subboard_solver.erl

-module(subboard_solver).
-export([gen_subboards/1]).
-define(VALID_SET, [1,2,3,4,5,6,7,8,9]).

%% Private
gen_subboards(Board) ->
    FlatBoard = flatten_board(Board),
    UsedNums = lists:foldl(fun(Num, Acc) -> 
				   add_used_num(Num, Acc) 
			   end, [], FlatBoard),
    UnusedPerms = generate_unused_perms(UsedNums),
    lists:foldl(fun(UnusedNums, Boards) ->
			Boards ++ [fill_subboard(UnusedNums, FlatBoard)]
		end, [], UnusedPerms).


flatten_board([Row1, Row2, Row3]) ->
    Row1 ++ Row2 ++ Row3.

%% flatten_sort_board(Board) ->
%%     lists:sort(flatten_board(Board)).

%% is_valid_board(Board) ->
%%     is_valid(flatten_board(Board)).

%% is_valid(?VALID_SET) ->
%%     true;
%% is_valid(_List) ->
%%     false.

add_used_num(Num, Used) when is_integer(Num) ->
    Used ++ [Num];
add_used_num(_Num, Used) ->
    Used.

%% 
%  Taken from 
%  http://erlang.org/doc/programming_examples/list_comprehensions.html#id65674
%%
perms([]) -> [[]];
perms(L)  -> [[H|T] || H <- L, T <- perms(L--[H])].

generate_unused_perms(UsedNums) ->
    UnusedNums = ?VALID_SET -- UsedNums,
    perms(UnusedNums).

find_unknown(FlatBoard) ->
    find_unknown_index(FlatBoard, 0).

find_unknown_index([unknown| _], Index) ->
    Index;
find_unknown_index([], _) -> 
    -1;
find_unknown_index([Num|Tl], Index) when is_integer(Num) ->
    find_unknown_index(Tl, Index+1).
    
replace_unknown(Num, FlatBoard) ->
    replace_unknown(Num, FlatBoard, find_unknown(FlatBoard)).

replace_unknown(_Num, FlatBoard, -1) ->
    FlatBoard;
replace_unknown(Num, FlatBoard, Index) ->
    lists:sublist(FlatBoard, Index) ++ [Num] ++ lists:nthtail(Index+1, FlatBoard).

fill_subboard(Unused, FlatBoard) ->
    lists:foldl(fun(Num, Board) -> 
			replace_unknown(Num, Board)
		end, FlatBoard, Unused).