<s>[INST] What is memoization and how can I use it in Python? 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?
 [/INST] 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)
        return self.memo[args]

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

factorial = Memoize(factorial)

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