#!/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;
}
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