Can you give an example of memoization?

What is memoization and can you give me an example?

Memoization is an optimization technique used to speed up function calls by storing the results of expensive function calls and returning the cached result when the same inputs occur again.

Can you show me a code example of memoization?

Sure! Here's a simple example in Python:

def memoize(f):
    cache = {}
    def helper(x):
        if x not in cache:
            cache[x] = f(x)
        return cache[x]
    return helper

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

In this example, the fibonacci function uses memoization to store previously computed values.

How does this improve performance?

By storing the results of previous calculations, memoization avoids redundant computations, significantly reducing the time complexity, especially for recursive functions like Fibonacci.