Write a Java Program for the Fibonacci series using recursion. In the Fibonacci sequence, each number is the sum of the two preceding numbers, starting with 0 and 1.

Approach: The recursive solution calculates the Fibonacci number at a given position by summing the values of the previous two positions. The base cases are when the position is 0 or 1, where the method directly returns the same value. The series is generated by repeatedly invoking the recursive method for each index.

Although recursion provides a clean and intuitive implementation, it recalculates the same values multiple times, making it less efficient for larger inputs.

Java Solution:

public class FibonacciSeriesRecursion {

    public static int fibonacci(int position) {
        if (position <= 1) {
            return position;
        }

        return fibonacci(position - 1) + fibonacci(position - 2);
    }

    public static void main(String[] args) {
        int numberOfTerms = 10;

        System.out.println("Fibonacci Series:");

        for (int index = 0; index < numberOfTerms; index++) {
            System.out.print(fibonacci(index) + " ");
        }
    }
}

Output: 0 1 1 2 3 5 8 13 21 34

Time Complexity: O(2^n), because each recursive call generates two additional recursive calls, resulting in repeated calculations.

Space Complexity: O(n), due to the recursion call stack depth reaching up to n levels.

Key Interview Points: • Recursive Fibonacci is commonly asked to evaluate understanding of recursion and base conditions. • This implementation is not optimal for large inputs because it performs duplicate computations. • Dynamic Programming or memoization can reduce the time complexity to O(n), while an iterative approach can achieve O(n) time with O(1) extra space.