ConvexHull_notfinished

-module(solution).
-compile(export_all).

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

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("test_case",read),
    {ok,Prom}=file:read_line(File),
    [Count,_]=string:split(Prom,"\n"),
    io:format("~s~n",[Count]),
    {ok,Bin}=file:read_file("test_case"),
    [First|Pairs]=binary:split(Bin,[<<"\n">>],[global]),
    Data=parse_bin(Pairs,[]),
    file:close(File),
    main(Data).


main([{A,B}|Points]) ->
    StartPoint=find_start_point({A,B},Points),
    io:format("SP = ~p~n",[StartPoint]),
    jarvis(StartPoint,lists:reverse([{A,B}|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.

jarvis(StartPoint,All) ->
    NewList=lists:sort(fun(X,Y)-> Rot=rotate(StartPoint,Y,X), if Rot<0 -> true; Rot>0 -> false; Rot==0 -> false end end,lists:delete(StartPoint,All)),
    prom(NewList,[lists:last(lists:reverse(NewList)),StartPoint]).

prom([{Fx,Fy}|List],[{Ax,Ay},{Bx,By}|Tail]) ->
    marvis(List,[{Ax,Ay},{Bx,By}|Tail]).

marvis([],[{Ax,Ay},{Bx,By}|Tail]) ->
    Perim=perim({Ax,Ay},lists:last(Tail)),
    perimetr([{Ax,Ay},{Bx,By}|Tail],Perim);

marvis([{Fx,Fy}|List],[{Ax,Ay},{Bx,By}|Tail]) ->
    Rot=rotate({Bx,By},{Ax,Ay},{Fx,Fy}),
    if Rot < 0 -> marvis([{Fx,Fy}|List], [{Bx,By}|Tail]);
       Rot > 0 -> marvis(List, [{Fx,Fy},{Ax,Ay},{Bx,By}|Tail]);
       Rot =:= 0 -> marvis(List, [{Ax,Ay},{Bx,By}|Tail])
    end.

perimetr([{_,_}],Perim) ->
    io:format("~p~n",[Perim]);
perimetr([{Ax,Ay},{Bx,By}|Tail],Perim) ->
    N = perim({Ax,Ay},{Bx,By}),
    perimetr([{Bx,By}|Tail],Perim+N).

perim({Ax,Ay},{Bx,By}) ->
    math:sqrt(math:pow(Bx-Ax,2)+math:pow(By-Ay,2)).