Created
March 24, 2012 23:31
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Generating hex puzzle models for the DLX solver
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| sub MAIN(Int $smallwidth, Int $height, Str :$exclude = '') { | |
| $exclude ~~ /^ [[<[a..z]><[1..9]>] ** ',']? $/ | |
| or die "Can't understand exclude format, should be e.g. 'a1,b2,d4'"; | |
| my @excluded = $exclude.comb(/\w*/); | |
| sub even { $^n %% 2 } | |
| # The algebra in the below subs is of the type "it works, OK?" | |
| sub falling_diag($row, $column) { | |
| my $groove | |
| = chr(ord('a') + $smallwidth - $column - 1 + ($row+1) div 2); | |
| my $digit = $row + 1; | |
| if ($row+1) div 2 > $column { | |
| $digit -= (($row+1) div 2 - $column) * 2 - 1; | |
| } | |
| return $groove ~ $digit; | |
| } | |
| sub horizontal($row, $column) { | |
| my $groove_offset = ord('a') + $smallwidth + $height div 2; | |
| my $groove = chr($groove_offset + $row); | |
| my $digit = $column + 1; | |
| return $groove ~ $digit; | |
| } | |
| sub rising_diag($row, $column) { | |
| my $groove_offset = ord('a') + $smallwidth + $height div 2 + $height; | |
| my $groove = chr($groove_offset + $column + $row div 2); | |
| my $digit = $height - $row; | |
| if $groove lt chr($groove_offset + ($height-1) div 2) { | |
| if even $height { | |
| $digit -= (($height-$row+1) div 2 - $column - 1) * 2; | |
| } | |
| else { | |
| $digit -= (($height-$row) div 2 - $column) * 2 - 1; | |
| } | |
| } | |
| return $groove ~ $digit; | |
| } | |
| my $bigwidth = $smallwidth + 1; | |
| for &falling_diag, &horizontal, &rising_diag -> &namer { | |
| for ^$height -> $row { | |
| my $width = even($row) ?? $smallwidth !! $bigwidth; | |
| my @places = gather for ^$width -> $column { | |
| my $name = &namer($row, $column); | |
| if $name eq any @excluded { | |
| $name = "XX"; | |
| } | |
| take $name; | |
| } | |
| my $prefix = even($row) ?? "# " !! "# "; | |
| say $prefix, @places.join(" "); | |
| } | |
| say ""; | |
| } | |
| for ^$height -> $row { | |
| for ^(even($row) ?? $smallwidth !! $bigwidth) -> $column { | |
| my @coordinates | |
| = (.($row, $column) | |
| for &falling_diag, &horizontal, &rising_diag); | |
| next if all(@coordinates) eq any(@excluded); | |
| my $coordinates = @coordinates.join(","); | |
| print $coordinates, "; "; | |
| } | |
| } | |
| say ""; | |
| my %coords; | |
| for &falling_diag, &horizontal, &rising_diag -> &namer { | |
| for ^$height -> $row { | |
| for ^(even($row) ?? $smallwidth !! $bigwidth) -> $column { | |
| my $coord = &namer($row, $column); | |
| %coords{$coord} = 1; | |
| } | |
| } | |
| } | |
| for ^$height -> $row { | |
| for ^(even($row) ?? $smallwidth !! $bigwidth) -> $column { | |
| next if | |
| all(&falling_diag, &horizontal, &rising_diag)($row, $column) | |
| eq any @excluded; | |
| print &horizontal($row, $column), "; "; | |
| } | |
| } | |
| my $groove = 'a'; | |
| repeat while %coords.exists( ++$groove ~ '1') { | |
| my $groove_length | |
| = (1..*).first({ !%coords.exists( $groove ~ $_ ) }) - 1; | |
| for 1 .. $groove_length-1 { | |
| next if any("$groove$_", $groove ~ ($_+1)) eq any(@excluded); | |
| print $groove ~ $_ ~ ($_+1), "; "; | |
| } | |
| } | |
| $groove = 'a'; | |
| repeat while %coords.exists( ++$groove ~ '1') { | |
| my $groove_length | |
| = (1..*).first({ !%coords.exists( $groove ~ $_ ) }) - 1; | |
| for 1 .. $groove_length-2 { | |
| next if any("$groove$_", $groove ~ ($_+1), $groove ~ ($_+2)) | |
| eq any(@excluded); | |
| print $groove ~ $_ ~ ($_+1) ~ ($_+2), "; "; | |
| } | |
| } | |
| say ""; | |
| } |
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| $ perl6 generate-coords-pieces 5 7 | |
| # e1 d1 c1 b1 a1 | |
| # f1 e2 d2 c2 b2 a2 | |
| # f2 e3 d3 c3 b3 | |
| # g1 f3 e4 d4 c4 b4 | |
| # g2 f4 e5 d5 c5 | |
| # h1 g3 f5 e6 d6 c6 | |
| # h2 g4 f6 e7 d7 | |
| # i1 i2 i3 i4 i5 | |
| # j1 j2 j3 j4 j5 j6 | |
| # k1 k2 k3 k4 k5 | |
| # l1 l2 l3 l4 l5 l6 | |
| # m1 m2 m3 m4 m5 | |
| # n1 n2 n3 n4 n5 n6 | |
| # o1 o2 o3 o4 o5 | |
| # p2 q4 r6 s7 t7 | |
| # p1 q3 r5 s6 t6 u6 | |
| # q2 r4 s5 t5 u5 | |
| # q1 r3 s4 t4 u4 v4 | |
| # r2 s3 t3 u3 v3 | |
| # r1 s2 t2 u2 v2 w2 | |
| # s1 t1 u1 v1 w1 | |
| e1,i1,p2; d1,i2,q4; c1,i3,r6; b1,i4,s7; a1,i5,t7; f1,j1,p1; e2,j2,q3; d2,j3,r5; | |
| c2,j4,s6; b2,j5,t6; a2,j6,u6; f2,k1,q2; e3,k2,r4; d3,k3,s5; c3,k4,t5; b3,k5,u5; | |
| g1,l1,q1; f3,l2,r3; e4,l3,s4; d4,l4,t4; c4,l5,u4; b4,l6,v4; g2,m1,r2; f4,m2,s3; | |
| e5,m3,t3; d5,m4,u3; c5,m5,v3; h1,n1,r1; g3,n2,s2; f5,n3,t2; e6,n4,u2; d6,n5,v2; | |
| c6,n6,w2; h2,o1,s1; g4,o2,t1; f6,o3,u1; e7,o4,v1; d7,o5,w1; | |
| i1; i2; i3; i4; i5; j1; j2; j3; j4; j5; j6; k1; k2; k3; k4; k5; l1; l2; l3; l4; | |
| l5; l6; m1; m2; m3; m4; m5; n1; n2; n3; n4; n5; n6; o1; o2; o3; o4; o5; a12; b12; | |
| b23; b34; c12; c23; c34; c45; c56; d12; d23; d34; d45; d56; d67; e12; e23; e34; | |
| e45; e56; e67; f12; f23; f34; f45; f56; g12; g23; g34; h12; i12; i23; i34; i45; | |
| j12; j23; j34; j45; j56; k12; k23; k34; k45; l12; l23; l34; l45; l56; m12; m23; | |
| m34; m45; n12; n23; n34; n45; n56; o12; o23; o34; o45; p12; q12; q23; q34; r12; | |
| r23; r34; r45; r56; s12; s23; s34; s45; s56; s67; t12; t23; t34; t45; t56; t67; | |
| u12; u23; u34; u45; u56; v12; v23; v34; w12; b123; b234; c123; c234; c345; c456; | |
| d123; d234; d345; d456; d567; e123; e234; e345; e456; e567; f123; f234; f345; | |
| f456; g123; g234; i123; i234; i345; j123; j234; j345; j456; k123; k234; k345; | |
| l123; l234; l345; l456; m123; m234; m345; n123; n234; n345; n456; o123; o234; | |
| o345; q123; q234; r123; r234; r345; r456; s123; s234; s345; s456; s567; t123; | |
| t234; t345; t456; t567; u123; u234; u345; u456; v123; v234; |
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| $ perl6 generate-coords-pieces --exclude=g1,f3,l1,l2,q1,r3 5 7 | |
| # e1 d1 c1 b1 a1 | |
| # f1 e2 d2 c2 b2 a2 | |
| # f2 e3 d3 c3 b3 | |
| # XX XX e4 d4 c4 b4 | |
| # g2 f4 e5 d5 c5 | |
| # h1 g3 f5 e6 d6 c6 | |
| # h2 g4 f6 e7 d7 | |
| # i1 i2 i3 i4 i5 | |
| # j1 j2 j3 j4 j5 j6 | |
| # k1 k2 k3 k4 k5 | |
| # XX XX l3 l4 l5 l6 | |
| # m1 m2 m3 m4 m5 | |
| # n1 n2 n3 n4 n5 n6 | |
| # o1 o2 o3 o4 o5 | |
| # p2 q4 r6 s7 t7 | |
| # p1 q3 r5 s6 t6 u6 | |
| # q2 r4 s5 t5 u5 | |
| # XX XX s4 t4 u4 v4 | |
| # r2 s3 t3 u3 v3 | |
| # r1 s2 t2 u2 v2 w2 | |
| # s1 t1 u1 v1 w1 | |
| e1,i1,p2; d1,i2,q4; c1,i3,r6; b1,i4,s7; a1,i5,t7; f1,j1,p1; e2,j2,q3; d2,j3,r5; | |
| c2,j4,s6; b2,j5,t6; a2,j6,u6; f2,k1,q2; e3,k2,r4; d3,k3,s5; c3,k4,t5; b3,k5,u5; | |
| e4,l3,s4; d4,l4,t4; c4,l5,u4; b4,l6,v4; g2,m1,r2; f4,m2,s3; e5,m3,t3; d5,m4,u3; | |
| c5,m5,v3; h1,n1,r1; g3,n2,s2; f5,n3,t2; e6,n4,u2; d6,n5,v2; c6,n6,w2; h2,o1,s1; | |
| g4,o2,t1; f6,o3,u1; e7,o4,v1; d7,o5,w1; | |
| i1; i2; i3; i4; i5; j1; j2; j3; j4; j5; j6; k1; k2; k3; k4; k5; l3; l4; l5; l6; | |
| m1; m2; m3; m4; m5; n1; n2; n3; n4; n5; n6; o1; o2; o3; o4; o5; a12; b12; b23; | |
| b34; c12; c23; c34; c45; c56; d12; d23; d34; d45; d56; d67; e12; e23; e34; e45; | |
| e56; e67; f12; f45; f56; g23; g34; h12; i12; i23; i34; i45; j12; j23; j34; j45; | |
| j56; k12; k23; k34; k45; l34; l45; l56; m12; m23; m34; m45; n12; n23; n34; n45; | |
| n56; o12; o23; o34; o45; p12; q23; q34; r12; r45; r56; s12; s23; s34; s45; s56; | |
| s67; t12; t23; t34; t45; t56; t67; u12; u23; u34; u45; u56; v12; v23; v34; w12; | |
| b123; b234; c123; c234; c345; c456; d123; d234; d345; d456; d567; e123; e234; | |
| e345; e456; e567; f456; g234; i123; i234; i345; j123; j234; j345; j456; k123; | |
| k234; k345; l345; l456; m123; m234; m345; n123; n234; n345; n456; o123; o234; | |
| o345; q234; r456; s123; s234; s345; s456; s567; t123; t234; t345; t456; t567; | |
| u123; u234; u345; u456; v123; v234; |
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| $ perl6 generate-coords-pieces \ | |
| --exclude=g1,f3,e4,d4,c4,b4,l1,l2,l3,l4,l5,l6,q1,r3,s4,t4,u4,v4 5 7 | |
| # e1 d1 c1 b1 a1 | |
| # f1 e2 d2 c2 b2 a2 | |
| # f2 e3 d3 c3 b3 | |
| # XX XX XX XX XX XX | |
| # g2 f4 e5 d5 c5 | |
| # h1 g3 f5 e6 d6 c6 | |
| # h2 g4 f6 e7 d7 | |
| # i1 i2 i3 i4 i5 | |
| # j1 j2 j3 j4 j5 j6 | |
| # k1 k2 k3 k4 k5 | |
| # XX XX XX XX XX XX | |
| # m1 m2 m3 m4 m5 | |
| # n1 n2 n3 n4 n5 n6 | |
| # o1 o2 o3 o4 o5 | |
| # p2 q4 r6 s7 t7 | |
| # p1 q3 r5 s6 t6 u6 | |
| # q2 r4 s5 t5 u5 | |
| # XX XX XX XX XX XX | |
| # r2 s3 t3 u3 v3 | |
| # r1 s2 t2 u2 v2 w2 | |
| # s1 t1 u1 v1 w1 | |
| e1,i1,p2; d1,i2,q4; c1,i3,r6; b1,i4,s7; a1,i5,t7; f1,j1,p1; e2,j2,q3; d2,j3,r5; | |
| c2,j4,s6; b2,j5,t6; a2,j6,u6; f2,k1,q2; e3,k2,r4; d3,k3,s5; c3,k4,t5; b3,k5,u5; | |
| g2,m1,r2; f4,m2,s3; e5,m3,t3; d5,m4,u3; c5,m5,v3; h1,n1,r1; g3,n2,s2; f5,n3,t2; | |
| e6,n4,u2; d6,n5,v2; c6,n6,w2; h2,o1,s1; g4,o2,t1; f6,o3,u1; e7,o4,v1; d7,o5,w1; | |
| i1; i2; i3; i4; i5; j1; j2; j3; j4; j5; j6; k1; k2; k3; k4; k5; m1; m2; m3; m4; | |
| m5; n1; n2; n3; n4; n5; n6; o1; o2; o3; o4; o5; a12; b12; b23; c12; c23; c56; d12; | |
| d23; d56; d67; e12; e23; e56; e67; f12; f45; f56; g23; g34; h12; i12; i23; i34; | |
| i45; j12; j23; j34; j45; j56; k12; k23; k34; k45; m12; m23; m34; m45; n12; n23; | |
| n34; n45; n56; o12; o23; o34; o45; p12; q23; q34; r12; r45; r56; s12; s23; s56; | |
| s67; t12; t23; t56; t67; u12; u23; u56; v12; v23; w12; b123; c123; d123; d567; | |
| e123; e567; f456; g234; i123; i234; i345; j123; j234; j345; j456; k123; k234; | |
| k345; m123; m234; m345; n123; n234; n345; n456; o123; o234; o345; q234; r456; | |
| s123; s567; t123; t567; u123; v123; | |
| $ perl6 generate-coords-pieces 5 3 | |
| # e1 d1 c1 b1 a1 | |
| # f1 e2 d2 c2 b2 a2 | |
| # f2 e3 d3 c3 b3 | |
| # g1 g2 g3 g4 g5 | |
| # h1 h2 h3 h4 h5 h6 | |
| # i1 i2 i3 i4 i5 | |
| # j2 k3 l3 m3 n3 | |
| # j1 k2 l2 m2 n2 o2 | |
| # k1 l1 m1 n1 o1 | |
| e1,g1,j2; d1,g2,k3; c1,g3,l3; b1,g4,m3; a1,g5,n3; f1,h1,j1; e2,h2,k2; d2,h3,l2; | |
| c2,h4,m2; b2,h5,n2; a2,h6,o2; f2,i1,k1; e3,i2,l1; d3,i3,m1; c3,i4,n1; b3,i5,o1; | |
| g1; g2; g3; g4; g5; h1; h2; h3; h4; h5; h6; i1; i2; i3; i4; i5; a12; b12; b23; | |
| c12; c23; d12; d23; e12; e23; f12; g12; g23; g34; g45; h12; h23; h34; h45; h56; | |
| i12; i23; i34; i45; j12; k12; k23; l12; l23; m12; m23; n12; n23; o12; b123; c123; | |
| d123; e123; g123; g234; g345; h123; h234; h345; h456; i123; i234; i345; k123; | |
| l123; m123; n123; |
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