Perl Cookbook

Program: permute

Problem

Have you ever wanted to generate all possible permutations of an array or to execute some code for every possible permutation? For example:

% echo man bites dog | permute

                  dog bites man
               
                  bites dog man
               
                  dog man bites
               
                  man dog bites
               
                  bites man dog
               
                  man bites dog

The number of permutations of a set is the factorial of the size of the set. This grows big extremely fast, so you don’t want to run it on many permutations:

Set Size            Permutations
1                   1
2                   2
3                   6
4                   24
5                   120
6                   720
7                   5040
8                   40320
9                   362880
10                  3628800
11                  39916800
12                  479001600
13                  6227020800
14                  87178291200
15                  1307674368000

Doing something for each alternative takes a correspondingly large amount of time. In fact, factorial algorithms exceed the number of particles in the universe with very small inputs. The factorial of 500 is greater than ten raised to the thousandth power!

use Math::BigInt;
sub factorial {
    my $n = shift;
    my $s = 1;
    $s *= $n-- while $n > 0;
    return $s;
}
print factorial(Math::BigInt->new("500"));

                  +1220136... (1035 digits total)

The two solutions that follow differ in the order of the permutations they return.

The solution in Example 4.3 uses a classic list permutation algorithm used by Lisp hackers. It’s relatively straightforward but makes unnecessary copies. It’s also hardwired to do nothing but print out its permutations.

Example 4-3. tsc-permute

#!/usr/bin/perl -n
# tsc_permute: permute each word of input permute([split], []); sub permute { my @items = @{ $_[0] }; my @perms = @{ $_[1] }; unless (@items) ...