Convexhull_h

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

rotate({A0,A1},{B0,B1},{C0,C1}) ->
    if(C0<A0 andalso C0<B0) -> ((B0-A0)*(C1-B1)-(B1-A1)*(C0-B0));
    true -> (B0-A0)*(C1-B1)-(B1-A1)*(C0-B0)
        end.

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.

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

main() ->
    {ok,[Count]}=io:fread("","~d"),
    {PPoints,StartPoint}=read_data(Count,[]),
    Prom=lists:delete(StartPoint,PPoints),
    Points=sort_list(StartPoint,Prom),
    SortedData=lists:delete(lists:nth(1,Points),Points),
    %%io:format("SortedList: ~p~nsecond: ~p~n",[SortedData,lists:nth(1,SortedData)]),
    marvis(SortedData,[lists:nth(1,Points),StartPoint]).

read_data(Count,Acc) when Count /=0 ->
    {ok,[A,B]}=io:fread("","~d~d"),
    read_data(Count-1,[{A,B}|Acc]);
read_data(Count,Acc) when Count==0 ->
    {lists:reverse(Acc),find_start_point(Acc)}.

marvis([],[{Ax,Ay},{Bx,By}|Tail]) ->
    io:format("~p~p~p~n",[{Ax,Ay},{Bx,By},Tail]),
    Perim=perim({Ax,Ay},lists:last(Tail)),
    perimetr(lists:reverse([{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 -> %%io:format("prom >0 : ~p~p~p~n",[{Fx,Fy},{Bx,By},Tail]),
          marvis(List, [{Fx,Fy},{Bx,By}|Tail]);
       Rot > 0 -> %%io:format("prom =<0 : ~p~p~p~p~n",[{Fx,Fy},{Ax,Ay},{Bx,By},Tail]),
        marvis(List, [{Fx,Fy},{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)).