Re^3: Derangements iterator (others)

[fxn]

(Re: Algorithm::Combinatorics) the logic in principle can be refined to skip some more permutations, but benchmarks showed no difference whatsoever, so I left the code that is easier to understand and added a comment about it:

    /* I tried an alternative approach that would in theory avoid the
    generation of some permutations with fixed-points: keeping track of
    the leftmost fixed-point, and reversing the elements to its right.
    But benchmarks up to n = 11 showed no difference whatsoever.
    Thus, I left this version, which is simpler.

    That n = 11 does not mean there was a difference for n = 12, it
    means I stopped benchmarking at n = 11. */

The current interface guarantees lexicographic order, but I plan to provide more algorithms that relax that condition if you don't need it and faster generators are available. I will write it before I die ideally.

[tye]

Thanks for the explanation.

The current interface guarantees lexicographic order

It is easy to adjust my iterator to get lexicographic order. For example, just add one reverse:

    $left= [ @$left, reverse @{$redo[$i]} ];

I plan to add a version to Algorithm::Loops before I die. (:

[Roy Johnson]

Here's a version you can add to Algorithm::Loops. It uses NestedLoops and is comparatively efficient about skipping invalid combinations. It also puts its results in numeric/lexicographic order and handles duplicates. The commented-out code is for watching/debugging the management of the "pool" of available numbers.

use strict;
use warnings;

use Algorithm::Loops 'NestedLoops';

sub derange {
  # Generate the list of possible values at each position
  # Skip a value if it's already used up (no more in the pool) or is i
+n its original position
  my %pool;
  ++$pool{$_} for (@_);
  my @orig = @_;
  no warnings 'numeric';
  my @values = sort {$a <=> $b or $a cmp $b} keys %pool;
  my @prev_values;
  NestedLoops(
    [(sub {
        # Generate all candidate values for this position
# print "Generating with \@_ = @_\n";
        my $pos = @_;
        # Update the pool: the last value on @_ has just changed, so
        # return the previous value(s) to the pool and remove the new
        # one.
        if (@_) {
          for (grep {defined $prev_values[$_]} $#_..$#orig-1) {
#print "Returning $prev_values[$_] to the pool\n";
            ++$pool{$prev_values[$_]};
            undef $prev_values[$_];
          }
#print "Removing $_[-1] from the pool\n";
          --$pool{$_[-1]};
#print "Valid values in the pool:\n";
#while (my ($k,$v) = each %pool) {
#  print "$k: $v\n" if $v;
#}
          $prev_values[$#_] = $_[-1]; 
        }
        [ grep {$orig[$pos] ne $_ and $pool{$_} > 0} @values ]
      }) x @orig]
  );
}

my @results;
my $iter = derange(@ARGV);
print "@results\n" while @results = $iter->();

As a possibly interesting note: if you simply remove $orig[$pos] ne $_ and, it becomes a permutations generator. But derange is not simply a permutations generator that filters out individual invalid permutations; it prunes entire sub-trees. (Similarly, the permutation generator doesn't loop through the whole cartesian space and filter it.)