Memoization in Ruby and Python

Wikipedia defines memoization as “an optimization technique used primarily to speed up computer programs by having function calls avoid repeating the calculation of results for previously-processed inputs.”. This typically means caching the returning value of a function in a dictionary of sorts using the parameters passed to the function as a key. This is done in order to reuse that returning value immediately without calculating it again, when the function is invoked with the same arguments. Even though we are trading space for time, it is often invaluable for speeding up certain recursive functions and when dealing with dynamic programming where intermediate calls are often repeated many times.

Using memoization in Ruby is very easy thanks to the memoize gem. The first step to getting started is therefore to install it:

$ sudo gem install memoize
Successfully installed memoize-1.2.3
1 gem installed
Installing ri documentation for memoize-1.2.3...
Installing RDoc documentation for memoize-1.2.3...

Now we can use the memoize method as illustrated in the example below:

require 'rubygems'
require 'memoize'
require 'benchmark'
include Memoize

def fib(n)
  return n if n < 2
  fib(n-1) + fib(n-2)
end

Benchmark.bm(15) do |b|
  b.report("Regular fib:") { fib(35) }
  b.report("Memoized fib:") { memoize(:fib); fib(35)}
end

In the first block we simply invoke fib(35), while in the second one we first invoke the method memoize(:fib) to memoize the method fib. Running this code on my machine prints the following:

                     user     system      total        real
Regular fib:    55.230000   0.160000  55.390000 ( 55.819205)
Memoized fib:    0.000000   0.000000   0.000000 (  0.001305)

We went from almost a minute of run time to an instantaneous execution. Optionally we could even pass a file location to the function memoize and this would use marshaling to dump and load the cached values on/from disk.

For Python we can write a simple decorator that behaves in a similar manner. In its simplest form it can be implemented as follows:

# memoize.py

def memoize(function):
    cache = {}
    def decorated_function(*args):
        try:
            return cache[args]
        except KeyError:
            val = function(*args)
            cache[args] = val
            return val
    return decorated_function

Or more efficiently:

# memoize.py

def memoize(function):
    cache = {}
    def decorated_function(*args):
        if args in cache:
            return cache[args]
        else:
            val = function(*args)
            cache[args] = val
            return val
    return decorated_function

When the memoized function has been invoked, we look in the cache to see if an entry for the given arguments already exist. If it does, we immediately return that value. If not, we call the function, cache the results and return its returning value.

Truth be told, the limit of this approach lies in the fact that since we are using a dictionary, only immutable objects can be used as keys. For example, we can use a tuple but are not allowed to have a list as a parameter. For the example within this article, this approach will suffice, but to take advantage of memoization when using arguments that are mutable, you may want to consider the approach described in this recipe.

We can now rewrite the Ruby example above in Python as follows:

import timeit
from memoize import memoize

def fib1(n):
    if n < 2:
        return n
    else:
        return fib1(n-1) + fib1(n-2)

@memoize
def fib2(n):
    if n < 2:
        return n
    else:
        return fib2(n-1) + fib2(n-2)	

t1 = timeit.Timer("fib1(35)", "from __main__ import fib1")
print t1.timeit(1)
t2 = timeit.Timer("fib2(35)", "from __main__ import fib2")
print t2.timeit(1)

Running this code on my machine prints the following:

9.32223105431
0.000314950942993

In Python 2.5’s case by employing memoization we went from more than nine seconds of run time to an instantaneous result.

Granted we don’t write Fibonacci applications for a living, but the benefits and principles behind these examples still stand and can be applied to everyday programming whenever the opportunity, and above all the need, arises.

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