Problem Statement

The factorial of a number, written as

n !

{\displaystyle n!}

, is defined as

n !

n ( n − 1 ) ( n − 2 ) . . . ( 2 ) ( 1 )

{\displaystyle n!=n(n-1)(n-2)...(2)(1)}

. Multifactorials generalize factorials as follows: In all cases, the terms in the products are positive integers. If we define the degree of the multifactorial as the difference in successive terms that are multiplied together for a multifactorial (the number of exclamation marks), then the task is twofold:

Note: The wikipedia entry on multifactorials gives a different formula. This task uses the Wolfram mathworld definition.

Let's start with the solution:

with Ada.Text_IO; use Ada.Text_IO;
procedure Mfact is

   function MultiFact (num : Natural; deg : Positive) return Natural is
      Result, N : Integer := num;
   begin
      if N = 0 then return 1; end if;
      loop
         N := N - deg; exit when N <= 0; Result := Result * N;
      end loop; return Result;
   end MultiFact;

begin
   for deg in 1..5 loop
      Put("Degree"& Integer'Image(deg) &":");
      for num in 1..10 loop Put(Integer'Image(MultiFact(num,deg))); end loop;
      New_line;
   end loop;
end Mfact;