def fib(n):
    if n == 0: return 1
    if n == 1: return 1
    return fib(n-1) + fib(n-2)
fib(33)

def fib_memo(n):
    # A[i] is going to hold fib(i)
    A = [None] * (n+1)
    A[0] = 1
    A[1] = 1
    for i in range(2,n+1):
        A[i] = A[i-1] + A[i-2]
    return A[n]
fib_memo(3)

def fib_fancy(n):
    prev1 = 1
    prev2 = 1
    for i in range(2,n+1):
        curr = prev1 + prev2
        # shift over
        prev2 = prev1
        prev1 = curr
    return curr
fib_fancy(8)

# Implicit Memoization
class Memoize:
    def __init__(self, function):
        self.function = function
        self.storage = {}
    def __call__(self, n):
        if n in self.storage:
            print("Using precomputed", n)            
            return self.storage[n]
        else:
            print("Computing the first time", n)
            ans = self.function(n)
            self.storage[n] = ans
            return ans

@Memoize
def fib(n):
    if n == 0: return 1
    if n == 1: return 1
    return fib(n-1) + fib(n-2)
fib(300)

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