Latin Squares in reduced form/Randomizing using Jacobson and Matthews’ Technique: Difference between revisions

Content added Content deleted
(added Raku programming solution)
(→‎{{header|Raku}}: fix oversight in squares generation)
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{{trans|Go}}
<lang perl6># 20210729 Raku programming solution
<lang perl6># 20210729 Raku programming solution

#!/usr/bin/env raku


sub makeCube(\from, Int \n) {
sub makeCube(\from, Int \n) {
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}
}


sub shuffleCube(@c is copy) {
sub shuffleCube(@c) {
my ($rx, $ry, $rz); my \n = +@c; my Bool \proper = $ = True;
my ($rx, $ry, $rz); my \n = +@c; my Bool \proper = $ = True;


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proper = False
proper = False
}
}
return @c
}
}


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@c = makeCube(@in, 4);
@c = makeCube(@in, 4);
for ^10_000 {
for ^10_000 {
@c = shuffleCube @c;
shuffleCube @c ;
my @m = toMatrix @c;
%freq{@c.&toMatrix.&toReduced».List.flat.Str}++
my @rm = toReduced @m;
%freq{@rm».List.flat.Str}++
}
}
for %freq.kv -> $k, $v {
for %freq.kv -> $k, $v {
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%freq = ();
%freq = ();
@c = makeCube(@in, 5);
@c = makeCube(@in, 5);
for ^10_000 {
for ^10_000 {
@c = shuffleCube @c;
shuffleCube @c ;
my @m = toMatrix @c;
%freq{@c.&toMatrix.&toReduced».List.flat.Str}++
my @rm = toReduced @m;
%freq{@rm».List.flat.Str}++
}
}
for %freq.values.kv -> $i, $j { printf "%2d(%3d)%s", $i+1, $j, ' ' }
for %freq.values.kv -> $i, $j { printf "%2d(%3d)%s", $i+1, $j, ' ' }
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say "\n\nPart 3: 750 latin squares of order 42, showing the last one:\n";
say "\n\nPart 3: 750 latin squares of order 42, showing the last one:\n";
@c = makeCube([], 42); # (1..42).pick(*)
@c = makeCube([], 42); # (1..42).pick(*)
# printAs1based ( toMatrix ( shuffleCube(@c) xx * )[749] )».List.flat ;
( for ^750 { shuffleCube @c } ) and printAs1based @c.&toMatrix».List.flat ;
my @m42;
for ^750 { $_==749 ?? (@m42 = toMatrix(shuffleCube @c)) !! shuffleCube(@c) }
printAs1based @m42».List.flat ;


say "\nPart 4: 1000 latin squares of order 256:\n";
say "\nPart 4: 100 latin squares of order 256:\n";
⚫
@c = makeCube([], 256);
my $snapshot = now;
my $snapshot = now;
⚫
@c = makeCube([], 256);
race for ^1000 { shuffleCube @c } # ; say "$_\t", now - $snapshot }
for ^100 { shuffleCube @c } # without hyper, will do only 100 cycles
say "Generated in { now - $snapshot } seconds."
say "Generated in { now - $snapshot } seconds."
</lang>
</lang>
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<pre>
<pre>
Part 1: 10,000 latin Squares of order 4 in reduced form:
Part 1: 10,000 latin Squares of order 4 in reduced form:

⚫
1 2 3 4
⚫
2 1 4 3
⚫
3 4 1 2
⚫
4 3 2 1

⚫
Occurs 2442 times.


1 2 3 4
1 2 3 4
Line 1,459: Line 1,460:
4 3 2 1
4 3 2 1


Occurs 2564 times.
Occurs 2705 times.


1 2 3 4
1 2 3 4
2 1 4 3
2 3 4 1
3 4 1 2
3 4 1 2
4 3 2 1
4 1 2 3


Occurs 2512 times.
Occurs 2548 times.


1 2 3 4
1 2 3 4
Line 1,473: Line 1,474:
4 3 1 2
4 3 1 2


Occurs 2406 times.
Occurs 2305 times.

⚫
1 2 3 4
⚫
2 3 4 1
⚫
3 4 1 2
⚫
4 1 2 3

⚫
Occurs 2518 times.


Part 2: 10,000 latin Squares of order 5 in reduced form:
Part 2: 10,000 latin Squares of order 5 in reduced form:


1(172) 2(172) 3(179) 4(169) 5(157) 6(189) 7(182) 8(165) 9(170) 10(147) 11(149) 12(198) 13(171) 14(212) 15(167) 16(205) 17(170) 18(199) 19(189) 20(179) 21(196) 22(184) 23(216) 24(218) 25(149) 26(191) 27(163) 28(240) 29(164) 30(182) 31(179) 32(192) 33(173) 34(154) 35(169) 36(145) 37(180) 38(173) 39(168) 40(182) 41(150) 42(150) 43(187) 44(212) 45(190) 46(180) 47(167) 48(163) 49(222) 50(170) 51(181) 52(186) 53(162) 54(171) 55(175) 56(175)
1(210) 2(191) 3(186) 4(158) 5(219) 6(164) 7(147) 8(160) 9(196) 10(188) 11(193) 12(168) 13(195) 14(173) 15(151) 16(184) 17(211) 18(171) 19(185) 20(155) 21(157) 22(191) 23(195) 24(177) 25(157) 26(191) 27(165) 28(178) 29(191) 30(180) 31(193) 32(176) 33(196) 34(178) 35(156) 36(168) 37(155) 38(152) 39(155) 40(223) 41(159) 42(165) 43(210) 44(175) 45(195) 46(188) 47(178) 48(154) 49(172) 50(176) 51(178) 52(164) 53(175) 54(196) 55(187) 56(189)


Part 3: 750 latin squares of order 42, showing the last one:
Part 3: 750 latin squares of order 42, showing the last one:


3 9 29 34 30 27 19 22 41 36 13 28 42 21 32 10 8 35 16 31 24 15 33 5 37 6 39 26 1 11 7 4 25 38 17 20 2 14 23 40 12 18
26 27 4 41 31 10 28 13 3 29 21 42 14 39 19 8 5 7 6 40 17 37 35 33 1 38 22 34 18 11 12 2 32 36 9 24 25 23 16 15 30 20
13 21 32 12 2 14 42 36 8 19 15 30 23 37 34 24 9 4 6 38 40 1 7 10 3 26 17 20 22 16 18 33 35 25 31 28 39 41 29 5 27 11
16 40 6 11 22 14 41 42 20 7 24 8 29 27 28 4 26 19 21 39 37 9 2 32 36 15 12 13 38 5 31 33 34 3 17 1 23 35 30 18 10 25
41 37 12 26 23 32 24 5 31 9 14 1 38 36 28 11 39 20 29 42 13 27 35 8 21 22 2 30 34 17 15 25 6 10 18 33 4 40 7 3 19 16
31 15 11 3 5 22 13 10 14 24 41 18 6 16 17 29 36 37 12 28 23 39 34 8 27 40 4 35 7 19 32 26 21 1 2 33 20 9 38 30 25 42
15 4 37 42 7 22 27 35 30 23 29 16 19 8 40 34 20 3 5 39 31 41 26 28 36 10 25 14 17 38 9 13 11 33 6 2 24 18 32 21 1 12
13 37 31 38 42 9 11 2 10 36 22 34 18 23 12 39 25 20 19 26 8 41 16 6 21 32 5 4 33 17 40 24 30 29 27 3 28 14 1 7 35 15
35 40 14 11 32 42 3 25 26 24 39 31 1 12 29 9 22 18 17 16 38 10 36 33 2 37 30 34 4 28 8 19 21 5 13 23 15 27 6 7 41 20
41 7 17 28 24 12 29 8 31 22 1 3 11 42 23 26 39 13 25 19 36 18 33 37 6 5 20 15 2 16 14 4 27 35 38 10 30 32 9 21 34 40
6 33 34 20 19 2 22 10 15 14 26 38 21 41 42 1 17 32 4 8 11 28 29 9 40 16 23 18 31 5 27 35 37 13 25 24 12 7 3 30 36 39
5 19 12 32 20 30 6 33 17 16 27 13 8 9 2 37 21 18 39 4 7 40 1 15 3 35 11 24 10 31 36 23 29 41 22 25 26 28 34 14 42 38
40 16 36 2 3 20 17 18 9 1 6 7 34 31 4 39 10 12 22 24 25 35 8 30 26 14 37 33 42 15 11 21 41 23 38 32 29 28 27 19 5 13
11 14 20 5 3 32 19 27 42 18 12 41 34 6 24 21 38 26 10 35 33 28 9 22 23 39 17 40 31 15 30 37 16 2 36 4 8 1 13 25 29 7
4 6 17 21 29 15 38 24 33 42 1 9 22 26 7 35 41 10 11 14 37 40 27 39 30 31 8 25 23 36 13 3 32 28 16 12 19 5 20 2 18 34
20 6 22 16 34 26 33 23 2 11 29 7 4 13 21 42 9 24 14 41 15 31 5 3 25 18 19 30 1 10 37 36 17 12 39 27 40 38 28 32 8 35
19 27 16 6 11 3 39 34 36 38 10 5 17 24 21 42 14 29 41 22 9 2 37 26 18 30 31 23 20 4 32 12 28 15 33 7 13 1 25 35 8 40
4 25 32 8 28 17 40 19 22 15 23 2 35 5 34 16 18 39 38 24 30 13 41 1 20 3 36 33 42 12 26 29 10 31 6 21 14 37 7 9 11 27
10 26 11 9 25 31 23 13 35 2 40 22 6 1 39 5 36 42 37 34 20 18 30 14 28 12 21 38 33 32 16 41 3 27 24 17 7 29 15 8 4 19
21 2 35 39 26 28 36 16 7 37 19 32 33 1 38 27 4 8 23 6 5 34 40 30 29 42 14 10 9 22 11 12 25 15 13 31 17 18 41 24 20 3
33 32 5 40 38 28 34 12 10 6 18 13 2 9 11 3 35 24 15 25 19 8 23 17 27 20 14 41 7 26 29 30 1 39 37 36 31 16 42 4 21 22
30 28 3 12 6 8 31 32 40 42 25 38 9 33 16 14 13 27 26 17 4 19 20 24 15 36 37 18 11 23 10 22 1 39 21 5 34 41 2 35 7 29
20 17 7 15 28 24 30 26 12 39 4 41 8 3 35 16 37 13 19 23 36 29 11 2 31 18 32 27 14 6 33 34 5 42 1 10 25 22 40 38 9 21
8 34 26 6 16 33 15 28 41 38 40 24 30 21 22 17 20 35 32 23 42 25 11 5 12 1 31 2 13 3 39 27 14 9 18 7 19 29 36 4 37 10
2 34 18 35 33 19 5 20 6 26 24 10 37 38 8 28 29 41 3 7 1 17 31 42 14 25 9 39 36 22 23 40 30 32 12 4 16 11 21 13 15 27
1 22 2 7 39 23 14 18 11 30 15 17 26 10 6 28 16 12 24 31 35 36 37 21 40 29 13 8 3 41 34 38 4 32 25 42 5 27 20 19 33 9
24 10 31 13 1 35 7 41 34 8 17 29 16 39 23 19 3 26 9 21 14 30 22 4 38 40 11 6 12 42 28 15 33 2 32 27 20 25 36 18 37 5
25 32 1 9 35 6 42 34 37 10 13 20 5 19 30 41 17 36 7 15 40 38 26 31 2 23 18 28 24 33 21 11 22 4 14 39 27 8 3 29 16 12
26 18 2 19 21 23 35 16 1 7 3 25 4 17 33 29 12 39 20 41 22 11 42 13 6 28 34 32 10 31 24 27 38 36 14 37 5 8 30 9 40 15
17 12 18 30 11 4 10 5 28 8 33 31 19 22 36 13 6 9 34 42 29 1 27 39 38 21 25 23 26 24 7 15 2 16 41 14 32 40 35 20 3 37
12 7 4 37 35 34 18 2 13 20 32 27 5 29 22 40 31 19 21 11 10 26 6 15 16 33 41 28 25 24 14 42 23 1 30 8 17 38 39 36 3 9
27 36 39 37 18 13 34 14 19 5 32 26 38 12 3 23 1 30 17 11 6 35 21 16 24 41 7 9 28 20 2 31 40 10 4 29 22 25 33 42 15 8
23 15 28 4 20 7 16 9 11 32 19 17 26 6 12 2 24 1 36 40 30 13 38 25 5 27 33 21 3 39 34 18 14 22 29 42 8 10 37 31 35 41
36 24 28 2 32 11 37 12 29 33 16 9 40 3 10 34 7 15 4 27 22 20 25 18 13 26 42 39 17 14 5 8 41 21 23 30 35 31 6 38 19 1
5 36 6 28 18 41 33 1 25 16 38 20 7 10 24 37 42 11 23 26 21 12 2 32 9 4 27 13 30 19 40 39 34 8 22 3 14 35 17 15 29 31
32 30 36 34 14 7 22 9 35 23 6 21 37 2 5 15 31 33 3 16 25 17 4 27 19 13 24 29 40 39 28 1 20 38 10 11 42 12 8 41 26 18
36 11 15 25 40 5 2 7 39 34 41 24 35 30 10 31 27 21 42 17 26 38 4 1 19 32 13 37 8 20 12 9 22 16 23 18 3 6 33 29 28 14
2 41 8 20 29 35 25 4 6 1 17 19 3 18 42 33 12 34 5 32 11 15 30 38 39 14 23 31 21 37 22 9 26 27 16 28 36 7 40 10 13 24
28 3 1 8 17 12 9 42 38 4 22 32 40 16 30 27 5 7 18 33 41 37 39 23 20 29 19 31 15 21 6 2 10 24 11 34 36 13 35 14 26 25
39 1 27 14 2 20 9 26 4 25 18 33 41 28 29 32 34 38 13 7 21 8 10 35 31 17 16 19 23 30 15 5 6 40 37 12 3 36 42 22 24 11
18 13 42 30 12 10 29 19 21 28 31 36 3 4 17 20 40 9 24 37 27 6 34 11 39 8 7 15 35 23 22 32 2 14 5 25 38 26 41 1 16 33
3 13 9 24 15 21 8 41 33 32 20 1 25 40 27 22 29 31 18 36 10 11 17 2 37 28 39 42 14 4 16 35 7 30 34 26 38 6 12 23 5 19
37 39 26 5 4 29 41 14 16 31 27 15 20 13 3 38 6 25 2 18 23 24 32 12 11 35 36 1 9 40 21 7 17 34 28 19 10 30 8 33 22 42
6 33 37 26 30 15 20 35 21 39 14 27 7 4 32 36 2 5 9 18 34 23 22 17 42 24 28 11 8 1 38 3 12 25 31 41 29 10 19 13 40 16
17 24 38 32 14 39 15 8 22 25 42 11 30 23 13 12 4 36 27 3 5 33 19 7 41 1 16 29 28 10 35 6 20 31 21 40 9 2 18 37 34 26
33 16 21 29 40 38 24 7 30 27 11 25 2 32 37 5 35 4 22 9 31 42 18 36 10 34 1 14 12 13 8 41 23 17 3 19 15 20 39 6 28 26
16 25 9 29 39 37 8 27 24 18 20 40 33 15 31 14 21 34 1 6 2 23 5 36 4 13 35 22 32 12 41 38 7 3 19 26 30 17 11 42 10 28
14 17 24 31 19 27 26 6 38 3 9 36 12 41 15 18 37 22 40 33 16 32 29 42 11 4 10 7 34 25 23 28 35 13 20 8 2 5 21 1 39 30
7 5 22 41 31 36 11 29 28 15 8 35 32 18 19 30 26 2 38 1 3 14 20 27 25 21 42 4 40 13 17 24 9 37 39 16 34 23 12 6 33 10
18 31 29 22 37 25 3 24 26 28 8 4 20 36 9 30 33 42 27 38 1 7 13 10 32 11 2 16 19 21 35 14 5 23 40 15 41 39 17 12 6 34
22 23 13 17 24 9 10 11 29 33 16 12 36 32 37 6 1 40 31 15 18 25 21 3 34 2 28 35 39 41 5 14 27 19 4 30 26 42 38 20 7 8
34 9 15 19 23 41 5 39 24 31 26 30 13 25 11 10 40 1 16 22 2 33 28 12 14 37 38 32 29 8 3 7 42 20 35 6 18 4 27 17 21 36
29 1 19 27 5 21 26 23 37 30 7 18 14 25 6 17 33 16 12 32 15 22 13 40 24 39 10 11 38 9 3 8 31 4 20 35 41 36 34 28 42 2
24 42 5 23 10 37 35 17 18 13 7 39 21 29 8 1 32 40 20 14 12 4 15 26 22 25 9 6 41 36 27 34 3 19 28 16 11 30 31 2 38 33
9 2 27 39 10 1 36 17 40 22 12 33 29 11 25 13 7 28 34 30 32 3 14 20 8 23 15 5 19 18 38 31 4 21 42 41 37 24 26 16 6 35
7 23 41 10 17 24 21 22 36 14 30 16 42 34 18 19 11 3 1 37 39 12 38 40 8 33 35 25 4 32 20 6 9 5 15 13 31 26 29 28 27 2
27 8 40 7 13 33 25 6 4 37 9 2 39 20 16 26 34 15 10 28 12 21 41 38 29 5 24 42 11 35 36 17 18 30 3 14 22 19 1 32 31 23
23 18 25 42 27 5 1 38 34 12 31 15 32 20 40 6 19 10 28 30 13 3 8 7 4 2 29 26 36 9 17 21 24 37 33 35 39 22 11 16 14 41
25 35 41 31 9 11 21 40 17 5 2 6 12 34 14 36 23 30 26 29 8 20 18 19 10 42 4 16 37 33 1 22 13 7 27 39 32 15 28 24 38 3
28 11 40 35 36 42 16 25 13 19 4 5 39 26 20 12 15 41 37 34 38 14 31 9 17 7 30 27 6 2 29 10 8 24 1 18 21 33 32 3 22 23
30 38 35 10 6 26 12 37 20 13 28 14 25 27 9 15 2 31 40 5 33 39 3 16 22 7 1 19 18 8 42 23 29 41 34 11 21 4 24 17 32 36
40 38 23 1 21 19 32 29 12 4 2 35 31 11 26 7 28 16 41 10 3 22 24 20 33 27 8 37 15 42 25 39 13 14 30 36 6 34 18 5 9 17
42 41 20 14 37 18 13 21 27 40 30 23 11 2 15 25 38 22 28 12 29 7 1 31 17 19 26 10 16 3 4 36 8 9 35 6 33 32 5 34 39 24
19 26 34 27 8 29 7 20 16 41 36 14 10 15 4 25 3 6 33 5 9 21 23 13 35 30 32 22 37 38 18 17 31 11 12 40 1 42 24 39 2 28
1 22 8 38 42 6 28 30 7 17 23 3 9 14 2 4 13 5 33 10 39 36 24 41 35 34 40 12 29 27 37 11 16 26 15 21 18 31 19 25 20 32
35 29 10 33 13 31 39 1 9 21 38 11 36 30 14 40 42 17 2 20 41 27 6 19 18 22 3 12 5 26 24 16 28 7 8 23 37 15 25 34 4 32
21 19 3 24 34 4 32 28 5 29 25 26 27 7 1 18 15 23 13 36 42 16 40 22 33 17 20 2 41 14 30 37 39 6 8 31 35 9 10 12 11 38
10 35 33 21 4 3 2 30 25 40 39 12 1 37 31 20 24 28 42 8 14 26 32 23 9 16 6 38 22 34 41 19 11 18 29 17 7 13 15 27 36 5
39 29 21 23 36 38 4 33 32 3 5 34 41 40 20 8 16 27 7 13 28 19 25 35 15 24 18 17 6 30 31 1 26 11 2 9 42 12 22 10 14 37
15 5 13 25 9 2 17 40 27 35 42 37 16 8 39 31 41 23 36 1 32 10 7 28 30 19 33 21 20 29 4 18 38 6 11 34 24 3 22 26 12 14
31 14 39 16 15 40 37 32 42 11 36 8 24 22 41 7 18 6 35 19 34 5 17 21 23 9 38 3 26 29 2 28 12 20 10 13 1 33 4 27 25 30
22 39 16 4 41 1 38 11 5 26 10 23 15 14 35 3 8 29 30 13 28 6 12 25 7 20 40 17 32 27 9 42 18 34 19 2 33 24 37 36 31 21
34 30 23 18 8 17 6 4 2 27 35 21 15 33 38 32 11 14 39 20 7 9 16 37 42 36 12 40 24 25 26 10 19 29 41 5 28 3 31 22 13 1
9 3 38 15 25 34 12 21 1 20 5 40 17 24 33 2 27 14 8 29 18 30 19 41 16 10 26 36 35 28 6 32 37 42 7 22 13 11 4 31 23 39
11 20 24 1 27 8 40 31 14 21 34 19 10 35 26 22 30 33 32 9 4 42 28 18 13 38 3 7 2 37 25 5 15 12 36 29 6 39 16 41 23 17
37 10 14 40 12 36 18 3 39 6 35 29 24 38 41 9 23 25 31 21 19 2 42 34 26 8 27 1 30 7 33 13 15 28 32 20 4 16 5 11 17 22
32 42 25 33 26 16 31 38 3 10 11 4 13 28 18 21 19 8 30 35 6 34 15 29 12 41 22 36 5 2 39 20 24 40 9 1 27 37 14 23 17 7
29 20 7 13 38 18 30 37 23 17 34 22 28 31 25 11 14 2 15 12 24 16 36 4 5 9 21 3 27 35 1 40 39 8 42 32 10 19 26 33 41 6
8 28 10 3 16 13 14 39 18 41 21 37 31 19 36 33 32 38 25 2 17 4 12 6 7 15 5 24 27 1 20 26 42 35 40 22 23 34 9 11 30 29
12 21 42 18 7 39 27 36 8 34 37 28 23 17 13 24 30 32 35 3 20 29 14 11 41 31 15 5 16 6 19 25 33 22 26 38 9 2 10 40 1 4
14 12 30 36 22 25 1 15 23 35 33 39 18 42 5 41 28 37 8 27 16 31 10 24 32 3 6 9 21 34 19 29 40 17 7 38 11 20 13 26 2 4
42 4 30 36 1 16 23 15 32 9 3 10 27 35 7 38 22 21 11 2 26 24 39 29 28 6 34 41 25 40 13 20 19 33 5 37 12 17 14 8 18 31
38 31 33 22 41 30 20 3 19 12 37 42 28 5 27 23 25 17 14 4 35 32 9 34 1 11 29 8 13 7 10 16 36 18 26 15 40 21 2 39 24 6
38 8 19 17 33 40 4 31 15 2 28 6 22 7 1 35 10 11 29 25 27 5 3 14 34 12 41 20 39 18 42 30 36 26 24 9 16 21 23 37 32 13


Part 4: 1000 latin squares of order 256:
Part 4: 100 latin squares of order 256:


Generated in 359.960275435 seconds.
Generated in 76.816295878 seconds.
</pre>
</pre>


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