  List::Permutor                : 27 wallclock secs (26.73 usr +  0.01 sys = 26.74 CPU)
  Memoization                   : 32 wallclock secs (32.55 usr +  0.02 sys = 32.57 CPU)
  perlfaq4                      : 36 wallclock secs (35.27 usr +  0.02 sys = 35.29 CPU)

Permutation of nine scalars (the Abigail's routine is commented out, because it stores all of the result in memory, swallows all of my machine's memory):

  Algorithm::Permute            :  43 wallclock secs ( 42.93 usr +  0.04 sys = 42.97 CPU)
  Algorithm::Permute qw(permute):  15 wallclock secs ( 14.82 usr +  0.00 sys = 14.82 CPU)
  List::Permutor                : 227 wallclock secs (226.46 usr +  0.22 sys = 226.68 CPU)
  Memoization                   : 307 wallclock secs (306.69 usr +  0.43 sys = 307.12 CPU)
  perlfaq4                      : 272 wallclock secs (271.93 usr +  0.33 sys = 272.26 CPU)

The benchmark script is included in the bench directory. I understand that speed is not everything. So here is the list of URLs of the alternatives, in case you hate this module.

  • Memoization is discussed in chapter 4 Perl Cookbook, so you can get it from O'Reilly: ftp://ftp.oreilly.com/published/oreilly/perl/cookbook

  • Abigail's: http://www.foad.org/~abigail/Perl

  • List::Permutor: http://www.cpan.org/modules/by-module/List

  • The classic way, usually used by Lisp hackers: perldoc perlfaq4


In Edwin's words: Yustina Sri Suharini - my ex-fiance-now-wife, for providing the permutation problem to me.


  • Data Structures, Algorithms, and Program Style Using C - Korsh and Garrett

  • Algorithms from P to NP, Vol. I - Moret and Shapiro


Edwin Pratomo <edpratomo@cpan.org> was the original author.

Stephan Loyd <sloyd@cpan.org> is co-maintainer after version 0.12.

The object oriented interface is taken from Tom Phoenix's List::Permutor. Robin Houston <robin@kitsite.com> invented and contributed the callback style interface.


This software is copyright (c) 1999 by Edwin Pratomo.

This is free software; you can redistribute it and/or modify it under the same terms as the Perl 5 programming language system itself.