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 (vs, es) t = recInternal (vs, es) [fst e | e <- es, snd e == t]
 where
  recInternal :: Graph -> [Vertex] -> Int
  recInternal (vs, es) [] = 0
  recInternal (vs, es) xs = 1 + recInternal (vs, es) [fst e | e <- es, x <- xs, snd e == x]

{-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])