Memoized, recursive factorial function?

Question

I know how to do memoization in Python easily but I need a faster way to compute them, so I am using C++. However, I have no clue how to memoize. I understand that it's about storing values into an array or vector and then scanning for its value when retrieving, but it'd be really helpful to see how this is done so I can try its speed.

Answer 1

Just for fun, here's a little generic memoizer I wrote some time ago. It requires variadic templates, naturally:

template <template <typename...> class Container, typename...> struct Memo;

template <typename R, typename... Args, template <typename...> class Container>
struct Memo<Container, R, std::tuple<Args...>>
{
  Memo(std::function<R(Args...)> f) : func(f) { }

  R operator()(Args && ...args)
  {
    const auto arg = std::make_tuple(args...);
    typename CacheContainer::const_iterator it = cache.find(arg);

    if (it == cache.cend())
    {
      it = cache.insert(typename CacheContainer::value_type(arg, func(std::forward<Args>(args)...))).first;
      std::cout << "New call, memoizing..." << std::endl;
    }
    else
    {
      std::cout << "Found it in the cache!" << std::endl;
    }

    return it->second;
  }

private:

  typedef Container<typename std::tuple<Args...>, R> CacheContainer;

  std::function<R(Args...)> func;
  CacheContainer cache;
};


template <typename R, typename... Args>
Memo<std::map, R, std::tuple<Args...>> OMapMemoize(R(&f)(Args...))
{
  return Memo<std::map, R, std::tuple<Args...>>(f);
}
template <typename R, typename... Args>
Memo<std::unordered_map, R, std::tuple<Args...>> UMapMemoize(R(&f)(Args...))
{
  return Memo<std::unordered_map, R, std::tuple<Args...>>(f);
}

I'm not entirely sure if I got the rvalue-forwardiness right, as it's a long time ago that I wrote this. Anyway, here's a test case:

int foo(double, char) { return 5; }

int main()
{
  auto f = OMapMemoize(foo);
  auto g = UMapMemoize(foo);

  int a, b;

  a = f(1.0, 'a');
  a = f(1.0, 'a');
  a = f(1.0, 'a');
  a = f(1.0, 'a');

  b = g(1.0, 'a');
  b = g(1.0, 'a');
  b = g(1.0, 'a');
  b = g(1.0, 'a');

  return a;
}

Answer 2

Well the neatest way I can think of to do this in C++ is probably using a function object to store the memoized values. I guess this is probably slightly similar to your python decorator, although I have never really done any python. The code would look something like this:

template <typename T, T (*calc)(T)>
class mem {
  std::map<T,T> mem_map;

public:
  T operator()(T input) {
    typename std::map<T,T>::iterator it;

    it = mem_map.find(input);
    if (it != mem_map.end()) {
      return it->second;
    } else {
      T output = calc(input);
      mem_map[input] = output;
      return output;
    }
  }
};

The code defines a template class that takes in a typename and a function pointer, the function operator is then defined on the class allowing it to be called. The function operator takes in an input value checks if said value is in a map, then either simply returns it from the map or calculates it (using the function pointer), adds it to the map and then returns it.

So assuming you define some processing function like say:

int unity(int in) { return in; }

You would use the code like this:

mem<int, unity> mem_unity;
int y;
y = mem_unity(10);

So we define an instance of the mem class which takes our value type and processing function as template parameters, then simply call this class as a function.

Answer 3

No one except a student learning recursion would calculate factorials that way.

Memoization is a very good idea, especially if you're going to call the method repeatedly. Why throw away good work?

Another consideration is a better way to calculate factorials: use the natural log of the gamma function. It'll hold out against overflow longer, because you return a double value. The natural log will grow more slowly than the value. If you're calculating combinations, the natural log changes multiplication and division into addition and subtraction.

But, by all means, memoize for any implementation you use. If you're writing it in C++, I'd recommend using a std:map with the argument x as the key and the ln(gamma(x)) as the value.

Sorry, it's been too long since I've written C++ and STL. I'd rather use a hash map with O(1) read access time to having to iterate over the keys in O(n) .

Answer 4

I like relying on lambda capture as in (uses std=c++14 )

template<typename R, typename... Args>
auto memoize(std::function<R(Args...)>&& f)
{
  using F = std::function<R(Args...)>;
  std::map<std::tuple<Args...>,R> cache;
  return ([cache = std::map<std::tuple<Args...>,R>{}, 
           f = std::forward<F>(f)](Args&&... args) mutable
    {
      std::tuple<Args...> t(args...);
      if (cache.find(t) == cache.end())
        {
          R r = f(std::forward<Args...>(args)...);
          cache[t] = r;
        }
      return cache[t];
    });
}