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I've been chewing on this problem for a day now. This is clearly problem with two logical parts. Part 1 is to generate all legal mappings of N columns of data into M buckets, given the constraints that no bucket can be empty, and that the columns need to stay ordered. The second part is apply these mappings to the input data, and select a mapping that yields a "best fit."

I focused on the first part, looking for a quicker, simpler solution. I think I have one. Here it is. Given a number of columns and a number of buckets, the code below calculates all legal mappings of columns to buckets, and returns these in a hash, where the key is a printable string, and the value is an anonymous array.

{ # map columns to buckets. key is string, value is anonymous array. my %c2bMap; sub c2bMappings { my($buckets, $columns) = @_; die "bogus args" unless $buckets > 1 && $columns > $buckets; %c2bMap = (); _genFrom(0, (0) x ($columns - $buckets), 1 .. ($buckets - 1)); return \%c2bMap; } sub _genFrom { my @c2bMap = @_; return if exists $c2bMap{"@c2bMap"}; print "@c2bMap\n"; #DEBUG $c2bMap{"@c2bMap"} = \@c2bMap; foreach my $i ( 2 .. $#c2bMap ) { my $n = $c2bMap[$i] - 1; if ( $c2bMap[$i - 2] == $n && $c2bMap[$i - 1] == $n ) { local $c2bMap[$i-1] = $c2bMap[$i]; _genFrom(@c2bMap); } } } } c2bMappings(4,6); __END__ 0 0 0 1 2 3 0 0 1 1 2 3 0 1 1 1 2 3 0 1 1 2 2 3 0 1 2 2 2 3 0 1 2 2 3 3 0 1 2 3 3 3 0 1 1 2 3 3 0 0 1 2 2 3 0 0 1 2 3 3
Recursion only happens with valid mappings. Note the selective localization of an element of the array that the code is about to recurse on.

In reply to Re: Puzzle: need a more general algorithm by dws
in thread Puzzle: need a more general algorithm by Ovid

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