Fibonacci Series in Java

Fibonacci Series in Java: The Fibonacci sequence is a sequence of numbers where each number is the sum of the two preceding ones, beginning with 0 and 1. This article will demonstrate how to generate the Fibonacci sequence in Java up to a specific term, denoted as N, where N represents the specified number.

In the Fibonacci sequence, each subsequent number is the total of the two preceding numbers. For instance, the sequence starts with 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on. The sequence begins with the numbers 0 and 1.

There are two methods to develop a program for the Fibonacci sequence in Java:

• Fibonacci Sequence without recursion
• Fibonacci Sequence with recursion

Fibonacci Series in Java without using recursion

• Initialize variables: Start by initializing the first two numbers of the series. Usually, the first two numbers are 0 and 1.
• Use a loop: Use a loop to calculate the next numbers in the series by adding the last two numbers.
• Update variables: Update the variables to hold the last two numbers for the next iteration.

Here’s a Java program to generate the Fibonacci series without using recursion:

public class Fibonacci {public static void main(String[] args) {    int n = 10; // Number of terms to display    int first = 0, second = 1;    System.out.println('Fibonacci Series without recursion:');    for (int i = 1; i <= n; ++i) {        System.out.print(first + ' ');        // Compute the next term        int next = first + second;        // Update variables        first = second;        second = next;    }}}

Explanation

Variables Initialization:

int first = 0, second = 1;

first and second are initialized to the first two numbers of the Fibonacci series.

Loop through the series:

for (int i = 1; i <= n; ++i) {System.out.print(first + ' ');int next = first + second;first = second;second = next;}/code>

• The loop runs n times to generate n terms of the series.
• System.out.print(first + ” “); prints the current term.
• int next = first + second; calculates the next term in the series.
• first = second; and second = next; update first and second for the next iteration.

Output:
The program will output the first 10 terms of the Fibonacci series:

0 1 1 2 3 5 8 13 21 34

Fibonacci Series using recursion in java

• Define the Base Cases: The first two numbers in the Fibonacci series are 0 and 1. These are our base cases.
• Define the Recursive Case: For any other number in the series, it is the sum of the two preceding numbers. So, fibonacci(n) = fibonacci(n-1) + fibonacci(n-2).

Here’s a simple Java program to calculate the Fibonacci series using recursion

public class Fibonacci {// Method to calculate Fibonacci numberpublic static int fibonacci(int n) {// Base casesif (n == 0) {return 0;}if (n == 1) {return 1;}// Recursive casereturn fibonacci(n - 1) + fibonacci(n - 2);}public static void main(String[] args) {int number = 10; // Let's find the first 10 Fibonacci numbersSystem.out.println('Fibonacci series up to ' + number + ' terms:');// Loop to print the Fibonacci seriesfor (int i = 0; i < number; i++) {System.out.print(fibonacci(i) + ' ');}}}