3 Different ways to print Fibonacci series in Java

Given a number N, we need to find the Fibonacci Series up to the N term.

The Fibonacci series is a series of elements where, the previous two elements are added to get the next element, starting with 0 and 1. 

Examples:

Input: N = 10 
Output: 0 1 1 2 3 5 8 13 21 34 
Here first term of Fibonacci is 0 and second is 1, so that 3rd term = first(o) + second(1) etc and so on.

Input: N = 15 
Output: 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377  

Method 1 – Iterative

 Initialize the first and second numbers to 0 and 1. Following this, we print the first and second numbers. Then we send the flow to the iterative while loop where we get the next number by adding the previous two numbers and simultaneously we swap the first number with the second and the second with the third. Below is the implementation of the above approach: 

Java

// Java program for the above approach

class GFG {

    // Function to print N Fibonacci Number
    static void Fibonacci(int N)
    {
        int num1 = 0, num2 = 1;

        int counter = 0;

        // Iterate till counter is N
        while (counter < N) {

            // Print the number
            System.out.print(num1 + " ");

            // Swap
            int num3 = num2 + num1;
            num1 = num2;
            num2 = num3;
            counter = counter + 1;
        }
    }

    // Driver Code
    public static void main(String args[])
    {
        // Given Number N
        int N = 10;

        // Function Call
        Fibonacci(N);
    }
}

Output

0 1 1 2 3 5 8 13 21 34 

Time Complexity: O(N) 
Auxiliary Space: O(1)

Method 2 – Using Recursion:

Since Fibonacci Number is the summation of the two previous numbers. We can use recursion as per the following condition:

1. Get the number whose Fibonacci series needs to be calculated.
2. Recursively iterate from value N to 1:
   • Base case: If the value called recursively is less than 1, the return 1 the function.
   • Recursive call: If the base case is not met, then recursively call for previous two value as:

recursive_function(N – 1) + recursive_function(N – 2);

• Return statement: At each recursive call(except the base case), return the recursive function for the previous two value as:

recursive_function(N – 1) + recursive_function(N – 2);

Below is the implementation of the above approach:

Java

// Recursive implementation of
// Fibonacci Series

class GFG {

    // Function to print the fibonacci series
    static int fib(int n)
    {
        // Base Case
        if (n <= 1)
            return n;

        // Recursive call
        return fib(n - 1)
            + fib(n - 2);
    }

    // Driver Code
    public static void
    main(String args[])
    {
        // Given Number N
        int N = 10;

        // Print the first N numbers
        for (int i = 0; i < N; i++) {

            System.out.print(fib(i) + " ");
        }
    }
}

Output

0 1 1 2 3 5 8 13 21 34 

Time Complexity: O(2^N)  
Auxiliary Space: O(1)

An alternate way to print the Fibonacci series  using memoization :

In above example, Its time complexity is O(2ⁿ)  which can reduce to O(n) using the memoization technique it will help to optimize recursion method. This is because the function computes each Fibonacci number only once and stores it in the array.

Java

/*package whatever //do not write package name here */

import java.io.*;

class GFG {
    public static void main(String[] args)
    {
        int n = 10; // Number of terms to print
        int[] memo = new int[n + 1];
        for (int i = 1; i <= n; i++) {
            System.out.print(fibonacci(i, memo) + " ");
        }
    }

    public static int fibonacci(int n, int[] memo)
    {
        if (memo[n] != 0)
            return memo[n];
        if (n == 1 || n == 2)
            return 1;
        else {
            memo[n] = fibonacci(n - 1, memo)
                      + fibonacci(n - 2, memo);
            return memo[n];
        }
    }
}

Output

1 1 2 3 5 8 13 21 34 55 

Time Complexity: O(n)  
Auxiliary Space: O(n)

Method 3 – Using Dynamic Programming

We can avoid the repeated work done in method 2 by storing the Fibonacci numbers calculated so far. Below are the steps:

1. Create an array arr[] of size N.
2. Initialize arr[0] = 0, arr[1] = 1.
3. Iterate over [2, N] and update the array arr[] as:

arr[i] = arr[i – 2] + arr[i – 1]

1. Print the value of arr[N].

Below is the implementation of the above approach: 

Java

// Dynamic Programming approach for
// Fibonacci Series

class fibonacci {

    // Function to find the fibonacci Series
    static int fib(int n)
    {

        // Declare an array to store
        // Fibonacci numbers.
        // 1 extra to handle case, n = 0
        int f[] = new int[n + 2];

        int i;

        // 0th and 1st number of
        // the series are 0 and 1
        f[0] = 0;
        f[1] = 1;

        for (i = 2; i <= n; i++) {

            // Add the previous 2 numbers
            // in the series and store it
            f[i] = f[i - 1] + f[i - 2];
        }

        // Nth Fibonacci Number
        return f[n];
    }

    public static void
    main(String args[])
    {
        // Given Number N
        int N = 10;

        // Print first 10 term
        for (int i = 0; i < N; i++)
            System.out.print(fib(i) + " ");
    }
}

Output

0 1 1 2 3 5 8 13 21 34 

Time Complexity: O(N)
Auxiliary Space: O(N)