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PORandomize matrix in perl, keeping row and column totals the same
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  1. PORandomize matrix in perl, keeping row and column totals the same
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    copied!<p>I have a matrix that I want to randomize a couple of thousand times, while keeping the row and column totals the same:</p> <pre><code> 1 2 3 A 0 0 1 B 1 1 0 C 1 0 0 </code></pre> <p>An example of a valid random matrix would be:</p> <pre><code> 1 2 3 A 1 0 0 B 1 1 0 C 0 0 1 </code></pre> <p>My actual matrix is a lot bigger (about 600x600 items), so I really need an approach that is computationally efficient.</p> <p>My initial (inefficient) approach consisted of shuffling arrays using the <a href="http://oreilly.com/catalog/9780596003135" rel="nofollow noreferrer">Perl Cookbook</a> <a href="http://faq.perl.org/perlfaq4.html#How_do_I_shuffle_an_" rel="nofollow noreferrer">shuffle</a></p> <p>I pasted my current code below. I've got extra code in place to start with a new shuffled list of numbers, if no solution is found in the while loop. The algorithm works fine for a small matrix, but as soon as I start scaling up it takes forever to find a random matrix that fits the requirements.</p> <p>Is there a more efficient way to accomplish what I'm searching for? Thanks a lot!</p> <pre><code>#!/usr/bin/perl -w use strict; my %matrix = ( 'A' =&gt; {'3' =&gt; 1 }, 'B' =&gt; {'1' =&gt; 1, '2' =&gt; 1 }, 'C' =&gt; {'1' =&gt; 1 } ); my @letters = (); my @numbers = (); foreach my $letter (keys %matrix){ foreach my $number (keys %{$matrix{$letter}}){ push (@letters, $letter); push (@numbers, $number); } } my %random_matrix = (); &amp;shuffle(\@numbers); foreach my $letter (@letters){ while (exists($random_matrix{$letter}{$numbers[0]})){ &amp;shuffle (\@numbers); } my $chosen_number = shift (@numbers); $random_matrix{$letter}{$chosen_number} = 1; } sub shuffle { my $array = shift; my $i = scalar(@$array); my $j; foreach my $item (@$array ) { --$i; $j = int rand ($i+1); next if $i == $j; @$array [$i,$j] = @$array[$j,$i]; } return @$array; } </code></pre>
 

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