Fibonacci Series

Fibonacci series is series of natural number where next number is equivalent to sum of previous two number e.g. fn = fn-1 + fn-2. First two numbers of Fibonacci series is always 1, 1. In this Java program example for Fibonacci series we create function to calculate Fibonacci number and then print those numbers on Java console. Another twist in this questions is that some time interviewer ask to write Java program for Fibonacci numbers using recursion, so its better you prepare for both iterative and recursive version of Fibonacci number.

package com.test;

import java.util.Scanner;

/**
 * Java program to calculate and print Fibonacci number using both recursion and Iteration.
 * Fibonacci number is sum of previous two Fibonacci numbers fn= fn-1+ fn-2
 * first 10 Fibonacci numbers are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55
 * @author
 */
public class Test2 {

    public static void main(String args[]) {
    
       //input to print Fibonacci series upto how many numbers
        System.out.println("Enter number upto which Fibonacci series to print: ");
        int number = new Scanner(System.in).nextInt();
      
        System.out.println("Fibonacci series upto " + number +" numbers : ");
        //printing Fibonacci series upto number
        for(int i=1; i<=number; i++){
            System.out.print(fibonacci2(i) +" ");
        }
    } 
  
    /*
     * Java program for Fibonacci number using recursion.
     * This program uses tail recursion to calculate Fibonacci number for a given number
     * @return Fibonacci number
     */
    public static int fibonacci(int number){
        if(number == 1 || number == 2){
            return 1;
        }
        return fibonacci(number-1) + fibonacci(number -2); //tail recursion
    }
  
    /*
     * Java program to calculate Fibonacci number using loop or Iteration.
     * @return Fibonacci number
     */
    public static int fibonacci2(int number){
        if(number == 1 || number == 2){
            return 1;
        }
        int fibo1=1, fibo2=1, fibonacci=1;
        for(int i= 3; i<= number; i++){
            fibonacci = fibo1 + fibo2; //Fibonacci number is sum of previous two Fibonacci number
            fibo1 = fibo2;
            fibo2 = fibonacci;
        }
        return fibonacci; //Fibonacci number
    }  
}

After asking to write simple Java program to print Fibonacci series and later asking for Fibonacci series using recursion, another important question interviewer ask is how do you improve your Fibonacci function both iterative and recursive one? A technique called memorization can be used to drastically improve performance of method which calculates Fibonacci number. if you look at the method it repetitive creates same Fibonacci number e.g. In order to calculate 10th Fibonacci number function first create first 9 Fibonacci number, this could be very time consuming if you just increase the upper limit from 10 to 10K. In memorization programming technique result of earlier calculation is cached and reused. So you don't need to create same Fibonacci number if you already have calculated it. You can write code for Fibonacci series with memorization by just using a HashMap  and checking if Fibonacci number for a corresponding number is already exits or not and calculate only if it doesn't exist.

    /*
     * Java Program to calculate Fibonacci numbers with memorization
     * This is quite fast as compared to previous Fibonacci function especially for
     * calculating factorial of large numbers.
     */
    public static int improvedFibo(int number){
        Integer fibonacci = cache.get(number);
        if(fibonacci != null){
            return fibonacci; //fibonacci number from cache
        }
        fibonacci = fibonacci2(number); //fibonacci number not in cache, calculating it
        cache.put(number, fibonacci); //putting fibonacci number in cache for future request
        return fibonacci;
    }

Comparison
        //comparison of performance of Fibonacci number with memorization
        int number = 100000000;
        long startTime = System.nanoTime();
        int result = fibonacci2(number); //fibonacci number with memorization
        long elapsedTime = System.nanoTime() - startTime;
        System.out.println("Time taken to calculate Fibonacci number upto 100M without memorization:" + elapsedTime);
      
        startTime = System.nanoTime();
        result = improvedFibo(number); //Fibonacci number with memorization
        elapsedTime = System.nanoTime() - startTime;

        System.out.println("Time taken to calculate Fibonacci number upto 100M with memorization:" + elapsedTime);

Interesting point is that improved method only shows better performance for large numbers like 100M otherwise iterative version of Fibonacci method is faster. That could be explained by extra work done by improved method in terms of storing value in cache and getting it from there.