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I was sent the following answer to the puzzle with the following challenge:

  • Why does this work
  • How efficient is is. i.e., how fast it calculates group_cats(50, 1..150) -- with the caveat that it might not be that efficient in memory.

If you think you know who sent this, please do not speculate! I will neither confirm nor deny ...

use strict; use Carp; use Data::Dumper; $Data::Dumper::Indent = 1; print Dumper [group_cats(3, 1..7)]; { my @sizes; my %ans; sub group_cats { (my $num, @sizes) = @_; %ans = (); my ($size, @partition) = _group_cats($num, 0, $#sizes); return @partition; } sub _group_cats { my $key = join ":", @_; my ($num, $start, $end) = @_; if (not exists $ans{$key}) { if ($num < 1) { $ans{$key} = [0]; } elsif (1 == $num) { my @part = map $sizes[$_], $start..$end; $ans{$key} = [sum(@part), \@part]; } else { my $num_a = int($num/2); my $num_b = $num - $num_a; my $min_mid = $start + $num_a - 1; my $max_mid = $end - $num_b; my $mid = int(($min_mid + $max_mid)/2); my ($last_a, @part_a) = _group_cats($num_a, $start, $mid); my ($last_b, @part_b) = _group_cats($num_b, $mid + 1, $end); my $best = max($last_a, $last_b); my @best_part = (@part_a, @part_b); while ($min_mid < $max_mid) { if ($last_a <= $last_b) { if ($min_mid < $mid) { $min_mid = $mid; } else { $min_mid = $mid + 1; } } else { $max_mid = $mid; } $mid = int(($min_mid + $max_mid)/2); ($last_a, @part_a) = _group_cats($num_a, $start, $mid); ($last_b, @part_b) = _group_cats($num_b, $mid + 1, $end); if (max($last_a, $last_b) < $best) { $best = max($last_a, $last_b); @best_part = (@part_a, @part_b); } } $ans{$key} = [$best, @best_part]; } } return @{$ans{$key}}; } } sub max { my $max = shift; for (@_) { $max = $_ if $max < $_; } $max; } sub sum { my $sum = 0; $sum += $_ for @_; return $sum; }

Cheers,
Ovid

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In reply to Puzzle for the puzzle: Re: Puzzle... by Ovid
in thread Puzzle: need a more general algorithm by Ovid

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