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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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