module Exercise_7 where

{-WETT-}
comp :: Eq b => [(Integer,(a,b))] -> [(Integer,(b,c))] -> [(Integer,(a,c))]
comp r s = [ (i1 + i2, (x,z))| (i1,(x,y1)) <- r, (i2, (y2,z)) <- s, y1 == y2]

remove_duplicates :: Eq a => [(Integer,(a,a))] -> [(Integer,(a,a))] -> [(Integer,(a,a))]
remove_duplicates [] acc = acc
remove_duplicates (r:rs) acc =
    let 
        (_, (a,b)) = r
        min_r = minimum [k | (k, (c,d)) <-(r:rs), c == a, d == b]
        rest = [(k, (c,d)) | (k, (c,d)) <-(r:rs), c /= a || d /= b]
    in
        remove_duplicates rest (acc ++ [(min_r, (a,b))])


trancl :: Eq a => [(Integer,(a,a))] -> [(Integer,(a,a))]
trancl r = find_transitives r

find_transitives rs = 
    let        
        oneSteps = remove_duplicates (rs ++ (comp rs rs)) []
    in
        if relEq oneSteps rs
            then rs
        else            
            find_transitives oneSteps

relEq :: Eq a => [(Integer,(a,a))] -> [(Integer,(a,a))] -> Bool
relEq [] [] = True
relEq _ [] = False
relEq [] _ = False
relEq (x:xs) rs = x `elem` rs && (relEq xs [r | r <- rs, r /= x])

{-TTEW-}