Memoizing previous results with lru_cache

The lru_cache decorator transforms a given function into a function that might perform more quickly. The LRU means Least Recently Used: a finite pool of recently used items is retained. Items not frequently used are discarded to keep the pool to a bounded size.

Since this is a decorator, we can apply it to any function that might benefit from caching previous results. We might use it as follows:

from functools import lru_cache
@lru_cache(128)
def fibc(n):
    """Fibonacci numbers with naive recursion and caching
    >>> fibc(20)
    6765
    >>> fibc(1)
    1
    """
    if n == 0: return 0
    if n == 1: return 1
    return fibc(n-1) + fibc(n-2)

This is an example based on Chapter 6, Recursions and Reductions. We've applied the @lru_cache decorator to the naïve Fibonacci number calculation. Because of this decoration, each call to the fibc(n) function will now be checked against a cache maintained by the decorator. If the argument...