Courses/CS 460/Fall 2005/Homework/Kelly Breed/Dec 3
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< Courses | CS 460 | Fall 2005 | Homework | Kelly Breed
[edit] HW 9
[edit] Sudoku Solver Using Finite Sets
A collaboration by Jay Donnell and Kelly Breed
declare
%% Some Sudoku puzzles:
Prob =
[x 6 x 1 x 4 x 5 x
x x 8 3 x 5 6 x x
2 x x x x x x x 1
8 x x 4 x 7 x x 6
x x 6 x x x 3 x x
7 x x 9 x 1 x x 4
5 x x x x x x x 2
x x 7 2 x 6 9 x x
x 4 x 5 x 8 x 7 x]
Prob2 =
[x x x 3 4 2 x x x
5 4 x x 7 x x 8 x
x x 2 x x 5 4 x 6
x 6 x 2 x x x x x
3 x 8 x x x 2 x 4
x x x x x 8 x 7 x
6 x 9 1 x x 5 x x
x 3 x x 8 x x 1 9
x x x 5 3 9 x x x]
Fiendish =
[x x x x x x x 1 4
2 x x 5 x x 6 x x
9 x x 3 x x x x x
x 5 x x 1 x x 3 x
x 8 x x 3 x x 7 x
x 6 x x 2 x x 9 x
x x x x x 8 x x 2
x x 3 x x 4 x x 1
5 7 x x x x x x x]
Blank =
[x x x x x x x x x
x x x x x x x x x
x x x x x x x x x
x x x x x x x x x
x x x x x x x x x
x x x x x x x x x
x x x x x x x x x
x x x x x x x x x
x x x x x x x x x]
proc {Sudoku Puz Sol}
%% Take the values from the puzzle and put appropriate entries into the solution sets.
{For 1 81 1
proc {$ N}
if {Nth Puz N}==x then skip
else {FS.include N {Nth Sol {Nth Puz N}}}
end
end
}
Col1 Col2 Col3 Col4 Col5 Col6 Col7 Col8 Col9
Row1 Row2 Row3 Row4 Row5 Row6 Row7 Row8 Row9
Block1 Block1 Block2 Block3 Block4 Block5 Block6 Block7 Block8 Block9
in
{FS.var.list.upperBound 9 [1#81] Sol}
{ForAll Sol proc {$ V} {FS.card V 9} end}
Row1 = {FS.var.bounds [1#9][1#9]}
Row2 = {FS.var.bounds [10#18][10#18]}
Row3 = {FS.var.bounds [19#27][19#27]}
Row4 = {FS.var.bounds [28#36][28#36]}
Row5 = {FS.var.bounds [37#45][37#45]}
Row6 = {FS.var.bounds [46#54][46#54]}
Row7 = {FS.var.bounds [55#63][55#63]}
Row8 = {FS.var.bounds [64#72][64#72]}
Row9 = {FS.var.bounds [73#81][73#81]}
Col1 = {FS.var.upperBound [1#81]}
{FS.card Col1 9}
{FS.include 1 Col1}
{FS.include 10 Col1}
{FS.include 19 Col1}
{FS.include 28 Col1}
{FS.include 37 Col1}
{FS.include 46 Col1}
{FS.include 55 Col1}
{FS.include 64 Col1}
{FS.include 73 Col1}
Col2 = {FS.var.upperBound [1#81]}
{FS.card Col2 9}
{FS.include 2 Col2}
{FS.include 11 Col2}
{FS.include 20 Col2}
{FS.include 29 Col2}
{FS.include 38 Col2}
{FS.include 47 Col2}
{FS.include 56 Col2}
{FS.include 65 Col2}
{FS.include 74 Col2}
Col3 = {FS.var.upperBound [1#81]}
{FS.card Col3 9}
{FS.include 3 Col3}
{FS.include 12 Col3}
{FS.include 21 Col3}
{FS.include 30 Col3}
{FS.include 39 Col3}
{FS.include 48 Col3}
{FS.include 57 Col3}
{FS.include 66 Col3}
{FS.include 75 Col3}
Col4 = {FS.var.upperBound [1#81]}
{FS.card Col4 9}
{FS.include 4 Col4}
{FS.include 13 Col4}
{FS.include 22 Col4}
{FS.include 31 Col4}
{FS.include 40 Col4}
{FS.include 49 Col4}
{FS.include 58 Col4}
{FS.include 67 Col4}
{FS.include 76 Col4}
Col5 = {FS.var.upperBound [1#81]}
{FS.card Col5 9}
{FS.include 5 Col5}
{FS.include 14 Col5}
{FS.include 23 Col5}
{FS.include 32 Col5}
{FS.include 41 Col5}
{FS.include 50 Col5}
{FS.include 59 Col5}
{FS.include 68 Col5}
{FS.include 77 Col5}
Col6 = {FS.var.upperBound [1#81]}
{FS.card Col6 9}
{FS.include 6 Col6}
{FS.include 15 Col6}
{FS.include 24 Col6}
{FS.include 33 Col6}
{FS.include 42 Col6}
{FS.include 51 Col6}
{FS.include 60 Col6}
{FS.include 69 Col6}
{FS.include 78 Col6}
Col7 = {FS.var.upperBound [1#81]}
{FS.card Col7 9}
{FS.include 7 Col7}
{FS.include 16 Col7}
{FS.include 25 Col7}
{FS.include 34 Col7}
{FS.include 43 Col7}
{FS.include 52 Col7}
{FS.include 61 Col7}
{FS.include 70 Col7}
{FS.include 79 Col7}
Col8 = {FS.var.upperBound [1#81]}
{FS.card Col8 9}
{FS.include 8 Col8}
{FS.include 17 Col8}
{FS.include 26 Col8}
{FS.include 35 Col8}
{FS.include 44 Col8}
{FS.include 53 Col8}
{FS.include 62 Col8}
{FS.include 71 Col8}
{FS.include 80 Col8}
Col9 = {FS.var.upperBound [1#81]}
{FS.card Col9 9}
{FS.include 9 Col9}
{FS.include 18 Col9}
{FS.include 27 Col9}
{FS.include 36 Col9}
{FS.include 45 Col9}
{FS.include 54 Col9}
{FS.include 63 Col9}
{FS.include 72 Col9}
{FS.include 81 Col9}
Block1 = {FS.var.upperBound [1#81]}
{FS.card Block1 9}
{FS.include 1 Block1}
{FS.include 2 Block1}
{FS.include 3 Block1}
{FS.include 10 Block1}
{FS.include 11 Block1}
{FS.include 12 Block1}
{FS.include 19 Block1}
{FS.include 20 Block1}
{FS.include 21 Block1}
Block2 = {FS.var.upperBound [1#81]}
{FS.card Block2 9}
{FS.include 4 Block2}
{FS.include 5 Block2}
{FS.include 6 Block2}
{FS.include 13 Block2}
{FS.include 14 Block2}
{FS.include 15 Block2}
{FS.include 22 Block2}
{FS.include 23 Block2}
{FS.include 24 Block2}
Block3 = {FS.var.upperBound [1#81]}
{FS.card Block3 9}
{FS.include 7 Block3}
{FS.include 8 Block3}
{FS.include 9 Block3}
{FS.include 16 Block3}
{FS.include 17 Block3}
{FS.include 18 Block3}
{FS.include 25 Block3}
{FS.include 26 Block3}
{FS.include 27 Block3}
Block4 = {FS.var.upperBound [1#81]}
{FS.card Block4 9}
{FS.include 28 Block4}
{FS.include 29 Block4}
{FS.include 30 Block4}
{FS.include 37 Block4}
{FS.include 38 Block4}
{FS.include 39 Block4}
{FS.include 46 Block4}
{FS.include 47 Block4}
{FS.include 48 Block4}
Block5 = {FS.var.upperBound [1#81]}
{FS.card Block5 9}
{FS.include 31 Block5}
{FS.include 32 Block5}
{FS.include 33 Block5}
{FS.include 40 Block5}
{FS.include 41 Block5}
{FS.include 42 Block5}
{FS.include 49 Block5}
{FS.include 50 Block5}
{FS.include 51 Block5}
Block6 = {FS.var.upperBound [1#81]}
{FS.card Block6 9}
{FS.include 34 Block6}
{FS.include 35 Block6}
{FS.include 36 Block6}
{FS.include 43 Block6}
{FS.include 44 Block6}
{FS.include 45 Block6}
{FS.include 52 Block6}
{FS.include 53 Block6}
{FS.include 54 Block6}
Block7 = {FS.var.upperBound [1#81]}
{FS.card Block7 9}
{FS.include 55 Block7}
{FS.include 56 Block7}
{FS.include 57 Block7}
{FS.include 64 Block7}
{FS.include 65 Block7}
{FS.include 66 Block7}
{FS.include 73 Block7}
{FS.include 74 Block7}
{FS.include 75 Block7}
Block8 = {FS.var.upperBound [1#81]}
{FS.card Block8 9}
{FS.include 58 Block8}
{FS.include 59 Block8}
{FS.include 60 Block8}
{FS.include 67 Block8}
{FS.include 68 Block8}
{FS.include 69 Block8}
{FS.include 76 Block8}
{FS.include 77 Block8}
{FS.include 78 Block8}
Block9 = {FS.var.upperBound [1#81]}
{FS.card Block9 9}
{FS.include 61 Block9}
{FS.include 62 Block9}
{FS.include 63 Block9}
{FS.include 70 Block9}
{FS.include 71 Block9}
{FS.include 72 Block9}
{FS.include 79 Block9}
{FS.include 80 Block9}
{FS.include 81 Block9}
{FS.card {FS.intersect {List.nth Sol 1} Row1} 1}
{FS.card {FS.intersect {List.nth Sol 1} Row2} 1}
{FS.card {FS.intersect {List.nth Sol 1} Row3} 1}
{FS.card {FS.intersect {List.nth Sol 1} Row4} 1}
{FS.card {FS.intersect {List.nth Sol 1} Row5} 1}
{FS.card {FS.intersect {List.nth Sol 1} Row6} 1}
{FS.card {FS.intersect {List.nth Sol 1} Row7} 1}
{FS.card {FS.intersect {List.nth Sol 1} Row8} 1}
{FS.card {FS.intersect {List.nth Sol 1} Row9} 1}
{FS.card {FS.intersect {List.nth Sol 1} Col1} 1}
{FS.card {FS.intersect {List.nth Sol 1} Col2} 1}
{FS.card {FS.intersect {List.nth Sol 1} Col3} 1}
{FS.card {FS.intersect {List.nth Sol 1} Col4} 1}
{FS.card {FS.intersect {List.nth Sol 1} Col5} 1}
{FS.card {FS.intersect {List.nth Sol 1} Col6} 1}
{FS.card {FS.intersect {List.nth Sol 1} Col7} 1}
{FS.card {FS.intersect {List.nth Sol 1} Col8} 1}
{FS.card {FS.intersect {List.nth Sol 1} Col9} 1}
{FS.card {FS.intersect {List.nth Sol 1} Block1} 1}
{FS.card {FS.intersect {List.nth Sol 1} Block2} 1}
{FS.card {FS.intersect {List.nth Sol 1} Block3} 1}
{FS.card {FS.intersect {List.nth Sol 1} Block4} 1}
{FS.card {FS.intersect {List.nth Sol 1} Block5} 1}
{FS.card {FS.intersect {List.nth Sol 1} Block6} 1}
{FS.card {FS.intersect {List.nth Sol 1} Block7} 1}
{FS.card {FS.intersect {List.nth Sol 1} Block8} 1}
{FS.card {FS.intersect {List.nth Sol 1} Block9} 1}
{FS.card {FS.intersect {List.nth Sol 2} Row1} 1}
{FS.card {FS.intersect {List.nth Sol 2} Row2} 1}
{FS.card {FS.intersect {List.nth Sol 2} Row3} 1}
{FS.card {FS.intersect {List.nth Sol 2} Row4} 1}
{FS.card {FS.intersect {List.nth Sol 2} Row5} 1}
{FS.card {FS.intersect {List.nth Sol 2} Row6} 1}
{FS.card {FS.intersect {List.nth Sol 2} Row7} 1}
{FS.card {FS.intersect {List.nth Sol 2} Row8} 1}
{FS.card {FS.intersect {List.nth Sol 2} Row9} 1}
{FS.card {FS.intersect {List.nth Sol 2} Col1} 1}
{FS.card {FS.intersect {List.nth Sol 2} Col2} 1}
{FS.card {FS.intersect {List.nth Sol 2} Col3} 1}
{FS.card {FS.intersect {List.nth Sol 2} Col4} 1}
{FS.card {FS.intersect {List.nth Sol 2} Col5} 1}
{FS.card {FS.intersect {List.nth Sol 2} Col6} 1}
{FS.card {FS.intersect {List.nth Sol 2} Col7} 1}
{FS.card {FS.intersect {List.nth Sol 2} Col8} 1}
{FS.card {FS.intersect {List.nth Sol 2} Col9} 1}
{FS.card {FS.intersect {List.nth Sol 2} Block1} 1}
{FS.card {FS.intersect {List.nth Sol 2} Block2} 1}
{FS.card {FS.intersect {List.nth Sol 2} Block3} 1}
{FS.card {FS.intersect {List.nth Sol 2} Block4} 1}
{FS.card {FS.intersect {List.nth Sol 2} Block5} 1}
{FS.card {FS.intersect {List.nth Sol 2} Block6} 1}
{FS.card {FS.intersect {List.nth Sol 2} Block7} 1}
{FS.card {FS.intersect {List.nth Sol 2} Block8} 1}
{FS.card {FS.intersect {List.nth Sol 2} Block9} 1}
{FS.card {FS.intersect {List.nth Sol 3} Row1} 1}
{FS.card {FS.intersect {List.nth Sol 3} Row2} 1}
{FS.card {FS.intersect {List.nth Sol 3} Row3} 1}
{FS.card {FS.intersect {List.nth Sol 3} Row4} 1}
{FS.card {FS.intersect {List.nth Sol 3} Row5} 1}
{FS.card {FS.intersect {List.nth Sol 3} Row6} 1}
{FS.card {FS.intersect {List.nth Sol 3} Row7} 1}
{FS.card {FS.intersect {List.nth Sol 3} Row8} 1}
{FS.card {FS.intersect {List.nth Sol 3} Row9} 1}
{FS.card {FS.intersect {List.nth Sol 3} Col1} 1}
{FS.card {FS.intersect {List.nth Sol 3} Col2} 1}
{FS.card {FS.intersect {List.nth Sol 3} Col3} 1}
{FS.card {FS.intersect {List.nth Sol 3} Col4} 1}
{FS.card {FS.intersect {List.nth Sol 3} Col5} 1}
{FS.card {FS.intersect {List.nth Sol 3} Col6} 1}
{FS.card {FS.intersect {List.nth Sol 3} Col7} 1}
{FS.card {FS.intersect {List.nth Sol 3} Col8} 1}
{FS.card {FS.intersect {List.nth Sol 3} Col9} 1}
{FS.card {FS.intersect {List.nth Sol 3} Block1} 1}
{FS.card {FS.intersect {List.nth Sol 3} Block2} 1}
{FS.card {FS.intersect {List.nth Sol 3} Block3} 1}
{FS.card {FS.intersect {List.nth Sol 3} Block4} 1}
{FS.card {FS.intersect {List.nth Sol 3} Block5} 1}
{FS.card {FS.intersect {List.nth Sol 3} Block6} 1}
{FS.card {FS.intersect {List.nth Sol 3} Block7} 1}
{FS.card {FS.intersect {List.nth Sol 3} Block8} 1}
{FS.card {FS.intersect {List.nth Sol 3} Block9} 1}
{FS.card {FS.intersect {List.nth Sol 4} Row1} 1}
{FS.card {FS.intersect {List.nth Sol 4} Row2} 1}
{FS.card {FS.intersect {List.nth Sol 4} Row3} 1}
{FS.card {FS.intersect {List.nth Sol 4} Row4} 1}
{FS.card {FS.intersect {List.nth Sol 4} Row5} 1}
{FS.card {FS.intersect {List.nth Sol 4} Row6} 1}
{FS.card {FS.intersect {List.nth Sol 4} Row7} 1}
{FS.card {FS.intersect {List.nth Sol 4} Row8} 1}
{FS.card {FS.intersect {List.nth Sol 4} Row9} 1}
{FS.card {FS.intersect {List.nth Sol 4} Col1} 1}
{FS.card {FS.intersect {List.nth Sol 4} Col2} 1}
{FS.card {FS.intersect {List.nth Sol 4} Col3} 1}
{FS.card {FS.intersect {List.nth Sol 4} Col4} 1}
{FS.card {FS.intersect {List.nth Sol 4} Col5} 1}
{FS.card {FS.intersect {List.nth Sol 4} Col6} 1}
{FS.card {FS.intersect {List.nth Sol 4} Col7} 1}
{FS.card {FS.intersect {List.nth Sol 4} Col8} 1}
{FS.card {FS.intersect {List.nth Sol 4} Col9} 1}
{FS.card {FS.intersect {List.nth Sol 4} Block1} 1}
{FS.card {FS.intersect {List.nth Sol 4} Block2} 1}
{FS.card {FS.intersect {List.nth Sol 4} Block3} 1}
{FS.card {FS.intersect {List.nth Sol 4} Block4} 1}
{FS.card {FS.intersect {List.nth Sol 4} Block5} 1}
{FS.card {FS.intersect {List.nth Sol 4} Block6} 1}
{FS.card {FS.intersect {List.nth Sol 4} Block7} 1}
{FS.card {FS.intersect {List.nth Sol 4} Block8} 1}
{FS.card {FS.intersect {List.nth Sol 4} Block9} 1}
{FS.card {FS.intersect {List.nth Sol 5} Row1} 1}
{FS.card {FS.intersect {List.nth Sol 5} Row2} 1}
{FS.card {FS.intersect {List.nth Sol 5} Row3} 1}
{FS.card {FS.intersect {List.nth Sol 5} Row4} 1}
{FS.card {FS.intersect {List.nth Sol 5} Row5} 1}
{FS.card {FS.intersect {List.nth Sol 5} Row6} 1}
{FS.card {FS.intersect {List.nth Sol 5} Row7} 1}
{FS.card {FS.intersect {List.nth Sol 5} Row8} 1}
{FS.card {FS.intersect {List.nth Sol 5} Row9} 1}
{FS.card {FS.intersect {List.nth Sol 5} Col1} 1}
{FS.card {FS.intersect {List.nth Sol 5} Col2} 1}
{FS.card {FS.intersect {List.nth Sol 5} Col3} 1}
{FS.card {FS.intersect {List.nth Sol 5} Col4} 1}
{FS.card {FS.intersect {List.nth Sol 5} Col5} 1}
{FS.card {FS.intersect {List.nth Sol 5} Col6} 1}
{FS.card {FS.intersect {List.nth Sol 5} Col7} 1}
{FS.card {FS.intersect {List.nth Sol 5} Col8} 1}
{FS.card {FS.intersect {List.nth Sol 5} Col9} 1}
{FS.card {FS.intersect {List.nth Sol 5} Block1} 1}
{FS.card {FS.intersect {List.nth Sol 5} Block2} 1}
{FS.card {FS.intersect {List.nth Sol 5} Block3} 1}
{FS.card {FS.intersect {List.nth Sol 5} Block4} 1}
{FS.card {FS.intersect {List.nth Sol 5} Block5} 1}
{FS.card {FS.intersect {List.nth Sol 5} Block6} 1}
{FS.card {FS.intersect {List.nth Sol 5} Block7} 1}
{FS.card {FS.intersect {List.nth Sol 5} Block8} 1}
{FS.card {FS.intersect {List.nth Sol 5} Block9} 1}
{FS.card {FS.intersect {List.nth Sol 6} Row1} 1}
{FS.card {FS.intersect {List.nth Sol 6} Row2} 1}
{FS.card {FS.intersect {List.nth Sol 6} Row3} 1}
{FS.card {FS.intersect {List.nth Sol 6} Row4} 1}
{FS.card {FS.intersect {List.nth Sol 6} Row5} 1}
{FS.card {FS.intersect {List.nth Sol 6} Row6} 1}
{FS.card {FS.intersect {List.nth Sol 6} Row7} 1}
{FS.card {FS.intersect {List.nth Sol 6} Row8} 1}
{FS.card {FS.intersect {List.nth Sol 6} Row9} 1}
{FS.card {FS.intersect {List.nth Sol 6} Col1} 1}
{FS.card {FS.intersect {List.nth Sol 6} Col2} 1}
{FS.card {FS.intersect {List.nth Sol 6} Col3} 1}
{FS.card {FS.intersect {List.nth Sol 6} Col4} 1}
{FS.card {FS.intersect {List.nth Sol 6} Col5} 1}
{FS.card {FS.intersect {List.nth Sol 6} Col6} 1}
{FS.card {FS.intersect {List.nth Sol 6} Col7} 1}
{FS.card {FS.intersect {List.nth Sol 6} Col8} 1}
{FS.card {FS.intersect {List.nth Sol 6} Col9} 1}
{FS.card {FS.intersect {List.nth Sol 6} Block1} 1}
{FS.card {FS.intersect {List.nth Sol 6} Block2} 1}
{FS.card {FS.intersect {List.nth Sol 6} Block3} 1}
{FS.card {FS.intersect {List.nth Sol 6} Block4} 1}
{FS.card {FS.intersect {List.nth Sol 6} Block5} 1}
{FS.card {FS.intersect {List.nth Sol 6} Block6} 1}
{FS.card {FS.intersect {List.nth Sol 6} Block7} 1}
{FS.card {FS.intersect {List.nth Sol 6} Block8} 1}
{FS.card {FS.intersect {List.nth Sol 6} Block9} 1}
{FS.card {FS.intersect {List.nth Sol 7} Row1} 1}
{FS.card {FS.intersect {List.nth Sol 7} Row2} 1}
{FS.card {FS.intersect {List.nth Sol 7} Row3} 1}
{FS.card {FS.intersect {List.nth Sol 7} Row4} 1}
{FS.card {FS.intersect {List.nth Sol 7} Row5} 1}
{FS.card {FS.intersect {List.nth Sol 7} Row6} 1}
{FS.card {FS.intersect {List.nth Sol 7} Row7} 1}
{FS.card {FS.intersect {List.nth Sol 7} Row8} 1}
{FS.card {FS.intersect {List.nth Sol 7} Row9} 1}
{FS.card {FS.intersect {List.nth Sol 7} Col1} 1}
{FS.card {FS.intersect {List.nth Sol 7} Col2} 1}
{FS.card {FS.intersect {List.nth Sol 7} Col3} 1}
{FS.card {FS.intersect {List.nth Sol 7} Col4} 1}
{FS.card {FS.intersect {List.nth Sol 7} Col5} 1}
{FS.card {FS.intersect {List.nth Sol 7} Col6} 1}
{FS.card {FS.intersect {List.nth Sol 7} Col7} 1}
{FS.card {FS.intersect {List.nth Sol 7} Col8} 1}
{FS.card {FS.intersect {List.nth Sol 7} Col9} 1}
{FS.card {FS.intersect {List.nth Sol 7} Block1} 1}
{FS.card {FS.intersect {List.nth Sol 7} Block2} 1}
{FS.card {FS.intersect {List.nth Sol 7} Block3} 1}
{FS.card {FS.intersect {List.nth Sol 7} Block4} 1}
{FS.card {FS.intersect {List.nth Sol 7} Block5} 1}
{FS.card {FS.intersect {List.nth Sol 7} Block6} 1}
{FS.card {FS.intersect {List.nth Sol 7} Block7} 1}
{FS.card {FS.intersect {List.nth Sol 7} Block8} 1}
{FS.card {FS.intersect {List.nth Sol 7} Block9} 1}
{FS.card {FS.intersect {List.nth Sol 8} Row1} 1}
{FS.card {FS.intersect {List.nth Sol 8} Row2} 1}
{FS.card {FS.intersect {List.nth Sol 8} Row3} 1}
{FS.card {FS.intersect {List.nth Sol 8} Row4} 1}
{FS.card {FS.intersect {List.nth Sol 8} Row5} 1}
{FS.card {FS.intersect {List.nth Sol 8} Row6} 1}
{FS.card {FS.intersect {List.nth Sol 8} Row7} 1}
{FS.card {FS.intersect {List.nth Sol 8} Row8} 1}
{FS.card {FS.intersect {List.nth Sol 8} Row9} 1}
{FS.card {FS.intersect {List.nth Sol 8} Col1} 1}
{FS.card {FS.intersect {List.nth Sol 8} Col2} 1}
{FS.card {FS.intersect {List.nth Sol 8} Col3} 1}
{FS.card {FS.intersect {List.nth Sol 8} Col4} 1}
{FS.card {FS.intersect {List.nth Sol 8} Col5} 1}
{FS.card {FS.intersect {List.nth Sol 8} Col6} 1}
{FS.card {FS.intersect {List.nth Sol 8} Col7} 1}
{FS.card {FS.intersect {List.nth Sol 8} Col8} 1}
{FS.card {FS.intersect {List.nth Sol 8} Col9} 1}
{FS.card {FS.intersect {List.nth Sol 8} Block1} 1}
{FS.card {FS.intersect {List.nth Sol 8} Block2} 1}
{FS.card {FS.intersect {List.nth Sol 8} Block3} 1}
{FS.card {FS.intersect {List.nth Sol 8} Block4} 1}
{FS.card {FS.intersect {List.nth Sol 8} Block5} 1}
{FS.card {FS.intersect {List.nth Sol 8} Block6} 1}
{FS.card {FS.intersect {List.nth Sol 8} Block7} 1}
{FS.card {FS.intersect {List.nth Sol 8} Block8} 1}
{FS.card {FS.intersect {List.nth Sol 8} Block9} 1}
{FS.card {FS.intersect {List.nth Sol 9} Row1} 1}
{FS.card {FS.intersect {List.nth Sol 9} Row2} 1}
{FS.card {FS.intersect {List.nth Sol 9} Row3} 1}
{FS.card {FS.intersect {List.nth Sol 9} Row4} 1}
{FS.card {FS.intersect {List.nth Sol 9} Row5} 1}
{FS.card {FS.intersect {List.nth Sol 9} Row6} 1}
{FS.card {FS.intersect {List.nth Sol 9} Row7} 1}
{FS.card {FS.intersect {List.nth Sol 9} Row8} 1}
{FS.card {FS.intersect {List.nth Sol 9} Row9} 1}
{FS.card {FS.intersect {List.nth Sol 9} Col1} 1}
{FS.card {FS.intersect {List.nth Sol 9} Col2} 1}
{FS.card {FS.intersect {List.nth Sol 9} Col3} 1}
{FS.card {FS.intersect {List.nth Sol 9} Col4} 1}
{FS.card {FS.intersect {List.nth Sol 9} Col5} 1}
{FS.card {FS.intersect {List.nth Sol 9} Col6} 1}
{FS.card {FS.intersect {List.nth Sol 9} Col7} 1}
{FS.card {FS.intersect {List.nth Sol 9} Col8} 1}
{FS.card {FS.intersect {List.nth Sol 9} Col9} 1}
{FS.card {FS.intersect {List.nth Sol 9} Block1} 1}
{FS.card {FS.intersect {List.nth Sol 9} Block2} 1}
{FS.card {FS.intersect {List.nth Sol 9} Block3} 1}
{FS.card {FS.intersect {List.nth Sol 9} Block4} 1}
{FS.card {FS.intersect {List.nth Sol 9} Block5} 1}
{FS.card {FS.intersect {List.nth Sol 9} Block6} 1}
{FS.card {FS.intersect {List.nth Sol 9} Block7} 1}
{FS.card {FS.intersect {List.nth Sol 9} Block8} 1}
{FS.card {FS.intersect {List.nth Sol 9} Block9} 1}
{FS.disjoint {List.nth Sol 1} {List.nth Sol 2}}
{FS.disjoint {List.nth Sol 1} {List.nth Sol 3}}
{FS.disjoint {List.nth Sol 1} {List.nth Sol 4}}
{FS.disjoint {List.nth Sol 1} {List.nth Sol 5}}
{FS.disjoint {List.nth Sol 1} {List.nth Sol 6}}
{FS.disjoint {List.nth Sol 1} {List.nth Sol 7}}
{FS.disjoint {List.nth Sol 1} {List.nth Sol 8}}
{FS.disjoint {List.nth Sol 1} {List.nth Sol 9}}
{FS.disjoint {List.nth Sol 2} {List.nth Sol 3}}
{FS.disjoint {List.nth Sol 2} {List.nth Sol 4}}
{FS.disjoint {List.nth Sol 2} {List.nth Sol 5}}
{FS.disjoint {List.nth Sol 2} {List.nth Sol 6}}
{FS.disjoint {List.nth Sol 2} {List.nth Sol 7}}
{FS.disjoint {List.nth Sol 2} {List.nth Sol 8}}
{FS.disjoint {List.nth Sol 2} {List.nth Sol 9}}
{FS.disjoint {List.nth Sol 3} {List.nth Sol 4}}
{FS.disjoint {List.nth Sol 3} {List.nth Sol 5}}
{FS.disjoint {List.nth Sol 3} {List.nth Sol 6}}
{FS.disjoint {List.nth Sol 3} {List.nth Sol 7}}
{FS.disjoint {List.nth Sol 3} {List.nth Sol 8}}
{FS.disjoint {List.nth Sol 3} {List.nth Sol 9}}
{FS.disjoint {List.nth Sol 4} {List.nth Sol 5}}
{FS.disjoint {List.nth Sol 4} {List.nth Sol 6}}
{FS.disjoint {List.nth Sol 4} {List.nth Sol 7}}
{FS.disjoint {List.nth Sol 4} {List.nth Sol 8}}
{FS.disjoint {List.nth Sol 4} {List.nth Sol 9}}
{FS.disjoint {List.nth Sol 5} {List.nth Sol 6}}
{FS.disjoint {List.nth Sol 5} {List.nth Sol 7}}
{FS.disjoint {List.nth Sol 5} {List.nth Sol 8}}
{FS.disjoint {List.nth Sol 5} {List.nth Sol 9}}
{FS.disjoint {List.nth Sol 6} {List.nth Sol 7}}
{FS.disjoint {List.nth Sol 6} {List.nth Sol 8}}
{FS.disjoint {List.nth Sol 6} {List.nth Sol 9}}
{FS.disjoint {List.nth Sol 7} {List.nth Sol 8}}
{FS.disjoint {List.nth Sol 7} {List.nth Sol 9}}
{FS.disjoint {List.nth Sol 8} {List.nth Sol 9}}
{FS.distribute naive Sol}
end
%%%%%%%%%%%%%%%%%%%%%%% procs for making output %%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Takes a list of sets and outputs 9 lists of 9
proc {OutputSolution In ?Out}
SetSize = 9
SolList = {MakeList SetSize}
{For 1 SetSize 1
proc {$ S}
{Nth SolList S} = {MakeList SetSize}
end
}
C={NewCell 1} %% For incrementing through every position in the Sudoku matrix
in
%% Nested Fors create 9 lists of 9 by iterating through the positions 1-81 and checking to see
%% which set the number in that position should come from.
{For 1 SetSize 1
proc {$ X} % for every set
{For 1 SetSize 1 % for every position in that set
proc {$ N}
{For 1 SetSize 1 % find out which solution set contains that postion and assign the corresponding number
proc {$ Y}
if {IsInSet {Nth In Y} @C} then {Nth {Nth SolList X} N} = Y end
end
}
C:=@C+1
end
}
end
}
Out = SolList
end
proc {IsInSet S M ?Out}
C={NewCell false} in
{FS.forAllIn S
proc {$ X}
if X==M then C:=true end
end
}
Out = @C
end
%%%%%%%%%%%%%%%%%%%%%%%%% End of output procs %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
{ExploreAll fun {$} {Sudoku Fiendish} end}
R={SearchOne fun {$} {Sudoku Fiendish} end}
%% SearchOne is returning a list of sets within a list and OutputSolution expects only a list of sets.
{Browse {OutputSolution R.1}}
