equilibrium.hs

{-# LANGUAGE ScopedTypeVariables #-}

import Test.QuickCheck



equilibrium :: forall a. (Eq a, Num a) => [a] -> [Int]
equilibrium [] = []
equilibrium [_] = []
equilibrium (x:xs) = equilibrium' 0 0 x (sum xs) xs
  where
    equilibrium' :: (Eq a, Num a) => Int -> a -> a -> a -> [a] -> [Int]
    equilibrium' i s1 m s2 []
      | s1 == s2 = [i]
      | otherwise = []
    equilibrium' i s1 m s2 (x:xs)
      | s1 == s2 = i : equilibrium' (i + 1) (s1 + m) x (s2 - x) xs
      | otherwise = equilibrium' (i + 1) (s1 + m) x (s2 - x) xs


prop xs = all (\i -> antes i xs == despues i xs) . equilibrium $ xs
  where
    antes i = sum . take i
    despues i = sum . drop (i + 1)