Writing Universal memoization function in C++11
Solution 1:
A compact one returning a lambda:
template <typename R, typename... Args>
std::function<R (Args...)> memo(R (*fn)(Args...)) {
std::map<std::tuple<Args...>, R> table;
return [fn, table](Args... args) mutable -> R {
auto argt = std::make_tuple(args...);
auto memoized = table.find(argt);
if(memoized == table.end()) {
auto result = fn(args...);
table[argt] = result;
return result;
} else {
return memoized->second;
}
};
}
In C++14, one can use generalized return type deduction to avoid the extra indirection imposed by returning std::function.
Making this fully general, permitting passing arbitrary function objects without wrapping them in std::function first is left as an exercise for the reader.
Solution 2:
The right way to do memoization in C++ is to mix the Y-combinator in.
Your base function needs a modification. Instead of calling itself directly, it takes a templateized reference to itself as its first argument (or, a std::function<Same_Signature> recursion as its first argument).
We start with a Y-combinator. Then we add in a cache on the operator() and rename it to memoizer, and give it a fixed signature (for the table).
The only thing left is to write a tuple_hash<template<class...>class Hash> that does a hash on a tuple.
The type of the function that can be memoized is (((Args...)->R), Args...) -> R, which makes the memoizer of type ( (((Args...) -> R), Args...) -> R ) -> ((Args...) -> R). Having a Y-combinator around to produce a 'traditional' recursive implementation can also be useful.
Note that if the function memoized modifies its args during a call, the memoizer will cache the results in the wrong spot.
struct wrap {};
template<class Sig, class F, template<class...>class Hash=std::hash>
struct memoizer;
template<class R, class...Args, class F, template<class...>class Hash>
struct memoizer<R(Args...), F, Hash> {
using base_type = F;
private:
F base;
mutable std::unordered_map< std::tuple<std::decay_t<Args>...>, R, tuple_hash<Hash> > cache;
public:
template<class... Ts>
R operator()(Ts&&... ts) const
{
auto args = std::make_tuple(ts...);
auto it = cache.find( args );
if (it != cache.end())
return it->second;
auto&& retval = base(*this, std::forward<Ts>(ts)...);
cache.emplace( std::move(args), retval );
return decltype(retval)(retval);
}
template<class... Ts>
R operator()(Ts&&... ts)
{
auto args = std::tie(ts...);
auto it = cache.find( args );
if (it != cache.end())
return it->second;
auto&& retval = base(*this, std::forward<Ts>(ts)...);
cache.emplace( std::move(args), retval );
return decltype(retval)(retval);
}
memoizer(memoizer const&)=default;
memoizer(memoizer&&)=default;
memoizer& operator=(memoizer const&)=default;
memoizer& operator=(memoizer&&)=default;
memoizer() = delete;
template<typename L>
memoizer( wrap, L&& f ):
base( std::forward<L>(f) )
{}
};
template<class Sig, class F>
memoizer<Sig, std::decay_t<F>> memoize( F&& f ) { return {wrap{}, std::forward<F>(f)}; }
live example with a hard-coded hash function based off this SO post.
auto fib = memoize<size_t(size_t)>(
[](auto&& fib, size_t i)->size_t{
if (i<=1) return 1;
return fib(i-1)+fib(i-2);
}
);
Solution 3:
Although @KerrekSB posted a link to another answer, I though I'd throw my answer in the ring as well (it's probably slightly less complicated than the linked answer, although in essence it's very similar):
#include <functional>
#include <map>
#include <tuple>
#include <utility>
/*! \brief A template functor class that can be utilized to memoize any
* given function taking any number of arguments.
*/
template <typename R, typename... Args>
struct memoize_wrapper
{
private:
std::map<std::tuple<Args...>, R> memo_;
std::function<R(Args...)> func_;
public:
/*! \brief Auto memoization constructor.
*
* \param func an the std::function to be memoized.
*/
memoize_wrapper(std::function<R(Args...)> func)
: func_(func)
{ }
/*! \brief Memoization functor implementation.
*
* \param a Argument values that match the argument types for the
* (previously) supplied function.
* \return A value of return type R equivalent to calling func(a...).
* If this function has been called with these parameters
* previously, this will take O(log n) time.
*/
R operator()(Args&&... a)
{
auto tup = std::make_tuple(std::forward<Args>(a)...);
auto it = memo_.find(tup);
if(it != memo_.end()) {
return it->second;
}
R val = func_(a...);
memo_.insert(std::make_pair(std::move(tup), val));
return val;
}
}; //end struct memoize_wrapper
Edit: Example usage:
Edit2: As pointed out, this doesn't work with recursive functions.
#include "utility/memoize_wrapper.hpp"
#include <memory>
#include <vector>
#include <algorithm>
#include <iostream>
long factorial(long i)
{
long result = 1;
long current = 2;
while(current <= i) {
result *= current;
++current;
}
return result;
}
int main()
{
std::vector<int> arg {10, 9, 8, 7, 6, 10, 9, 8, 7, 6};
std::transform(arg.begin(), arg.end(), arg.begin(), memoize_wrapper<long, long>(factorial));
for(long i : arg) {
std::cout << i << "\n";
}
}
Solution 4:
I struggled with the same problem. I created macro that also support (with small modification in recursive code) recursion. Here it is:
#include <map>
#include <tuple>
#define MEMOIZATOR(N, R, ...) \
R _ ## N (__VA_ARGS__); \
std::map<std::tuple<__VA_ARGS__>, R> _memo_ ## N; \
template <typename ... Args> \
R N (Args ... args) { \
auto& _memo = _memo_ ## N; \
auto result = _memo.find(std::make_tuple(args...)); \
if (result != _memo.end()) { \
return result->second; \
} \
else { \
auto result = _ ## N (args...); \
_memo[std::make_tuple(args...)] = result; \
return result; \
} \
}
The usage is really simple:
MEMOIZATOR(fibonacci, long int, int);
long int _fibonacci(int n) { // note the leading underscore
// this makes recursive function to go through wrapper
if (n == 1 or n == 2) {
return 1;
}
return fibonacci(n - 1) + fibonacci(n - 2);
}
fibonacci(40) // uses memoizator so it works in linear time
// (try it with and without memoizator)
See it in action: http://ideone.com/C3JEUT :)
Solution 5:
Below is a (thread safe) C++17 function template that acts like std::invoke but memoizes the result:
/**
* @brief Drop-in replacement for std::invoke which memoizes the return
* result.
*
* @param[in] function The function whose result needs to be cached
* @param[in] args The function arguments
*
* @tparam Function The function type
* @tparam Args The argument types
*
* @return A value obtained either by evaluating the function, or by
* recalling it from a cache.
*
* @note The function provided must not be a type-erase function object
* like a raw function pointer or std::function, because this
* function depends on the uniqueness of the Function template
* parameter. If you were to call invoke_memoized(f, a) and
* invoke_memoized(g, b) in the same translation unit, where f and g
* were function pointers of the same type, and a and b were
* arguments of the same type, you'd end up using the same cache for
* both functions f and g. A reasonable attempt is made to detect
* these misuse cases via static_assert.
*/
template<typename Function, typename... Args>
auto invoke_memoized(Function function, Args... args)
{
using key_type = std::tuple<Args...>;
using value_type = std::invoke_result_t<Function, Args...>;
static_assert(! std::is_same_v<Function, std::function<value_type(Args...)>>,
"cannot memoize on std::function (use a lambda instead)");
static_assert(! std::is_same_v<Function, value_type(*)(Args...)>,
"cannot memoize on function pointer (use a lambda instead)");
static std::mutex mutex;
static std::map<key_type, value_type> cache;
auto key = std::tuple(args...);
auto lock = std::lock_guard<std::mutex>(mutex);
if (cache.count(key))
{
return cache[key];
}
return cache[key] = std::apply(function, key);
}
You can use it like this:
auto c = invoke_memoized(std::plus<>(), 1, 2.3);
A static cache is maintained for each combination of the function object and argument types. As noted std::function and raw function pointers are rejected, as type-erased functions would get their caches mixed up. You can easily modify this function to impose limits on the cache size.