Efficient table for Dynamic Programming in Haskell

Question

I\'ve coded up the 0-1 Knapsack problem in Haskell. I\'m fairly proud about the laziness and level of generality achieved so far.

I start by providing functions for crea

Answer 1

To memoize functions, I recommend a library like Luke Palmer's memo combinators. The library uses tries, which are unbounded and have O(key size) lookup. (In general, you can't do better than O(key size) lookup because you always have to touch every bit of the key.)

knapsack :: (Int,Int) -> Solution
knapsack = memo f
    where
    memo    = pair integral integral
    f (i,j) = ... knapsack (i-b,j) ...

Internally, the integral combinator probably builds an infinite data structure

data IntTrie a = Branch IntTrie a IntTrie

integral f = \n -> lookup n table
     where
     table = Branch (\n -> f (2*n)) (f 0) (\n -> f (2*n+1))

Lookup works like this:

lookup 0 (Branch l a r) = a
lookup n (Branch l a r) = if even n then lookup n2 l else lookup n2 r
     where n2 = n `div` 2

There are other ways to build infinite tries, but this one is popular.