In mathematics, the Fibonacci series is a series of numbers, starting from 0 and 1, where every n-th number is the sum of (n-1)-th and (n-2)-th. It is named after Leonardo Fibonacci, an Italian mathematician who is considered as the most talented mathematician of the Middle Ages. He wrote about the series in his book Liber Abaci (Book of Calculation).
The Fibonacci numbers are used in the computational run-time analysis of Euclid’s algorithm to determine the greatest common divisor of two integers, in some pseudo-random number generator algorithms, in the IFF 8SVX audio file format lossy compression, etc.
The Fibonacci series in Java can be calculated in both recursive and non-recursive way. Of course, the recursive way is the worst since it can cause a stack overflow when the function is recursively called for large Fibonacci numbers.
Fibonacci Series without recursion
To see how to calculate the Fibonacci series using iteration, create a class called IterativeFibonacci with the following code:
IterativeFibonacci.java
package com.javacodegeeks.examples;
import java.util.Scanner;
public class IterativeFibonacci {
public static void main(String[] args) {
long primo = 0, secondo = 1;
long terzo;
Scanner stdIn = new Scanner(System.in);
System.out.print("How many numbers do you want to print? ");
int iter = stdIn.nextInt();
for (int i=0;i<iter;i++) {
System.out.print(primo + " ");
terzo = primo + secondo;
primo = secondo;
secondo = terzo;
}
stdIn.close();
}
}
In this example, I started the series from 0 and 1. Firstly, I get the amount of Fibonacci numbers the program has to print, then I make the calculations for the numbers.
This program makes the calculations based on three numbers. Initially, the program shows the first number, after that it calculates the third, then it moves to another number triplet; by making the second number its first and the third number its second. In the end, it goes to the initial point of printing the first number of the triplet, and so on.
The output of this program is this:
How many numbers do you want to print? 7 0 1 1 2 3 5 8
Fibonacci numbers with recursion
There is also another way of generating Fibonacci series, even though it may cause some problems sometimes. By using the recurrence relation Fn = Fn-1 + Fn-2 we can come up with a program to calculate the values of Fibonacci series using a recursive method.
To see this, create a class called RecursiveFibonacci with the following source code:
RecursiveFibonacci.java
package com.javacodegeeks.examples;
import java.util.Scanner;
public class RecursiveFibonacci {
public static long fibonacci(long n) {
if (n<0) throw new IllegalArgumentException("Can't accept negative arguments");
return (n < 2) ? n : fibonacci(n-1) + fibonacci(n-2);
}
public static void main(String[] args) {
Scanner stdIn = new Scanner(System.in);
System.out.print("How many numbers do you want to print? ");
int iter = stdIn.nextInt();
for (int i=0;i<iter;i++) {
System.out.print(fibonacci(i) + " ");
}
stdIn.close();
}
}
The static fibonacci(long n) method is the one which calculates the n-th item. If n is smaller than 2 (i.e. 0 or 1), it returns that value. If n is greater than 2, it calculates the Fibonacci value based on the recurrence relation. Of course, since we can’t calculate Fibonacci values for negative numbers, the method would throw an IllegalArgumentException.
The output would be the same as in the first example:
How many numbers do you want to print? 7 0 1 1 2 3 5 8
Download Code
You can download the full source code of this example here : FibonacciSeries
