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### Re: Re: Puzzle: need a more general algorithm

by Ovid (Cardinal)
 on Jul 09, 2002 at 02:56 UTC ( #180388=note: print w/replies, xml ) Need Help??

in reply to Re: Puzzle: need a more general algorithm
in thread Puzzle: need a more general algorithm

It appears that I have confused a few people here. What I need "minimized" is the aggregate height per column as summed from @height data.

Given the heights of qw/ 10 10 15 20 10 10 /, I could conceivably construct a table with no column having greater than 20 items in it:

```  10  15  20  10
10          10

The following solution, would fail because one of the columns has 25 items:

```  10  10  20  10
15      10

Part of the problem, I suspect, is that I had a bug in my original code because I accidentally posted the wrong version. The @distribution array needs to be reset every iteration. The following is correct:

```#!/usr/bin/perl -w
use strict;
use Data::Dumper;

my @height      = qw/ 10 15 25 30 10 13 /;
my @columns     = (\$height[0],0,0,\$height[-1]);
my \$curr_height = 0;

# set this unreasonably high to ensure that subsequent
# heights will be lower
\$curr_height    += \$_ foreach @height;
my @distribution;

for my \$a (0..1) {
\$columns[\$a] += \$height[1];
for my \$b (0..2) {
\$columns[\$b] += \$height[2];
for my \$c (1..3) {
\$columns[\$c] += \$height[3];
for my \$d (2..3) {
\$columns[\$d] += \$height[4];

my \$this_height = ( sort @columns )[-1];
my \$valid_dist;
foreach ( @columns ) {
\$valid_dist = \$_;
last if ! \$valid_dist;
}
if ( \$valid_dist and \$this_height < \$curr_height ) {
\$curr_height = \$this_height;
@distribution = ([1],[],[],[6]);
push @{\$distribution[\$a]}, 2;
push @{\$distribution[\$b]}, 3;
push @{\$distribution[\$c]}, 4;
push @{\$distribution[\$d]}, 5;
}
\$columns[\$d] -= \$height[4];
}
\$columns[\$c] -= \$height[3];
}
\$columns[\$b] -= \$height[2];
}
\$columns[\$a] -= \$height[1];
}
print Dumper \@distribution;

I hope that's clear, now :)

I also have to add that there's a heck of a lot more discussion on this than I thought there would be.

Cheers,
Ovid

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