--------------------------------------------
-- Josephus problem using a discrete loop --
--------------------------------------------

with Gnat.IO, Ada.Numerics.Aux;
use Gnat.IO, Ada.Numerics.Aux;

procedure main
is

	-- function ceiling:
	function ceiling (r: double) return positive
	is
	begin
		if r <= 0.0 then
			raise constraint_error;
		elsif double(positive (r)) = r then
			return positive (r);
		else
			return positive (r) + 1;
		end if;
	end ceiling;
   
	-- function josephus: N...number of suicides, m...cycle length
	function josephus (N: positive; m: positive) return positive
	is
		x : positive;
		a : double;
	begin
		a := double(m);
		discrete d := 1 in 1..((m-1)*N) 
			new d := ceiling((a/(a-1.0))*double(d))
		loop
			d := ceiling((a/(a-1.0))*double(d));
			x := d;
		end loop;
		return m*N+1-x;
	end josephus;

	N, m : integer;

begin
	put ("------------------"); new_line;
	put ("josephus algorithm"); new_line;
	put ("------------------"); new_line (2);

	loop
		put ("number of suicides (0 to quit) ? "); get (N);      
		exit when N <= 0;
		put ("length of cycle (> 1) ? "); get (m);
		if m > 1 then
			put ("--> survivor = ");
			put (josephus (N, m));
		else
			put ("--> invalid circle length!");
		end if;
		new_line (2);
	end loop;
	new_line; put ("Bye, bye!"); new_line;
end main;