#!/usr/bin/perl

use strict;
use warnings 'all';

sub partition ($$);

my $columns = 4;
my @sizes   = qw /10 15 25 30 10 13/;
    
    
sub partition ($$) {
    my ($b, $h) = @_;
      
    return [(0) x $h] unless $b;
    return [$b]       if $h < 2;   

    map {my $__ = $_; map {[$__ => @$_]} partition $b - $__, $h - 1} 0 .. $b;
}
    
my @r = partition @sizes, $columns; 
        
my @regex;
foreach my $r (@r) {
    my $c = 0;
    push @regex => join ":" => map {
        $c += my $__ = $_;
        join ("" => map {"-" x $_} @sizes [$c - $__ .. $c - 1]) . "-*"} @$r;
}

my $regex = join "|" => map {"(?:$_)"} @regex;
    
my $try = 1;

{   exit !print "Minimum required height: $try\n" if
          join (":" => map {"-" x $try} 1 .. $columns) =~ /$regex/;
    $try ++;
    redo;
}