@Jose_A_Alonso Exercitium: Particiones de enteros positivos

01-particiones.hs

-- www.glc.us.es/~jalonso/exercitium/particiones-de-enteros-positivos/

zen :: ([a] -> [a]) -> [a] -> [a] -> [a]
zen f a b =
  let a' = f a
      b' = b ++ a
  in case a' of
       [] -> b'
       _  -> zen f a' b'

  
particiones n = zen cultivarParticiones [[n]] []

cultivarParticion particion = 
  case particion of
    [x]     -> [[x-z,z]    | z <- [1 .. (div x 2)]]  -- z <= x - z
    (x:y:t) -> [(x-z):z:y:t| z <- [y .. (div x 2)]]  -- z <= x - z 

cultivarParticiones particiones = 
   particiones >>= cultivarParticion

02-particiones.hs

gen f =  concat . takeWhile (/=[]) . iterate f
 
particiones = gen cultivarParticiones . return . return
 
cultivarParticion particion = case particion of
    [x]     -> [[x-z,z]    | z <- [1 .. (div x 2)]]
    (x:y:t) -> [(x-z):z:y:t| z <- [y .. (div x 2)]]
 
cultivarParticiones particiones = particiones >>= cultivarParticion