How would you program a recursive solution to find the nth Fibonacci number?

Question Analysis

The problem requires you to implement a recursive solution to find the nth Fibonacci number. The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1. The sequence typically looks like this: 0, 1, 1, 2, 3, 5, 8, and so on. The goal is to compute the nth number in this sequence using recursion, which is a method where the solution to a problem depends on solutions to smaller instances of the same problem.

Answer

To implement a recursive solution for finding the nth Fibonacci number, follow these steps:

1. Base Cases:
   • If n is 0, return 0.
   • If n is 1, return 1.
2. Recursive Case:
   • For n >= 2, the nth Fibonacci number is the sum of the two preceding Fibonacci numbers: fib(n) = fib(n-1) + fib(n-2).

Here is a simple implementation in Python:

def fibonacci(n):
    # Base cases
    if n == 0:
        return 0
    elif n == 1:
        return 1
    # Recursive case
    else:
        return fibonacci(n-1) + fibonacci(n-2)

# Example usage:
n = 5
print(f"The {n}th Fibonacci number is: {fibonacci(n)}")

Explanation:

• The function fibonacci takes an integer n as input.
• It checks if n is 0 or 1, returning 0 or 1 respectively.
• For any other value of n, it recursively calls itself to compute the sum of the Fibonacci numbers at positions n-1 and n-2.

Note:

• This recursive approach is straightforward but not the most efficient for large n due to redundant calculations. Consider using memoization or an iterative approach for better efficiency in practical scenarios.