Implementation

Python decorators are generic and very powerful. You can find many examples of how they can be used at the decorator library of python.org (j.mp/pydeclib). In this section, we will see how we can implement a memoization decorator (j.mp/memoi). All recursive functions can benefit from memoization, so let's try a function number_sum() that returns the sum of the first n numbers. Note that this function is already available in the math module as fsum(), but let's pretend it is not.

First, let's look at the naive implementation (the number_sum_naive.py file):

def number_sum(n): 
    '''Returns the sum of the first n numbers''' 
    assert(n >= 0), 'n must be >= 0' 

    if n == 0:
        return 0
    else:
        return n + number_sum(n-1)  

if __name__ == '__main__': 
    from timeit import Timer 
    t = Timer('number_sum(30)', 'from __main__ import number_sum')
    print('Time: ', t.timeit())

A sample execution of this example shows how slow this implementation is. It...