What are Fibonacci algorithms and how do they work?

What are Fibonacci algorithms and how do they work?

Fibonacci algorithms are methods to compute Fibonacci numbers, which are part of a sequence where each number is the sum of the two preceding ones.

Can you show me a simple implementation in Python?

Sure! Here's a simple recursive implementation:

def fibonacci(n):
    if n <= 1:
        return n
    return fibonacci(n-1) + fibonacci(n-2)

What are the time complexities of different Fibonacci algorithms?

The recursive approach has an exponential time complexity of O(2^n), while the iterative approach is O(n) and the matrix exponentiation method is O(log n).

Are there any real-world applications of Fibonacci algorithms?

Yes, Fibonacci algorithms are used in computer science, financial modeling, and even in nature to describe patterns in growth.