What is memoization and how can I use it in Python

Question

I just started Python and I ve got no idea what memoization is and how to use it  Also  may I have a simplified example

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New to Python 3 2 is functools lru cache  By default  it only caches the 128 most recently used calls  but you can set the maxsize to None to indicate that the cache should never expire   import functools   functools lru cache maxsize None  def fib num       if num  lt  2          return num     else          return fib num-1    fib num-2    This function by itself is very slow  try fib 36  and you will have to wait about ten seconds    Adding lru cache annotation ensures that if the function has been called recently for a particular value  it will not recompute that value  but use a cached previous result  In this case  it leads to a tremendous speed improvement  while the code is not cluttered with the details of caching

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I ve found this extremely useful  def memoize function       from functools import wraps      memo            wraps function      def wrapper  args           if args in memo              return memo args          else              rv   function  args              memo args    rv             return rv     return wrapper    memoize def fibonacci n       if n  lt  2  return n     return fibonacci n - 1    fibonacci n - 2   fibonacci 25

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Memoization is keeping the results of expensive calculations and returning the cached result rather than continuously recalculating it    Here s an example   def doSomeExpensiveCalculation self  input       if input not in self cache           lt do expensive calculation gt          self cache input    result     return self cache input    A more complete description can be found in the wikipedia entry on memoization

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Memoization effectively refers to remembering   memoization     memorandum    to be remembered  results of method calls based on the method inputs and then returning the remembered result rather than computing the result again  You can think of it as a cache for method results  For further details  see page 387 for the definition in Introduction To Algorithms  3e   Cormen et al   A simple example for computing factorials using memoization in Python would be something like this   factorial memo      def factorial k       if k  lt  2  return 1     if k not in factorial memo          factorial memo k    k   factorial k-1      return factorial memo k    You can get more complicated and encapsulate the memoization process into a class   class Memoize      def   init   self  f           self f   f         self memo          def   call   self   args           if not args in self memo              self memo args    self f  args           Warning  You may wish to do a deepcopy here if returning objects         return self memo args    Then   def factorial k       if k  lt  2  return 1     return k   factorial k - 1   factorial   Memoize factorial    A feature known as  decorators  was added in Python 2 4 which allow you to now simply write the following to accomplish the same thing    Memoize def factorial k       if k  lt  2  return 1     return k   factorial k - 1    The Python Decorator Library has a similar decorator called memoized that is slightly more robust than the Memoize class shown here

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Well I should answer the first part first  what s memoization   It s just a method to trade memory for time  Think of Multiplication Table   Using mutable object as default value in Python is usually considered bad  But if use it wisely  it can actually be useful to implement a memoization   Here s an example adapted from http   docs python org 2 faq design html why-are-default-values-shared-between-objects  Using a mutable dict in the function definition  the intermediate computed results can be cached  e g  when calculating factorial 10  after calculate factorial 9   we can reuse all the intermediate results   def factorial n   cache  1 1            try                      return  cache n                 except IndexError           cache n    factorial n-1  n         return  cache n

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The other answers cover what it is quite well  I m not repeating that  Just some points that might be useful to you    Usually  memoisation is an operation you can apply on any function that computes something  expensive  and returns a value  Because of this  it s often implemented as a decorator  The implementation is straightforward and it would be something like this  memoised function   memoise actual function    or expressed as a decorator   memoise def actual function arg1  arg2       body

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Let s not forget the built-in hasattr function  for those who want to hand-craft  That way you can keep the mem cache inside the function definition  as opposed to a global    def fact n       if not hasattr fact   mem            fact mem    1  1      if not n in fact mem          fact mem n    n   fact n - 1      return fact mem n

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cache      def fib n       if n  lt   1          return n     else          if n not in cache              cache n    fib n-1    fib n-2          return cache n

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Here is a solution that will work with list or dict type arguments without whining   def memoize fn          returns a memoized version of any function that can be called     with the same list of arguments      Usage  foo   memoize foo          def handle item x           if isinstance x  dict               return make tuple sorted x items             elif hasattr x     iter                  return make tuple x          else              return x      def make tuple L           return tuple handle item x  for x in L       def foo  args    kwargs           items cache   make tuple sorted kwargs items             args cache   make tuple args          if  args cache  items cache  not in foo past calls              foo past calls  args cache  items cache     fn  args   kwargs          return foo past calls  args cache  items cache       foo past calls          foo   name      memoized     fn   name       return foo   Note that this approach can be naturally extended to any object by implementing your own hash function as a special case in handle item  For example  to make this approach work for a function that takes a set as an input argument  you could add to handle item   if is instance x  set       return make tuple sorted list x

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Memoization is the conversion of functions into data structures  Usually one wants the conversion to occur incrementally and lazily  on demand of a given domain element--or  key    In lazy functional languages  this lazy conversion can happen automatically  and thus memoization can be implemented without  explicit  side-effects

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Just wanted to add to the answers already provided  the Python decorator library has some simple yet useful implementations that can also memoize  unhashable types   unlike functools lru cache

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Solution that works with both positional and keyword arguments independently of order in which keyword args were passed  using inspect getargspec    import inspect import functools  def memoize fn       cache   fn cache           functools wraps fn      def memoizer  args    kwargs           kwargs update dict zip inspect getargspec fn  args  args            key   tuple kwargs get k  None  for k in inspect getargspec fn  args          if key not in cache              cache key    fn   kwargs          return cache key      return memoizer   Similar question  Identifying equivalent varargs function calls for memoization in Python

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Memoization is basically saving the results of past operations done with recursive algorithms in order to reduce the need to traverse the recursion tree if the same calculation is required at a later stage   see http   scriptbucket wordpress com 2012 12 11 introduction-to-memoization   Fibonacci Memoization example in Python   fibcache      def fib num       if num in fibcache          return fibcache num      else          fibcache num    num if num  lt  2 else fib num-1    fib num-2          return fibcache num

[python] What is memoization and how can I use it in Python?

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