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Here is a recent article describing a simpler algorithm for sampling derangements. I also found slides for the presentation. Since the paper is so recent, I guess this means that a small modification of Fisher-Yates is unlikely to generate derangements, since someone would have already come up with it by now. Still, their algorithm is in-place and has better expected running time than retrying Fisher-Yates until you get a derangement.

Here is a Perl implementation I whipped up. It is slightly odd because I followed their lead and used array indexing from 1.

sub rand_derangement { my $n = shift; return if $n == 1; ## no derangements of size 1 ## precompute $D[n] == number of derangements of size n my @D = (1,0); push @D, $#D * ($D[-1] + $D[-2]) while $#D < $n; my @A = (undef, 1 .. $n); my @mark = (1, (0) x $n); my ($i, $u) = ($n, $n); while ($u > 1) { if (! $mark[$i]) { my $j = 0; $j = 1 + int rand($i-2) while $mark[$j]; @A[$i,$j] = @A[$j,$i]; if ( rand(1) < ($u-1) * $D[$u-2] / $D[$u] ) { $mark[$j] = 1; $u--; } $u--; } $i--; } return @A[1..$n]; }


In reply to Re^3: Random Derangement Of An Array by blokhead
in thread Random Derangement Of An Array by Limbic~Region

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