Fibonacci numbers using Big Integers

Lecture 76:-  Fibonacci numbers using Big Integers

To calculate Fibonacci numbers using BigInteger in Java, you can use a loop or recursion. Here's an example using a loop to generate Fibonacci numbers:

javaCopy code
import java.math.BigInteger;

public class FibonacciWithBigInteger {
    public static void main(String[] args) {
        int n = 50; // Number of Fibonacci numbers to generate

        // Generate and print Fibonacci numbers
        for (int i = 0; i < n; i++) {
            BigInteger fibonacciNumber = fibonacci(i);
            System.out.println("Fibonacci(" + i + "): " + fibonacciNumber);
        }
    }

    public static BigInteger fibonacci(int n) {
        BigInteger a = BigInteger.ZERO;
        BigInteger b = BigInteger.ONE;

        if (n == 0) {
            return a;
        } else if (n == 1) {
            return b;
        } else {
            for (int i = 2; i <= n; i++) {
                BigInteger next = a.add(b);
                a = b;
                b = next;
            }
            return b;
        }
    }
}

In this example, we create a method fibonacci that calculates the nth Fibonacci number using BigInteger. We initialize a and b to BigInteger.ZERO and BigInteger.ONE, respectively. Then, we use a loop to calculate the Fibonacci numbers from 0 to n. Each Fibonacci number is the sum of the previous two numbers (a and b), and we update the values of a and b accordingly.

The main method calls the fibonacci method to generate and print the first n Fibonacci numbers.

Note that BigInteger allows you to handle large Fibonacci numbers that may not fit into primitive data types like int or long.

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