Tuesday, November 14, 2006


I've got sudoku fever! Actually, no, I don't, I don't really like sudoku at all but I decided to write a solver in erlang. It was pretty trivial. The basic algorithm is as follows:
1) Create a list of every blank square and the possible values that can go into that square
2) Find the square with the least number of possible values
3) Iterate over the list of possible numbers that can be in that square, create a new board with that value in it and recurse on the new board
4) Continue until there are no more possible values (in which case it failed) or the puzzle is solved.

The code is not the prettiest stuff in the world but it appears to solve the problem (specifically the remove_* functions).

Usage looks like:

Eshell V5.5.1 (abort with ^G)
1> {solved, Res} = sudoku:solve([
1> [9, 5, b, b, b, 6, 4, 7, b],
1> [4, b, 8, 7, b, 2, b, b, b],
1> [6, 2, b, 4, b, b, b, 5, b],
1> [5, b, 2, b, 6, b, 3, b, b],
1> [b, b, b, 2, b, 7, b, b, b],
1> [b, b, 4, b, 1, b, 2, b, 8],
1> [b, 7, b, b, b, 9, b, 3, 4],
1> [b, b, b, 1, b, 3, 7, b, 5],
1> [b, 4, 3, 5, b, b, b, 2, 9]]).
2> sudoku:print(Res).
9 5 1 8 3 6 4 7 2
4 3 8 7 5 2 9 6 1
6 2 7 4 9 1 8 5 3
5 8 2 9 6 4 3 1 7
3 1 9 2 8 7 5 4 6
7 6 4 3 1 5 2 9 8
8 7 5 6 2 9 1 3 4
2 9 6 1 4 3 7 8 5
1 4 3 5 7 8 6 2 9

Code (can be downloaded here):


-export([solve/1, print/1]).

solve(Puzzle) when is_list(Puzzle) ->

print(Puzzle) ->
lists:foreach(fun(X) ->
lists:foreach(fun(Y) ->
io:format("~w ", [dict:fetch({X, Y}, Puzzle)])
end, lists:seq(0, 8)),
io:format("~n", [])
end, lists:seq(0, 8)).

dict_from_list(List) ->
element(2, lists:foldl(fun(Elm, {X, Dict}) ->
{_, DDict} = lists:foldl(fun(Elem, {Y, NDict}) ->
{Y + 1, dict:store({X, Y}, Elem, NDict)}
end, {0, Dict}, Elm),
{X + 1, DDict}
end, {0, dict:new()}, List)).

solve_puzzle(Puzzle) ->
case generate_open_spots(Puzzle) of
[{{X, Y}, Set} | _] ->
try_value({X, Y}, Set, Puzzle);
[] ->
{solved, Puzzle}

try_value(_, [], Puzzle) ->
io:format("~n", []),
try_value({X, Y}, [H | R], Puzzle) ->
case solve_puzzle(dict:store({X, Y}, H, Puzzle)) of
{solved, RPuzzle} ->
{solved, RPuzzle};
failed ->
try_value({X, Y}, R, Puzzle)

generate_open_spots(Puzzle) ->
OpenSquareList = dict:fold(fun(Key, b, Acc) ->
[Key | Acc];
(_Key, _Value, Acc) ->
end, [], Puzzle),
lists:sort(fun({{_X1, _Y1}, E1}, {{_X2, _Y2}, E2}) when length(E1) < length(E2) ->
(_E1, _E2) ->
end, generate_open_values(OpenSquareList, Puzzle)).

generate_open_values(List, Puzzle) ->
generate_open_values(List, [], Puzzle).

generate_open_values([], Acc, _Puzzle) ->
generate_open_values([{X, Y} | R], Acc, Puzzle) ->
generate_open_values(R, [{{X, Y}, remove_region_vals({X, Y},
remove_y_vals(X, lists:seq(1, 9),
Puzzle)} | Acc],

remove_x_vals(Y, List, Puzzle) ->
lists:foldl(fun(Idx, Acc) ->
case dict:fetch({Idx, Y}, Puzzle) of
b ->
E ->
lists:delete(E, Acc)
List, lists:seq(0, 8)).

remove_y_vals(X, List, Puzzle) ->
lists:foldl(fun(Idx, Acc) ->
case dict:fetch({X, Idx}, Puzzle) of
b ->
E ->
lists:delete(E, Acc)
List, lists:seq(0, 8)).

remove_region_vals({X, Y}, List, Puzzle) ->
{RX, RY} = find_region(X, Y),
lists:foldl(fun(IX, AccX) ->
lists:foldl(fun(IY, AccY) ->
case dict:fetch({IX, IY}, Puzzle) of
b ->
E ->
lists:delete(E, AccY)
end, AccX, lists:seq(RY, RY + 2))
end, List, lists:seq(RX, RX + 2)).

find_region(X, Y) ->
{find_region(X), find_region(Y)}.

find_region(V) when V >= 0, V < 3 ->
find_region(V) when V >= 3, V < 6 ->
find_region(V) when V >= 6, V < 9 ->


Anonymous Anonymous said...

Nice. As a comparision; perhaps you could solve it by using the new Prolog plugin for Erlang (see User Contrib at trapexit.org).

15 November, 2006 02:57  
Blogger orbitz said...

Hrm solving it in Prolog does seem rather interesting. I unfortunately don't know much Prolog but I will look into it, thanks

15 November, 2006 23:47  
Anonymous Anonymous said...

Some ideas to make the world's leading scalable sudoku solver:
* solving alphabetical sudoku's (with a, b, c,.. instead of 1, 2 and 3)
* solving graphical sudoku's (with pictures instead of numbers)
* integrate it in ErlyWeb for a userfriendly front end
* solving other special sudoku's (e.g. there exists a sudoku in which you also need to have the numbers 1 to 9 diagonally on the sudoku.

16 November, 2006 15:51  
Blogger Jordan Wilberding said...

Just thought you might be interested in this.


I ran your code, it took me 1.7 seconds with it.

30 March, 2007 23:20  
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