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 v = longestPathHelp g v (findStart g)

longestPathHelp :: Graph -> Vertex -> Vertex -> Int
longestPathHelp g v start = if v == start then 0 else maximum (longestPathHelp2 (findVor g v)) + 1
    where longestPathHelp2 xs = [longestPathHelp g x start | x <- xs ]


findStart :: Graph -> Vertex
findStart (g1,g2) = head (g1 \\ [y | (_, y) <- g2])

findVor :: Graph -> Vertex -> [Vertex]
findVor (g1, g2) v = [x | (x,y) <- g2, y==v]
{-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])