What is Fibonacci Series?
In Fibonacci series, next number is the sum of previous two numbers. The first two numbers of Fibonacci series are 0 and 1.
The Fibonacci numbers are significantly used in the computational run-time study of algorithm to determine the greatest common divisor of two integers.In arithmetic, the Wythoff array is an infinite matrix of numbers resulting from the Fibonacci sequence.
The Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, ...
Java code using For Loop
//Using For Loop
public class FibonacciExample {
public static void main(String[] args)
{
// Set it to the number of elements you want in the Fibonacci Series
int maxNumber = 10;
int previousNumber = 0;
int nextNumber = 1;
System.out.print("Fibonacci Series of "+maxNumber+" numbers:");
for (int i = 1; i <= maxNumber; ++i)
{
System.out.print(previousNumber+" ");
/* On each iteration, we are assigning second number
* to the first number and assigning the sum of last two
* numbers to the second number
*/
int sum = previousNumber + nextNumber;
previousNumber = nextNumber;
nextNumber = sum;
}
}
} Output:
Fibonacci Series of 10 numbers:0 1 1 2 3 5 8 13 21 34
Program Logic: - previousNumber is initialized to 0 and nextNumber is initialized to 1
- For Loop iterates through
maxNumber - Display the previousNumber
- Calculates sum of previousNumber and nextNumber
- Updates new values of previousNumber and nextNumber
Java code using While Loop
You can also generate Fibonacci Series using a While loop in Java.
//Using While Loop
public class FibonacciWhileExample {
public static void main(String[] args)
{
int maxNumber = 10, previousNumber = 0, nextNumber = 1;
System.out.print("Fibonacci Series of "+maxNumber+" numbers:");
int i=1;
while(i <= maxNumber)
{
System.out.print(previousNumber+" ");
int sum = previousNumber + nextNumber;
previousNumber = nextNumber;
nextNumber = sum;
i++;
}
}
} Output:
Fibonacci Series of 10 numbers:0 1 1 2 3 5 8 13 21 34
The only difference in the program logic is use of WHILE Loop to print Fibonacci Numbers
Fibonacci Series Based On The User Input
//fibonacci series based on the user input
import java.util.Scanner;
public class FibonacciExample {
public static void main(String[] args)
{
int maxNumber = 0;
int previousNumber = 0;
int nextNumber = 1;
System.out.println("How many numbers you want in Fibonacci:");
Scanner scanner = new Scanner(System.in);
maxNumber = scanner.nextInt();
System.out.print("Fibonacci Series of "+maxNumber+" numbers:");
for (int i = 1; i <= maxNumber; ++i)
{
System.out.print(previousNumber+" ");
/* On each iteration, we are assigning second number
* to the first number and assigning the sum of last two
* numbers to the second number
*/
int sum = previousNumber + nextNumber;
previousNumber = nextNumber;
nextNumber = sum;
}
}
} Program Logic: The logic is same as earlier. Instead of hardcoding the number of elements to show in Fibonacci Series, the user is asked to write number.
Java code using Recursion
//Using Recursion
public class FibonacciCalc{
public static int fibonacciRecursion(int n){
if(n == 0){
return 0;
}
if(n == 1 || n == 2){
return 1;
}
return fibonacciRecursion(n-2) + fibonacciRecursion(n-1);
}
public static void main(String args[]) {
int maxNumber = 10;
System.out.print("Fibonacci Series of "+maxNumber+" numbers: ");
for(int i = 0; i < maxNumber; i++){
System.out.print(fibonacciRecursion(i) +" ");
}
}
}
Output:
Fibonacci Series of 10 numbers: 0 1 1 2 3 5 8 13 21 34
Program Logic: A recursive function is one that has the capability to call itself.
fibonacciRecursion():
- Takes an input number. Checks for 0, 1, 2 and returns 0, 1, 1 accordingly because Fibonacci sequence starts with 0, 1, 1.
- When input n is >=3, The function will call itself recursively. The call is done two times. Let’s see example for input of 4.
fibonacciRecursion (4)
It will recursively call fibonacciRecursion function for values 2 and 3
fibonacciRecursion (2) \\ call for value 0 and 1
fibonacciRecursion (0) = 0
fibonacciRecursion (1) = 1
fibonacciRecursion (3) \\ It will call for 1 and 2
fibonacciRecursion (1) = 1
fibonacciRecursion (2) \\ It will call for 0 and 1
fibonacciRecursion (0) = 0
fibonacciRecursion (1) = 1
Now result is added 0+1+1+0+1=3
