module Exercise02 where

import Data.List
import Data.Ord

{-H2.1a)-}
twoThirdsAverageWinners :: [(String, Int)] -> [String]
twoThirdsAverageWinners gs = [fst g | g <- gs, abs (avg - snd g) == minimum [abs (avg - snd g) | g <- gs]]
  where
    avg = floor $ (2 / 3) * fromIntegral (sum [snd g | g <- gs]) / fromIntegral (length gs)

{-H2.1b)-}
lowestUniqueBidder :: [(String, Int)] -> String
lowestUniqueBidder bs = head $ [fst b | b <- ls, snd b == minimum [snd b | b <- ls, length (filter (\t -> snd t == snd b) ls) == 1]]
  where
    ls = bs ++ [("Nobody", 101)]

{-H2-}

-- returns the shortest list in a list of lists
shortest :: [[Int]] -> [Int]
shortest = minimumBy (comparing length)

-- returns the set of all players in a tournament
players :: [[Int]] -> [Int]
players tournament = [1 .. length tournament]

-- returns the dominion of player i
dominion :: [[Int]] -> Int -> [Int]
dominion tournament i = tournament !! (i - 1)

{-H2.2a)-}
dominators :: [[Int]] -> Int -> [Int]
dominators tournament i = [p | p <- players tournament, i `elem` dominion tournament p]

{-H2.2b)-}
covers :: [[Int]] -> Int -> Int -> Bool
covers tournament i j = [p | p <- dominion tournament j, p `elem` dominion tournament i] == dominion tournament j

{-2.2c)-}
dominant :: [[Int]] -> [Int] -> Bool
dominant tournament gs = not (null gs) && [g | g <- gs, dominion tournament g \\ gs == players tournament \\ gs] == gs

{-WETT-}

{-H2.2d)-}
copeland :: [[Int]] -> [Int]
copeland tournament = (\p -> maximum (map length tournament) == length (dominion tournament p)) `filter` players tournament

{-H2.2e)-}
uncoveredSet :: [[Int]] -> [Int]
uncoveredSet tournament = (\p -> all (\x -> not $ covers tournament x p) (p `delete` players tournament)) `filter` players tournament

{-H2.2f)-}
topCycle :: [[Int]] -> [Int]
topCycle tournament = tournament `helper2` length tournament

helper2 :: [[Int]] -> Int -> [Int]
helper2 tournament 0 = copeland tournament
helper2 tournament i = xs `union` concatMap (tournament `dominators`) xs
  where
    xs = helper2 tournament (i -1)

{-MCCOMMENT
--slow but short :/
topCycle :: [[Int]] -> [Int]
topCycle tournament = shortest $ filter (tournament `dominant`) (subsequences $ players tournament)
-}
{-TTEW-}