Recursion: Fibonacci Series

Fibonacci Series generates subsequent number by adding two previous numbers. Fibonacci series starts from two numbers − F₀ & F₁. The initial values of F₀ & F₁ can be taken 0, 1 or 1, 1 respectively.

Fibonacci series satisfies the following conditions −

Fn = Fn-1 + Fn-2

So a Fibonacci series can look like this −

F₈ = 0 1 1 2 3 5 8 13

or, this −

F₈ = 1 1 2 3 5 8 13 21

For illustration purpose, fibonacci of F₈ is displayed below −

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Fibonacci Iterative Algorithm

First we try to draft iterative algorithm for Fibonacci series.

Procedure Fibonacci(n)
   declare f0, f1, fib, loop 
   
   set f0 to 0
   set f1 to 1
   
   display f0, f1
   
   for loop ← 1 to n
   
      fib ← f0 + f1   
      f0 ← f1
      f1 ← fib

      display fib
   end for
	
end procedure

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Fibonacci Recursive Algorithm

Now we shall learn how to create recursive algorithm Fibonacci series. The base criteria of recursion.

START
Procedure Fibonacci(n)
   declare f0, f1, fib, loop 
   
   set f0 to 0
   set f1 to 1
   
   display f0, f1
   
   for loop ← 1 to n
   
      fib ← f0 + f1   
      f0 ← f1
      f1 ← fib

      display fib
   end for

END