Hi, A question. Actually 2. Given a weight matrix : 

id   0  1  2  3  4  5
 |-------------------
0|   4,-1,-2,-2, 0,-1
1|  -1, 5, 0, 2,-3, 1
2|  -2, 0, 6, 1,-3, 5
3|  -2, 2, 1, 7,-3, 0
4|   0,-3,-3,-3, 8,-3
5|  -1, 1, 5, 0,-3, 9

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I wish to extract all combinations of k-mers (k-id segments) which have a total score larger than let say 17. 
let k = 3 then
 3,4,5  -> score 7+8+9 = 24 > 17
 0,1,2  -> score 4+5+6 = 15 < 17

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and all those simmilar enough with the same criterion. wher similar means ler a k-mer be 2,3,4 -> 6+7+8 = 21 and similar to that one is 5,3,4 
 2->5 = 5
 3->3 = 7
 4->4 = 8

so 2,3,4 -> 5,3,4 = 5+7+8 = 20 > 17

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so positional similarity is only relevant. the naive approach for k = 3 would be : 
#!/usr/bin/perl

use strict;


my $MTX = [
[4,-1,-2,-2, 0,-1],
[-1,5, 0, 2,-3, 1],
[-2,0, 6, 1,-3, 5],
[-2,2, 1, 7,-3, 0],
[0,-3,-3,-3, 8,-3],
[-1,1, 5, 0,-3, 9],
];

for (my $i =0; $i<6; $i++){
   for(my $j = 0; $j< 6; $j++){
      for(my $k = 0; $k< 6; $k++){
         my $sc = ($MTX->[$i]->[$i] + $MTX->[$j]->[$j] + $MTX->[$k]->[
+$k]);
         if ($sc < 17){
            next;
         }else{
            for (my $ii =0; $ii<6; $ii++){
               for(my $jj = 0; $jj< 6; $jj++){
                  for(my $kk = 0; $kk< 6; $kk++){
                     my $score = ($MTX->[$i]->[$ii] + $MTX->[$j]->[$jj
+] + $MTX->[$k]->[$kk]);
                     if($score > 17){
                        print " $i,$j,$k -> $ii,$jj,$kk = $score\n";
                     }
                  }
               }
            }
         }
      }
   }
}

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also the rule is : if any id is changed, the score for a mismatch (2->5) cannot be greated than (2->2): 
score(2->5) < score(2->2)

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and the other qouestion is: what would be the best way to generalize this to any k, not just 3 as in my example above?
am I making any sense ?

thnx PS: code not necessary.

thank you

UPDATE:

Ok , after thinking a bit about it. i guess the answer to the secong question is straight forward. sinc the alphabet size is constant (6) each k-mer can be encoded onto a unique position from 1 to 6^k. Thus the first three for-loops can be replaced by a singe one. (the sam goes for the second three) and therefore the loop problem dissapears and iterations can easaly be generalized to any k size k-mer. Which leaves the first question still open.. UPDATE: To elaborate on my previous Update: this is what i ment : 


my $k = 3;

for (my $i =0; $i<6**$k; $i++){
   my $t = &decode($i, 6,$k);
   print "@{$t}\n";

}


sub decode{
   
   my ($int, $alpha, $k) = @_;
   
   my $r = 0;
   my $e = $int;
   my $rq = 0;
   my $rr = 0;
   my $p = 0;
   my @aa;
   my $j = $k-1;
   my $i = 0;
   for($i=0; $i < $k-1 ;$i++, $j--){
        $p = $alpha**$j;
        $rr = $e%$p;
      $rq = $e/$p;
      $aa[$i] = int($rq);
      $e = $rr;
   }
   $aa[$i] = $e;
   return \@aa;
}

=pod
## for starting with 1 instead of 0
sub decode{
   
   my ($int, $alpha, $k) = @_;
   
   my $r = 0;
   my $e = $int;
   my $rq = 0;
   my $rr = 0;
   my $p = 0;
   my @aa;
   my $j = $k-1;
   my $i = 0;
   for($i=0; $i < $k-1 ;$i++, $j--){
        $p = $alpha**$j;
        $rr = $e%$p;
      $rq = $e/$p;
        if($rr == 0){
            $rr = ($e-1)%$p;
         $rq = ($e-1)/$p;
            $r = 1;
        }
      $aa[$i] = int($rq);
      $e = $rr;
   }
   $aa[$i] = $e+$r-1;
   return \@aa;
}
=cut

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Yes ofcourse this can be optimized and done in more perlish way. but this is just a conceptual problem requiring conceptual solution :) thnx

In reply to Combinatorial problem by baxy77bax

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