module Exercise_5 where
import Test.QuickCheck
import Data.List

{- H5.3 -}
{-WETT-}
type Vertex = Int
type Edge = (Vertex, Vertex)
type Graph = ([Vertex], [Edge])

longestPath :: Graph -> Vertex -> Int
longestPath g t = magic t 0
    where magic v n
            | null $ before v = n
            | otherwise = maximum [magic x (n+1) | x <- before v]
          before w = [fst x | x <- (snd g), (snd x == w)]

{-
longestPath :: Graph -> Vertex -> Int
longestPath g t = magic findFirst
    where findFirst = head $ filter (\x -> not $ elem x (map snd (snd g))) (fst g)
          magic v
            | v == t = 0
            | null $ getNext v = -1
            | otherwise = maximum [(magic x) + 1 | x <- getNext v, x >= 0]
          getNext w = [snd x | x <- (snd g), (fst x == w)]
-}
{-TTEW-}

-- generates a DAG with u vertices and only one node without incoming edges
-- you can use this function to test your implementation using QuickCheck
genDag :: Int -> Gen Graph
genDag n = let v = [1..n] in
  do b <- mapM (\i -> choose (1,n-i)) [1..n-1]
     t <- mapM (\(c,i) -> vectorOf c (choose (i+1, n))) (zip b [1..n])
     let e = nub $ ([(1, i) | i<-[2..n]] ++ edges t 1 [])
     return $ (v,e)
  where
    edges [] _ acc = acc
    edges (ts:xs) i acc = edges xs (i+1) (acc ++ [(i,t) | t<-ts])