module Exercise02 where

import Data.List
import Data.Ord
import Data.Graph
import Data.Ix

{-H2.1a)-}
twoThirdsAverageWinners :: [(String, Int)] -> [String]
twoThirdsAverageWinners gs = [fst x | x <- gs, abs(snd x - av) == ee]
  where 
    ss = 2 * (sum [snd x | x <- gs])
    av = div ss (length gs * 3)
    ee = minimum [abs(snd x - av) | x <- gs]

{-H2.1b)-}
lowestUniqueBidder :: [(String, Int)] -> String
lowestUniqueBidder bs
 | length un == 0 = "Nobody"
 | otherwise = head ee
 where 
   un = [x | x <- bs, length [y | y <- bs, snd y == snd x] == 1]
   mm = minimum [snd x | x <- un]
   ee = [fst x | x <- un, snd x == mm]


{-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 = [x | x <- players tournament, elem i (dominion tournament x)]

{-H2.2b)-}
covers :: [[Int]] -> Int -> Int-> Bool
covers tournament i j = all over (dominion tournament j)
  where
  over ::Int -> Bool
  over x = elem x (dominion tournament i)


{-2.2c)-}
dominant :: [[Int]] -> [Int] -> Bool
dominant tournament [] = False
dominant tournament xs = all pos xs
  where
  pos ::Int -> Bool
  pos x = all rr (dominators tournament x) 
  rr :: Int -> Bool
  rr y = elem y xs
{-WETT-}
{-H2.2d)-}
copeland :: [[Int]] -> [Int]
copeland tournament = [x | x <- players tournament, length (dominion tournament x) == mx]
  where 
    mx = maximum [length (dominion tournament x) | x <- players tournament]
{-H2.2e)-}
uncoveredSet :: [[Int]] -> [Int]
uncoveredSet tournament = [x | x <- players tournament, length [y | y <- dominators tournament x, covers tournament y x] == 0]
{-H2.2f)-} 
topCycle :: [[Int]] -> [Int]
topCycle tournament = flattenSCC (last (stronglyConnComp [(x,x,dominion tournament x) | x <- players tournament]))
{-TTEW-}