Randomizing an Array

Problem

You want to shuffle the elements of an array randomly. The obvious application is writing a card game, where you must shuffle a deck of cards, but it is equally applicable to any situation where you want to deal with elements of an array in a random order.

Solution

Swap each element in the array with another randomly selected, element:

# fisher_yates_shuffle( \@array ) : generate a random permutation # of @array in place sub fisher_yates_shuffle {
 my $array = shift; my $i;
for ($i = @$array; --$i; ) {
 my $j = int rand ($i+1); next if $i == $j; @$array[$i,$j] = @$array[$j,$i];
}
} fisher_yates_shuffle( \@array ); # permutes @array in place

Or, pick a random permutation using the code in Example 4.4:

$permutations = factorial( scalar @array ); @shuffle = @array [ n2perm( 1+int(rand $permutations), $#array ) ];

Discussion

Shuffling is a surprisingly tricky process. It's easy to write a bad shuffle:

sub naive_shuffle {
 # don't do this for (my $i = 0; $i < @_; $i++) {
 my $j = int rand @_; # pick random element ($_[$i], $_[$j]) = ($_[$j], $_[$i]); # swap 'em
}
}

This algorithm is biased; the list's possible permutations don't all have the same probability of being generated. The proof of this is simple: take the case where we're passed a 3-element list. We generate three random numbers, each of which can have three possible values, yielding 27 possible outcomes here. There are only 6 permutations of the 3-element list, though. Because 27 isn't evenly divisible by 6, some outcomes are more likely than others.

The Fisher-Yates shuffle avoids this bias by changing the range of the random numbers it selects.