module Kopapir where

type Sign = Int

validSigns :: (Sign -> Sign -> a) -> Sign -> Sign -> a
validSigns f a b
  | a >= 0 && a < 3 && b >= 0 && b < 3 = f a b
validSigns _ a b = error $ "validSigns: invalid values: (" ++ show a ++ "," ++ show b ++ ")"

beats :: Sign -> Sign -> Bool
0 `beats` 2 = True
1 `beats` 0 = True
2 `beats` 1 = True
a `beats` b = validSigns f a b
   where f _ _ = False

isDraw :: Sign -> Sign -> Bool
isDraw a b = validSigns f a b
   where f x y = x == y

result :: Sign -> Sign -> Int
result a b
  | isDraw a b  = 0
  | a `beats` b = 1
  | otherwise   = -1

type Play = [Sign]
type Rounds = (Play, Play)

tournament :: Rounds -> Int
tournament (xs, ys)
 | l < 0     = 2
 | l > 0     = 1
 | otherwise = 0
   where
     l = sum $ map (\(x,y) -> result x y) $ zip xs ys

partitionRounds :: Rounds -> ([Sign], [Sign], [Sign])
partitionRounds (xs,ys) = ([ b | (a, b) <- r, a == 1], [ b | (a, b) <- r, a == 0], [ b | (a, b) <- r, a == -1])
    where
      r = map (\(x,y) -> (result x y, x)) $ zip xs ys

next :: Sign -> Sign
next 0 = 1
next 1 = 2
next 2 = 0

frequency :: Eq a => a -> [a] -> Int
frequency _ []   = 0
frequency a (x:xs)
  | x == a    = 1 + frequency a xs
  | otherwise = frequency a xs

mostFrequent :: Ord a => [a] {-nem üres-} -> a
mostFrequent x = snd $ maximum $ map (\a -> (frequency a x, a)) $ nub x

type Strategy = Rounds -> Sign -- (Play, Play) -> Sign

strategy1 :: Strategy
strategy1 ([],[])    = 0
strategy1 (x:_, y:_)
  | result x y == 1 = y
  | otherwise       = next y


strategy2 :: Strategy
strategy2 ([],[]) = 2
strategy2 (_, ys) = next $ mostFrequent ys

strategy3 :: Strategy
strategy3 ([],[]) = 1
strategy3 rounds
 | length (won r) == length (lost r) = next $ mostFrequent (tie r)
 | length (won r) >  length (lost r) = mostFrequent (won r)
 | otherwise                         = next $ mostFrequent (lost r)
   where
      r = partitionRounds rounds
      won  (a,_,_) = a
      tie  (_,b,_) = b
      lost (_,_,c) = c

applyStrategies :: Strategy -> Strategy -> Rounds -> Rounds
applyStrategies s1 s2 r@(xs,ys) = (s1 r : xs, s2 (ys, xs) : ys)

play :: Int -> Strategy -> Strategy -> Rounds
play n s1 s2
  | n <= 0    = ([], [])
  | otherwise = applyStrategies s1 s2 (play (n-1) s1 s2)

winningStrategy :: Strategy -> [Strategy] -> [Int]
winningStrategy = winningStrategyN 1
  where
   winningStrategyN :: Int ->  Strategy -> [Strategy] -> [Int]
   winningStrategyN _ _ [] = []
   winningStrategyN n s (x:xs)
     | (tournament $ play 10 s x) == 2 = n : winningStrategyN (n+1) s xs
     | otherwise                       = winningStrategyN (n+1) s xs