What is fibonacci series in Java with example?
How do you calculate Fibonacci in Java?
What is a Fibonacci series example?
How do you find the sum of the Fibonacci series in Java?
In this blog, we will understand the concept of Fibonacci series in Java language. But before going ahead, we need to understand the Fibonacci series and its properties. The Fibonacci series in Java is a series of numbers in which each member is obtained by adding the previous two members. Each item of the Fibonacci series is called a Fibonacci number.
To comprehend this model, you ought to realize the essential Java programming subjects like capabilities, circles, contingent proclamations, and so on. So kindly allude to those subjects prior to hopping into the Fibonacci series in java issue.
Eg :- 0,1,1,2,3,5,8,13,21,34 etc is an example of fibonacci series
The first fibonacci numbers are 0 and 1 respectively
F(N) = F(N-1)+F(N-2)
The above expression is the general equation followed by every Fibonacci number. The above equation also helps us to find the following Fibonacci numbers.
Next, we will discuss printing the Fibonacci series in java language. There are multiple ways in which one could print the Fibonacci series in Java. But we will discuss the most common one in detail. We will also discuss the other crucial method in brief.
- Print Fibonacci Series in Java using Recursion
- Print Fibonacci Series in Java Iteratively
Print Fibonacci Series in Java using Recursion
Since the Fibonacci Number is nothing but the summation of the two previous numbers, we can use Recursion with the following condition:
- Get which Fibonacci series term needs to be calculated, i.e., 1st,2nd,3rd etc.
- Recursively iterate from value N to 1:
- Base case: Here, we need to specify two conditions to meet the base case, i.e., if n is equal to 1 or n is equal to 0, return n.Since we are making two recursive calls at one time for fib_2, we will call fib_1 and fib_0. If we specify the base case only when n equals 1, our code will get a recursion depth error since fib_0 will not meet the base case.
- Recursive call: If the base case condition is not met, then we will make a recursive call for the last two numbers, i.e., n-1,n-2 as:
recursive_function(N – 1) + recursive_function(N – 2);
- Return statement: At each recursive call, return the sum of the Fibonacci value of the previous two numbers found using recursion
recursive_function(N – 1) + recursive_function(N – 2);
Below we can see the implementation of the above approach:
Code:-
//Import scanner
import java.util.Scanner;
// Fibonacci Series in Java using Recursion Implementation
class coding_ninja {
// Function to print the fibonacci series
public static int fibonacci(int n) {
// Base Case
if (n==1||n==0) {
return n;
}
// Recursive call
return fibonacci(n – 1)+ fibonacci(n – 2);
}
// Main Function
public static void main(String [] args) {
// Create scanner object
Scanner sc = new Scanner(System.in);
// Take N input
int N = sc.nextInt();
// Print the first N numbers
for (int i = 0; i < N; i++) {
System.out.print(fibonacci(i) + “,”);
}
}
}
Output:-
8
0,1,1,2,3,5,8,13,
Print Fibonacci Series in Java Iteratively
For printing the Fibonacci series in Java using iteration, we first need to Initialize the first and second numbers to 0 and 1 (These two num1 and num2 represent the first two numbers of the series). Following this, we will print the first and second numbers. After that, we will enter the flow to the iterative for a loop. We will get the next series member by adding the previous two members. Simultaneously, we swap the first number with the second number and the second number with the third number.
Code:-
// Import scanner
import java.util.Scanner;
public class coding_ninja {
// Fibonacci Function
public static void Fibonacci(int N) {
// Initialising the first two fibonacci number
int num1 = 0, num2 = 1;
// Initialising Counter
for(int i=0;i<N;i+=1) {
System.out.print(num1+”,”);
// Swap
int num3 = num2 + num1;
num1 = num2;
num2 = num3;
}
}
public static void main(String[] args) {
// Create scanner object
Scanner sc = new Scanner(System.in);
// Take N input
int N = sc.nextInt();
// Call fibonacci function to get N fibonacci Numbers
Fibonacci(N);
// Close Scanner
sc.close();
}
Output:-
8
0,1,1,2,3,5,8,13,
Approach: (Dynamic Programming)
The Third approach for the Fibonacci series in Java problem is as follows.
- Create an array arr1[] of size N.
- Initiate arr1[0] = 0, arr1[1] = 1.
- Loop over [2, N] and update the following array arr1[] as:
- arr1[i] = arr1[i – 2] + arr1[i – 1]
- Print the value of arr1[N].
Example for Fibonacci series
Example : Let’s take a number N=7.
Code
// Program to print Fibonacci series in java
// Dynamic Programming approach for
// Fibonacci Series
class fab {
// Function to find the N fibonacci Series
static int fib_series(int n)
{
// initialize an array to store Fibonacci numbers.
// 1 extra to handle case, n = 0
int fx[] = new int[n + 2];
int i;
// 0th and 1st number of
// the series are 0 and 1
fx[0] = 0;
fx[1] = 1;
for (i = 2; i <= n; i++) {
// Add the last 2 numbers
// in the series and store it
fx[i] = fx[i – 1] + fx[i – 2];
}
// Nth Fibonacci Number
return fx[n];
}
public static void
main(String args[])
{
// provide Number N
int N = 7;
// Print first 10 Fibonacci Number
for (int i = 0; i < N; i++)
System.out.print(fib_series(i) + ” “);
}
}
Output
0 1 1 2 3 5 8
There are numerous ways to solve or get the n Fibonacci number series. Other than the above-discussed codes. We could tweak the above code in different ways, i.e., by using a while loop, creating a method for Fibonacci number calculation, and much more. But some effective or promising approaches could be used to get the Fibonacci series in Java.
- The first method is using Recursion, which we have explained above.
- The second method is by using Dynamic Programming. Repeated work done in the recursion method code could be avoided by storing the Fibonacci numbers we have calculated.
- Another method to get the Fibonacci series in Java is using the direct formula for the nth term of the Fibonacci series.
Fn = {[(√5 + 1)/2] ^ n} / √5
- One more way to get the nth Fibonacci series is Using the power of the matrix {{1, 1}, {1, 0}}: This approach is another O(n) time .Solution to the method is if we multiply n times the matrix M = {{1,1},{1,0}} to itself (in other words we are calculating power(M, n)), then we will get the (n+1)th Fibonacci number as the element at the row 0 and column 0 i.e, at index (0, 0) in the resultant matrix.
- Above discussed approach could be optimized to work in O(Logn) time complexity. We could reduce the time complexity by making a recursive multiplication to get power(M, n)
Conclusion
In this article, we have learned about the Fibonacci series. We have discussed multiple concepts about it and learned how to print the Fibonacci series in java easily. In java, multiple concepts can be learned at an initial and mid-level to get expertise in java. Some concepts include final keywords in java, java basics, oops concepts etc.
