module Exercise02 where

import Data.List
import Data.Ord

{-H2.1a)-}
twoThirdsAverageWinners :: [(String, Int)] -> [String]
twoThirdsAverageWinners gs = [fst x | x <- gs, cmp2 (foldl1 cmp gs) x]
  where
    avg = div (2 * sum [snd x | x <- gs]) (3 * length gs)
    cmp x y = if abs (snd x - avg) <= abs (snd y - avg) then x else y
    cmp2 x y = abs (snd x - avg) == abs (snd y - avg)

{-H2.1b)-}
lowestUniqueBidder :: [(String, Int)] -> String
lowestUniqueBidder bs
  | null bs = "Nobody"
  | length bs == 1 = fst (head bs)
  | otherwise = if length bsSorted - 1 == length bsFiltered then fst (head bsSorted) else lowestUniqueBidder bsFiltered
  where
    bsSorted = sortOn snd bs
    bsFiltered = filter cmp (tail bsSorted)
    cmp x = snd x /= snd (head bsSorted)

{-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 = [snd y | y <- filter fst (zip [i `elem` x | x <- tournament] (players tournament))]

{-H2.2b)-}
covers :: [[Int]] -> Int -> Int -> Bool
covers tournament i j = all not [x `notElem` domI | x <- dominion tournament j]
  where
    domI = dominion tournament i

{-2.2c)-}
dominant :: [[Int]] -> [Int] -> Bool
dominant tournament xs
  | null xs = False
  | otherwise = all not [y `notElem` dominion tournament x | x <- xs, y <- [x | x <- players tournament, x `notElem` xs]]

{-WETT-}

{-H2.2d)-}
copeland :: [[Int]] -> [Int]
copeland tournament = map (+ 1) $maximum x `elemIndices` x
  where
    x = map length tournament

{-H2.2e)-}
uncoveredSet :: [[Int]] -> [Int]
uncoveredSet tournament = players tournament \\ [y | x <- players tournament, y <- players tournament, covers tournament x y, x /= y]

{-H2.2f)-}
topCycle :: [[Int]] -> [Int]
topCycle tournament = (\xs -> nub $concatMap (tournament `dominators`) xs ++ xs) `iterate` copeland tournament !! length tournament

{-TTEW-}