-module(misc).
-compile(export_all).

sq(X) -> X * X.

sumsq(X,Y) -> sq(X) + sq(Y).

f(A) -> sumsq(A+1,A*2).

%% -----------

sqrtIter(Guess, X) ->
    case goodEnough(Guess, X) of
        true ->
	    Guess;
        false ->
	    sqrtIter(improved(Guess, X), X)
    end.

improved(Guess,X) -> average(Guess, X/Guess).

average(X,Y) -> (X+Y)/2.

goodEnough(Guess,X) -> abs(sq(Guess) - X) < 0.00001.

sqrt(X) -> sqrtIter(1.0, X).

%% ----------

%% @spec factorial1(N::integer()) ->
%%                       F::integer()
%% @pre N >= 0.
%%   F == N!
factorial1(0) -> 1;
factorial1(N) when N>0 ->
    N * factorial1(N-1).

factorial2(N) when N >= 0 ->
    factorial2(N,1,1).
factorial2(N,Product,Counter) ->
    if (Counter > N) ->
	    Product;
       true ->
	    factorial2(N, Product*Counter, Counter+1)
    end.

factorial21(N) when N >= 0 ->
    factorial21(N,1,1).

factorial21(N,Product,Counter) when Counter > N ->
    Product;
factorial21(N,Product,Counter) ->
    factorial21(N, Product*Counter, Counter+1).

%% @pre : N >= 0.
factorial3(N) ->
    factorial3(1,N).
factorial3(Product, 0) ->
    Product;
factorial3(Product, Counter) ->
    factorial3(Product*Counter, Counter-1).

%% -----------

map(_F,[]) -> [];
map(F,[X|Xs]) -> [F(X)|map(F,Xs)].

%% -----------

%% @spec fib(N::integer()) ->
%%               F::integer().
%% @pre 0 =< N.
%% F az N-edik Fibonacci-szám
fib1(0) -> 0;
fib1(1) -> 1;
fib1(N) when N>1 -> fib1(N-1)+fib1(N-2).

fib2(N) when N>=0 -> fib2(N,0,0,1).

fib2(N,N,A,_B) -> A;
fib2(N,I,A,B) -> fib2(N,I+1,A+B,A).

fib3(N) when N>=0 -> fib3(N,0,1).

fib3(0,A,_B) -> A;
fib3(I,A,B) -> fib3(I-1,A+B,A).

%% -----------

valtas(Osszeg) ->
    valtas(Osszeg,5).

valtas(Osszeg,Ermefajta) ->
    if Osszeg < 0 orelse Ermefajta == 0 ->
	    0;
       Osszeg == 0 ->
	    1;
       true ->
	    valtas(Osszeg, Ermefajta-1) +
		valtas(Osszeg-cimlet(Ermefajta), Ermefajta)
    end.

cimlet(1) -> 1;
cimlet(2) -> 5;
cimlet(3) -> 10;
cimlet(4) -> 25;
cimlet(5) -> 50.

%% misc:valtas(10) == 4. misc:valtas(100) == 292.

%% -----------

%% @spec expt1(B::integer(),N::integer()) -> R::integer().
%% @pre N >= 0.
%% B N-edik hatványa R.
expt1(_B,0) -> 1;
expt1(B,N) when N>0 -> B * expt1(B,N-1).

expt2(B,N) when N>=0 -> expt2(B,N,1).

expt2(_B,0,P) -> P;
expt2(B,N,P) ->
    expt2(B,N-1,B*P).

expt3(_B,0) -> 1;
expt3(B,N) when N>0 ->
    case even(N) of
	true ->
	    sq(expt3(B,N div 2));
	false ->
	    B * expt3(B,N-1)
    end.

even(N) -> N rem 2 == 0.

expt4(B,N) when N>=0 -> expt4(B,N,1).

expt4(_B,0,R) -> R;
expt4(B,N,R) ->
    case even(N) of
	true ->
	    expt4(B,N div 2,R*R);
	false ->
	    expt4(B,N-1,R*B)
    end.

%% f(), X0 = misc:expt4(2,0), X1 = misc:expt4(2,1), X2 = misc:expt4(2,2), X4 = misc:expt4(2,4), {X0,X1,X2,X4}.

expt5(_B,0) -> 1;           %% \textrm{Kell ez a klóz!}
expt5(B,N) when N>0 -> expt5(B,N,B).

expt5(_B,1,R) -> R;
expt5(B,N,R) ->
    case even(N) of
	true ->
	    expt5(B,N div 2,R*R);
	false ->
	    expt5(B,N-1,R*B)
    end.

%% f(), X0 = misc:expt5(2,0), X1 = misc:expt5(2,1), X2 = misc:expt5(2,2), X3 = misc:expt5(2,3), X4 = misc:expt5(2,4), X5 = misc:expt5(2,5), X6 = misc:expt5(2,6), X7 = misc:expt5(2,7), X8 = misc:expt5(2,8), {X0,X1,X2,X3,X4,X5,X6,X7,X8}.

expt6(_B,0) -> 1;           %% \textrm{Kell ez a klóz!}
expt6(B,N) when N>0 -> expt6(B,N-1,B).

expt6(_B,0,R) -> R;
expt6(B,N,R) ->
    case even(N) of
	true ->
	    expt6(B,N div 2,B*B*R);
	false ->
	    expt6(B,N-1,R*B)
    end.


expt7(_B,0) -> 1;           %% \textrm{Kell ez a klóz!}
expt7(B,N) when N>0 -> expt7(B,N,B).

expt7(_B,1,R) -> R;
expt7(B,N,R) ->
    case even(N) of
	true ->
	    expt7(B,N div 2,B*B*R);
	false ->
	    expt7(B,N-1,R*B)
    end.