Beefy Boxes and Bandwidth Generously Provided by pair Networks
laziness, impatience, and hubris

comment on

( #3333=superdoc: print w/replies, xml ) Need Help??
And here is an optimized version. Add in the question of what optimizations are present, and why they work. Some are more obvious than others. The thoughtful hacker might also wonder at why the $max_mid, $min_mid logic switched.

Oh right. And this adds the restriction that the heights should be integers. I think that is a reasonable rule for the speedup...

use strict; { use integer; my @sizes; my %ans; my @align; sub group_cats { (my $num, @sizes) = @_; %ans = (); my $a = 1; for my $i (1..$#sizes) { if ($a + $a < $i) { $a += $a; } $align[$i] = $a; } $align[0] = 0; my ($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 == $num) { my @part = @sizes[$start..$end]; my $sum = 0; $sum += $_ for @part; $ans{$key} = [$sum, \@part]; } else { my $num_a = $align[$num]; my $num_b = $num - $num_a; my $min_mid = $start + $num_a - 1; my $max_mid = $end - $num_b; my $mid = $min_mid + $align[$max_mid - $min_mid]; my ($last_a, @part_a) = _group_cats($num_a, $start, $mid); my ($last_b, @part_b) = _group_cats($num_b, $mid + 1, $end); my $best = $last_a < $last_b ? $last_b : $last_a; my @best_part = (@part_a, @part_b); while ($min_mid < $max_mid) { if ($last_b <= $last_a) { if ($max_mid > $mid) { $max_mid = $mid; } else { $max_mid--; } } else { $min_mid = $mid; } $mid = $min_mid + $align[$max_mid - $min_mid]; ($last_a, @part_a) = _group_cats($num_a, $start, $mid); ($last_b, @part_b) = _group_cats($num_b, $mid + 1, $end); my $max = $last_a < $last_b ? $last_b : $last_a; if ($max < $best) { $best = $max; @best_part = (@part_a, @part_b); } } $ans{$key} = [$best, @best_part]; } } return @{$ans{$key}}; } }
BTW the original question had an straightforward recursive solution that scaled exponentially. I found that too easy, hence the faster solution.

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

Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post; it's "PerlMonks-approved HTML":

  • Are you posting in the right place? Check out Where do I post X? to know for sure.
  • Posts may use any of the Perl Monks Approved HTML tags. Currently these include the following:
    <code> <a> <b> <big> <blockquote> <br /> <dd> <dl> <dt> <em> <font> <h1> <h2> <h3> <h4> <h5> <h6> <hr /> <i> <li> <nbsp> <ol> <p> <small> <strike> <strong> <sub> <sup> <table> <td> <th> <tr> <tt> <u> <ul>
  • Snippets of code should be wrapped in <code> tags not <pre> tags. In fact, <pre> tags should generally be avoided. If they must be used, extreme care should be taken to ensure that their contents do not have long lines (<70 chars), in order to prevent horizontal scrolling (and possible janitor intervention).
  • Want more info? How to link or How to display code and escape characters are good places to start.
Log In?

What's my password?
Create A New User
Domain Nodelet?
and the web crawler heard nothing...

How do I use this? | Other CB clients
Other Users?
Others rifling through the Monastery: (1)
As of 2023-03-22 19:24 GMT
Find Nodes?
    Voting Booth?
    Which type of climate do you prefer to live in?

    Results (60 votes). Check out past polls.