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```#!/usr/bin/perl

use List::Util qw(sum max);

use Memoize;
memoize('make_cols');

my @height = qw/ 10 15 25 30 10 13 /;
my \$cols = 4;

my (\$maxheight, @cols) = make_cols(\$cols, @height);

print "max height is \$maxheight\n";
print join(" ", map "[@\$_]", @cols), "\n";

sub make_cols {
my (\$cols, @height) = @_;
my \$warnmsg = "computing for \$cols cols with @height =>";

## non-recursive case:
if (\$cols <= 1) {
warn "\$warnmsg returning trivial [@height]\n";
return sum(@height), [@height] if \$cols <= 1;
}

## oops, work to do.  Search for a pivot.
## first, get a trial solution:

my @leftcol = shift @height;
my (\$rightmax, @rightcols) = make_cols(\$cols-1, @height);
my @best = (max(sum(@leftcol), \$rightmax), [@leftcol], @rightcols);

## now iterate until we are producing worse solutions:
while (@height > \$cols - 1) {
push @leftcol, shift @height;
my (\$rightmax, @rightcols) = make_cols(\$cols-1, @height);
my @try = (max(sum(@leftcol), \$rightmax), [@leftcol], @rightcols);
next if \$try[0] >= \$best[0]; # that's worse
@best = @try;
}

warn "\$warnmsg returning", map(" [@\$_]", @best[1..\$#best]), "\n";
return @best;
}

In reply to Balance columns by merlyn

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