Functools Module


Python changed it's sorting methods to accept a key function. Those functions take a value and return a key which is used to sort the arrays.

Old comparison functions used to take two values and return -1, 0 or +1 if the first argument is small, equal or greater than the second argument respectively. This is incompatible to the new key-function.

That's where functools.cmp_to_key comes in:

>>> import functools
>>> import locale
>>> sorted(["A", "S", "F", "D"], key=functools.cmp_to_key(locale.strcoll))
['A', 'D', 'F', 'S']

Example taken and adapted from the Python Standard Library Documentation.


The @lru_cache decorator can be used wrap an expensive, computationally-intensive function with a Least Recently Used cache. This allows function calls to be memoized, so that future calls with the same parameters can return instantly instead of having to be recomputed.

@lru_cache(maxsize=None)  # Boundless cache
def fibonacci(n):
    if n < 2:
        return n
    return fibonacci(n-1) + fibonacci(n-2)

>>> fibonacci(15)

In the example above, the value of fibonacci(3) is only calculated once, whereas if fibonacci didn't have an LRU cache, fibonacci(3) would have been computed upwards of 230 times. Hence, @lru_cache is especially great for recursive functions or dynamic programming, where an expensive function could be called multiple times with the same exact parameters.

@lru_cache has two arguments

  • maxsize: Number of calls to save. When the number of unique calls exceeds maxsize, the LRU cache will remove the least recently used calls.
  • typed (added in 3.3): Flag for determining if equivalent arguments of different types belong to different cache records (i.e. if 3.0 and 3 count as different arguments)

We can see cache stats too:

>>> fib.cache_info()
CacheInfo(hits=13, misses=16, maxsize=None, currsize=16)

NOTE: Since @lru_cache uses dictionaries to cache results, all parameters for the function must be hashable for the cache to work.

Official Python docs for @lru_cache. @lru_cache was added in 3.2.


The partial function creates partial function application from another function. It is used to bind values to some of the function's arguments (or keyword arguments) and produce a callable without the already defined arguments.

>>> from functools import partial
>>> unhex = partial(int, base=16)
>>> unhex.__doc__ = 'Convert base16 string to int'
>>> unhex('ca11ab1e')

partial(), as the name suggests, allows a partial evaluation of a function. Let's look at at following example:

In [2]: from functools import partial

In [3]: def f(a, b, c, x):
   ...:     return 1000*a + 100*b + 10*c + x

In [4]: g = partial(f, 1, 1, 1)

In [5]: print g(2)

When g is created, f, which takes four arguments(a, b, c, x), is also partially evaluated for the first three arguments, a, b, c,. Evaluation of f is completed when g is called, g(2), which passes the fourth argument to f.

One way to think of partial is a shift register; pushing in one argument at the time into some function. partial comes handy for cases where data is coming in as stream and we cannot pass more than one argument.


In Python 3.x, the reduce function already explained here has been removed from the built-ins and must now be imported from functools.

from functools import reduce
def factorial(n):
    return reduce(lambda a, b: (a*b), range(1, n+1))


When we want to create an orderable class, normally we need to define the methods __eq()__, __lt__(), __le__(), __gt__() and __ge__().

The total_ordering decorator, applied to a class, permits the definition of __eq__() and only one between __lt__(), __le__(), __gt__() and __ge__(), and still allow all the ordering operations on the class.

class Employee:


    def __eq__(self, other):
        return ((self.surname, == (other.surname,

    def __lt__(self, other):
        return ((self.surname, < (other.surname,

The decorator uses a composition of the provided methods and algebraic operations to derive the other comparison methods. For example if we defined __lt__() and __eq()__ and we want to derive __gt__(), we can simply check not __lt__() and not __eq()__.

Note: The total_ordering function is only available since Python 2.7.