As we saw in Chapter 10, The Functools Module, many algorithms can benefit from memoization. We'll start with a review of some previous examples to characterize the kinds of functions that can be helped with memoization.

In Chapter 6, Recursions and Reductions, we looked at a few common kinds of recursions. The simplest kind of recursion is a tail recursion with arguments that can be easily matched to values in a cache. If the arguments are integers, strings, or materialized collections, then we can compare arguments quickly to determine if the cache has a previously computed result.

We can see from these examples that integer numeric calculations such as computing factorial or locating a Fibonacci number will be obviously improved. Locating prime factors and raising integers to powers are more examples of numeric algorithms that apply to integer values.

When we looked at the recursive version of a Fibonacci number calculator, we saw that it contained two tail-call recursions...