module Exercise02 where

import Data.List
import Data.Ord

{-H2.1a)-}
twoThirdsAverageWinners :: [(String, Int)] -> [String]
twoThirdsAverageWinners gs = [name | (name, guess) <- gs, abs (guess-correct) ==  minimum [ abs ( g - correct) | (_,g) <- gs]]
    where correct = div (2 * sum [i | (_, i) <- gs]) (3*length gs)

{-H2.1b)-}
lowestUniqueBidder :: [(String, Int)] -> String
lowestUniqueBidder bs = head ( [name | (name, guess) <- bs, guess == minimum ([g | (n, g) <- bs, null [(s, i) | (s, i) <- bs, i == g, n /= s] ] ++ [101])] ++ ["Nobody"] )


{-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 = filter (\j -> i `elem` dominion tournament j) $ players tournament

{-H2.2b)-}
covers :: [[Int]] -> Int -> Int-> Bool
covers tournament i j = null $ dominion tournament j \\ dominion tournament i

{-2.2c)-}
dominant :: [[Int]] -> [Int] -> Bool
dominant tournament xs = not (null xs) && null ( (players tournament \\ xs) \\ foldr1 intersect [dominion tournament i | i <- xs])

-- 63 tokens
{-WETT-}

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

{-H2.2e)-}
uncoveredSet :: [[Int]] -> [Int]
uncoveredSet tournament = players tournament \\ [i | i <- players tournament, p <- dominators tournament i, covers tournament p i]

{-H2.2f)-} 
topCycle :: [[Int]] -> [Int]
topCycle tournament = head $ dominant tournament `filter` inits ((Down . length . dominion tournament) `sortOn` players tournament)
{-TTEW-}

{- MCCOMMENT
an even shorter, but much slower version of topCycle:
topCycle tournament = shortest $ dominant tournament `filter` subsequences (players tournament)
-}