How do I write a generic memoize function?

Question

I\'m writing a function to find triangle numbers and the natural way to write it is recursively:

function triangle (x)
   if x == 0 then return 0 end
   retu         


        

Answer 1

Extending the idea, it's also possible to memoize functions with two input parameters:

function memoize2 (f)
   local cache = {}
   return function (x, y)
             if cache[x..','..y] then
                return cache[x..','..y]
             else
                local z = f(x,y)
                cache[x..','..y] = z
                return z
             end
          end
end

Notice that parameter order matters in the caching algorithm, so if parameter order doesn't matter in the functions to be memoized the odds of getting a cache hit would be increased by sorting the parameters before checking the cache.

But it's important to note that some functions can't be profitably memoized. I wrote memoize2 to see if the recursive Euclidean algorithm for finding the greatest common divisor could be sped up.

function gcd (a, b) 
   if b == 0 then return a end
   return gcd(b, a%b)
end

As it turns out, gcd doesn't respond well to memoization. The calculation it does is far less expensive than the caching algorithm. Ever for large numbers, it terminates fairly quickly. After a while, the cache grows very large. This algorithm is probably as fast as it can be.