对于大学，我必须实现一种算法，为给定的边长和特定的总和创建所有可能的幻方。对于 n=3，算法按预期工作。但是当一段时间后为 n=4 生成所有幻方时，我的内存不足。任务描述中已经提到了这个问题。我已经尝试优化 a 代码，但它仍然无法正常工作。所以我希望有人能给我一些建议。
我的基本想法是：首先我生成所有可能的行，我可以使用给定的数字，然后我试图以一种完全满足幻方限制的方式组合这些行。这是通过回溯发生的。我认为问题是在makeRows存储所有行之后消耗太多内存的函数。
如果您需要我可以提供的代码的更多解释！
magicSquare(N, Value) ->
Squares = buildSquare(N, makeRows(N, N*N, Value, N)),
io:fwrite("Squares ready"), io:fwrite("~n"),
Result = lists:filter(fun(X) -> testsquare(X, N, Value) end, Squares),
io:write(length(Result)),
Result.
buildSquare(0, _) -> [[]];
buildSquare(Rows, AvailableRows) ->
[ [X|L] || L <- buildSquare(Rows-1, AvailableRows), X <- AvailableRows, onlyUniqueNumbers(lists:flatten([X|L]))].
onlyUniqueNumbers(List) -> erlang:length(List) == sets:size(sets:from_list(List)).
%produces all possible rows with a dimension of Fields and the Numbers from 1 to Numbers and the right sum for each row
makeRows(0,_,_,_) -> [[]];
makeRows(Fields, Numbers, Value, TargetLength) ->
[ [X|L] || X <- makeRows(Fields-1, Numbers, Value, TargetLength), L <- lists:seq(1,Numbers), checkRow([X|L], TargetLength, Value)].
checkRow(Row, Length, Value) when length(Row) < Length -> true;
checkRow(Row, Length, Value) ->
Sum = lists:sum(Row),
if Sum == Value -> true;
true -> false
end.
testsquare(Square, N, Value) -> checkAllDiagonal(Square, Value) andalso checkAllHorizontal(Square, Value) andalso checkAllVertical(Square, N, Value).
checkAllHorizontal([H|T], Value) ->
case checkHorizontal(H, Value, 0) of
true -> checkHorizontal(lists:nth(1, T), Value, 0);
false -> false
end;
checkAllHorizontal([], Value) -> true.
checkHorizontal([H|T], Value, Summe) -> checkHorizontal(T, Value, Summe + H);
checkHorizontal([], Value, Summe) when Summe == Value -> true;
checkHorizontal([], Value, Summe) -> false.
checkAllVertical(Square, N, Value) -> checkAllVertical(Square, N, Value, 1).
checkAllVertical(Square, N, Value, Column) ->
if
Column > N -> true;
true ->
case checkVertical(Square, Value, 0, Column) of
true -> checkAllVertical(Square, N, Value, Column + 1);
false -> false
end
end.
checkVertical([], Value, Summe, Column) when Summe == Value -> true;
checkVertical([], Value, Summe, Column) -> false;
checkVertical([H|T], Value, Summe, Column) -> checkVertical(T, Value, Summe + lists:nth(Column, H), Column).
checkAllDiagonal(Square, Value) ->
case checkDiagonal(Square, Value, 0, 1,1) of
true -> case checkDiagonal(Square, Value, 0, length(lists:nth(1, Square)),-1) of
true -> true;
false -> false
end;
false -> false
end.
checkDiagonal([H|T], Value, Summe, Position, Richtung) -> checkDiagonal(T, Value, Summe + lists:nth(Position, H), Position + Richtung, Richtung);
checkDiagonal([], Value, Summe, Position, Richtung) when Summe == Value -> true;
checkDiagonal([], Value, Summe, Position, Richtung) -> false.
好的，我尝试在计算过程的早期添加对行和正方形的检查。以下是修改后的功能。
buildSquare(0, _, _, _) -> [[]];
buildSquare(Rows, AvailableRows, RowLength, Value) ->
[ [X|L] || L <- buildSquare(Rows-1, AvailableRows, RowLength, Value), X <- AvailableRows, validateSquare([X|L], RowLength, Value)].
checkOnlyUniqueNumbers(List) -> erlang:length(lists:flatten(List)) == sets:size(sets:from_list(lists:flatten(List))).
validateSquare(List, RowLength, Value) when length(List) == RowLength -> testsquare(List, RowLength, Value) andalso checkOnlyUniqueNumbers(List);
validateSquare(List, _,_) -> checkOnlyUniqueNumbers(List).
%produces all possible rows with a dimension of Fields and the Numbers from 1 to Numbers
makeRows(0,_,_,_) -> [[]];
makeRows(Fields, Numbers, Value, TargetLength) ->
[ [X|L] || L <- makeRows(Fields-1, Numbers, Value, TargetLength), X <- lists:seq(1,Numbers), checkRow([X|L], TargetLength, Value)].
%Checks if the sum of the row is Value when the row has the needed length Length
checkRow(Row, Length, _) when length(Row) < Length -> checkOnlyUniqueNumbers(Row);
checkRow(Row, _, Value) ->
Sum = lists:sum(Row),
Sum == Value andalso checkOnlyUniqueNumbers(Row).