Concave_polygon

-module(solution).
-export([main/0]).

rotate({A0,A1},{B0,B1},{C0,C1}) ->
        (B0-A0)*(C1-B1)-(B1-A1)*(C0-B0).

sort_list(StartPoint,All) ->
    lists:sort(fun(X,Y)-> Rot=rotate(StartPoint,X,Y), if Rot=<0 -> true; Rot>0 -> false end end,All).

find_start_point([{A,B}|[]]) -> {A,B};
find_start_point([{A,B},{C,D}|Points]) ->
    if (A < C orelse B < D) -> find_start_point([{A,B}|Points]);
       (A >= C orelse B >= D) -> find_start_point([{C,D}|Points])
       end.

main() ->
    {ok,File}=file:open("test4",read),
    {ok,Prom}=file:read_line(File),
    [Count,_]=string:split(Prom,"\n"),
    {ok,Bin}=file:read_file("test4"),
    [First|Pairs]=binary:split(Bin,[<<"\n">>],[global]),
    Data=parse_bin(Pairs,[]),
    file:close(File),
    main(lists:reverse(Data)).

main(Points) ->
    StartPoint=find_start_point(Points),
    io:format("~s~n",[concave(sort_list(StartPoint,Points))]).

parse_bin([],List) -> List;
parse_bin([Pair|Tail],List) ->
    if Pair == <<>> ->
        parse_bin([],List);
       Pair /= <<>> ->
        [A,B]=binary:split(Pair,[<<" ">>],[global]),
        parse_bin(Tail,[{binary_to_integer(A),binary_to_integer(B)}|List])
    end.

concave([{_,_},{_,_}|Tail]) -> no.
concave([{A,B},{C,D},{E,F}|Tail]) ->
    Rot=rotate({A,B},{C,D},{E,F}),
    if Rot>0  -> yes;
       Rot<0  -> concave([{C,D},{E,F}|Tail]);
       Rot ==0 -> concave([{C,D},{E,F}|Tail])
    end;