Fibonacci series in Ada using recursion

Question

In this code, I am trying to write a program that prints out the Fibonacci series based on the users' input (Index, Size). An then, the program should print out all the Fibonacci numbers between Index..Size. I have trouble, writing a recursion that calculates and prints out the Fibonacci numbers. Any suggestions?

with Ada.Text_IO;         use Ada.Text_IO;
with Ada.Integer_Text_IO; use Ada.Integer_Text_IO;
with Ada.Text_IO, Ada.Unchecked_Deallocation;

procedure Fibonacci is
   type Arr is array (Positive range <>) of Integer;
   type Array_Access is access Arr;
   Size, Index : Positive;
   Variable    : Array_Access;
   procedure Free is new Ada.Unchecked_Deallocation (Arr, Array_Access);

   procedure Recursion (Item : Arr) is                  --Recursion
   begin
      Put_Line
        (Item (Item'First)'Image);                   --Prints out the numbers
      Recursion
        (Item
           (Item'First + Item'First + 1 ..
                Item'Last));     --Calculating the Fibonacci numbers
   end Recursion;

begin
   Put ("Welcome to the Fibonacci number series!");
   Put
     ("Enter an initial value and how many Fibonacci numbers you want to print: ");
   Get (Index);
   Get (Size);
   Variable := new Arr (Index .. Size);
   Recursion (Variable);
end Fibonacci;

Example: Enter Index (the initial value of the Fibonacci series): 1
Enter Size (how many Fibonacci numbers to print): 5
The first 5 Fibonacci numbers are: 1 1 2 3 5

Answer 1

From Wikipedia,

In mathematics, the Fibonacci numbers, commonly denoted F_n, form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1. That is,
F₀ = 0
F₁ = 1
and
F_n = F_{n - 1} + F_{n - 2}

which translates pretty directly into

function Fibonacci (N : Natural) return Natural is
  (case N is
      when 0 => 0,
      when 1 => 1,
      when others => Fibonacci (N - 1) + Fibonacci (N - 2));

or, old style,

function Fibonacci (N : Natural) return Natural is
begin
   if N = 0 then
      return 0;
   elsif N = 1 then
      return 1;
   else
      return Fibonacci (N - 1) + Fibonacci (N - 2);
   end if;
end Fibonacci;

You do have to do your printing outside the function, and admittedly there’s an inefficiency in repeatedly calculating the lower results, but you weren’t asking for efficiency.

Answer 2

Here is how you can do it (this code is based on https://rosettacode.org/wiki/Fibonacci_sequence#Recursive)

with Ada.Text_IO;
with Ada.Integer_Text_IO;

procedure Fibonacci is

   First, Amount: Positive;

   function Fib(P: Positive) return Positive is --Recursion
   begin
      if P <= 2 then
         return 1;
      else
         return Fib(P-1) + Fib(P-2);
      end if;
   end Fib;

begin
   Ada.Text_IO.Put_Line("Welcome to the Fibonacci number series!");
   Ada.Text_IO.Put_Line("Enter an initial value and how many Kombinacci numbers you want to print: ");
   Ada.Integer_Text_IO.Get(First);
   Ada.Integer_Text_IO.Get(Amount);
   for I in First .. First + Amount loop
      Ada.Text_IO.Put("Fibonacci(" & Positive'Image(I) & " ) = ");
      Ada.Text_IO.Put_Line(Positive'Image(Fib(I)));
   end loop;
end Fibonacci;