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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; }

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