## Fibonacci Series - Data Structures and Algorithms

Fibonacci series generates the 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

Hence, 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 as :

1. Fibonacci Iterative Algorithm

First we try to draft the 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

2. Fibonacci Recursive Algorithm

Let us learn how to create a 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

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