## Thursday, July 12, 2012

### Java program - Fibonacci series with recursion example

Write a Java program to print Fibonacci series up to a given number or create simple Java program to calculate Fibonacci number is common Java questions on fresher interview and homework. Fibonacci series is also a popular topic on various programming exercises in school and colleges. 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. One more coding question which is quite popular is printing prime numbers in Java which I have discussed earlier. In this tutorial we will see example of both recursive and iterative algorithm for Fibonacci numbers:

Code Example to calculate and print Fibonacci numbers in Java
Here is complete code example of printing Fibonacci Series in Java. Fibonacci series is printed using both Iterative method and recursive method implemented using Java programming language.

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 FibonacciCalculator {

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

}

}

Output:
Enter number upto which Fibonacci series to print:
12
Fibonacci series upto 12 numbers :
1 1 2 3 5 8 13 21 34 55 89 144

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.

## Fibonacci number in Java with memorization

Here is the code example of printing Fibonacci number with memorization technique :
/*
* 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);

Output:
Time taken to calculate Fibonacci number upto 100M without memorization:149479613
Time taken to calculate Fibonacci number upto 100M with memorization:118972384

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 or am I missing something?

That's all on writing Java program to calculate and print Fibonacci number. Fibonacci number is good question for programming exercise but when asked as question in Java interview you just need to be more detailed and precise about what you are doing.

1. I had a homework exercise to write a Java program to print Fibonacci series up-to 100. Can I use your Java program to print Fibonacci series, is using recursion in a homework or programming exercise is valid ?

2. Shouldn't that be called "memoization" ?

3. The comments in your code are wrong : you are indeed using recursion, but not tail-recursion.

Tail recursion means that the last action performed by the method is directly returning the value from the recursive call, without modifying it.

In your example, your function calls itself recursively twice, before adding the two return values and returning the result. Hence, you aren't performing tail recursion.

A correct tail recursion implementation would be :

public static int tailRecursiveFibonacci(long number) {
// Bootstrap
return tailRecursiveFibonacci(3, 1, 1, number - 3);
}
private static int tailRecursiveFibonacci(long currentRank, int antePreviousResult, int previousResult, long howManyMoreRanks) {
final int resultForCurrentRank = antePreviousResult + previousResult;
if (howManyMoreRanks == 0) return resultForCurrentRank;
return tailRecursiveFibonacci(currentRank + 1, previousResult, resultForCurrentRank, howManyMoreRanks - 1);
}

4. There is overflow for 48th fibonacci number for int return type.

1. See other comment about recursion vs tail recursion. The tail recursive solution carries everything it needs with it rather than leaving it behind to be recombined when the stack is unwound, thus does not need multiple stack frames and won't cause a stack overflow.

5. Anonymous is correct.. this program will overflow the moment it crosses integer bounds.. i think we should use double as the datatype to initialize the variables.