Re: Code to solve the "matrix formation" puzzle

in reply to Code to solve the "matrix formation" puzzle

Hi,Rhose
Wonderful it works very well. Is it something easy to dertermine the order of your algorithm ?. That will give idea of how long it can take to run. I obsereved that for higher dimension it takes much longer.

Thanks,
artist

Comment on Re: Code to solve the "matrix formation" puzzle

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Re: Re: Code to solve the "matrix formation" puzzle by tall_man (Parson) on Jun 20, 2003 at 19:04 UTC
It looks like exponential-order to me. I added some code to sum up the number of permutations of the sets: `$bigtotal += Math::NumberCruncher::Permutation(scalar(@Num),MATRIX_D +IM); @Sol=CheckSolution(\@Num);` [download] Here are the results: `Order 4: Maximum divisor is 416, solution is 2496-9152-1664-2080 Checked 19301184 cases 1445.940u 5.500s 27:10.91 88.9% 0+0k 0+0io 364pf+0w Order 3: Maximum divisor is 44, solution is 132-792-660 Checked 140526 cases 10.690u 0.050s 0:14.69 73.1% 0+0k 0+0io 364pf+0w Order 2:Maximum divisor is 7, solution is 21-84 Checked 820 cases 0.290u 0.010s 0:00.33 90.9% 0+0k 0+0io 364pf+0w` [download] At that rate, order 5 will test about 1 billion cases and take over a day to run. But I think it might be feasible if bad solution sets are eliminated early. The big problem is the permutations, which are factorial order. I would suggest picking the corner two items first. They have to have the same top digit. Then that determines the possible top digits of the rest of the rows.	[reply] [d/l] [select]

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Re: Re: Code to solve the "matrix formation" puzzle
by tall_man (Parson) on Jun 20, 2003 at 19:04 UTC

  $bigtotal += Math::NumberCruncher::Permutation(scalar(@Num),MATRIX_D
+IM);
  @Sol=CheckSolution(\@Num);
[download]

Order 4:
Maximum divisor is 416, solution is 2496-9152-1664-2080
Checked 19301184 cases
1445.940u 5.500s 27:10.91 88.9% 0+0k 0+0io 364pf+0w

Order 3:
Maximum divisor is 44, solution is 132-792-660
Checked 140526 cases
10.690u 0.050s 0:14.69 73.1%    0+0k 0+0io 364pf+0w

Order 2:Maximum divisor is 7, solution is 21-84
Checked 820 cases
0.290u 0.010s 0:00.33 90.9%     0+0k 0+0io 364pf+0w
[download]

The big problem is the permutations, which are factorial order. I would suggest picking the corner two items first. They have to have the same top digit. Then that determines the possible top digits of the rest of the rows.

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