What is memoization and how can I use it in Python?

Question

I just started Python and I've got no idea what memoization is and how to use it. Also, may I have a simplified example?

Answer 1

Memoization effectively refers to remembering ("memoization" → "memorandum" → to be remembered) results of method calls based on the method inputs and then returning the remembered result rather than computing the result again. You can think of it as a cache for method results. For further details, see page 387 for the definition in Introduction To Algorithms (3e), Cormen et al.

A simple example for computing factorials using memoization in Python would be something like this:

factorial_memo = {}
def factorial(k):
    if k < 2: return 1
    if k not in factorial_memo:
        factorial_memo[k] = k * factorial(k-1)
    return factorial_memo[k]

You can get more complicated and encapsulate the memoization process into a class:

class Memoize:
    def __init__(self, f):
        self.f = f
        self.memo = {}
    def __call__(self, *args):
        if not args in self.memo:
            self.memo[args] = self.f(*args)
        #Warning: You may wish to do a deepcopy here if returning objects
        return self.memo[args]

Then:

def factorial(k):
    if k < 2: return 1
    return k * factorial(k - 1)

factorial = Memoize(factorial)

A feature known as "decorators" was added in Python 2.4 which allow you to now simply write the following to accomplish the same thing:

@Memoize
def factorial(k):
    if k < 2: return 1
    return k * factorial(k - 1)

The Python Decorator Library has a similar decorator called memoized that is slightly more robust than the Memoize class shown here.