What is Fibonacci memoization and how does it work?

What is Fibonacci memoization and how does it work?

Fibonacci memoization is an optimization technique used to improve the efficiency of calculating Fibonacci numbers by storing previously computed values.

Can you show me an example of Fibonacci memoization in Python?

Sure! Here's a simple example:

def fibonacci(n, memo={}):
    if n in memo:
        return memo[n]
    if n <= 1:
        return n
    memo[n] = fibonacci(n-1, memo) + fibonacci(n-2, memo)
    return memo[n]

This function uses a dictionary to store previously calculated Fibonacci numbers.

What are the benefits of using memoization?

The main benefits of using memoization are reduced time complexity, as it avoids redundant calculations, and improved performance, especially for large inputs.

Are there any downsides to using memoization?

Yes, the downsides include increased memory usage due to storing results and potential overhead in managing the memoization structure.