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 (_,[]) end = 0
longestPath g end = aux (findStartingNode g) 0
  where 
    aux current acc = let paths = findCurrentPossiblePaths g current in 
      if current == end then acc else 
        if paths == [] then minBound :: Int else maximum [aux p (acc + 1) | p <- paths]

findCurrentPossiblePaths :: Graph -> Vertex -> [Vertex]
findCurrentPossiblePaths (_, xs) current = [snd x | x <- xs, fst x == current]

findStartingNode :: Graph -> Vertex
findStartingNode (xs, ys) = let outgoing = [snd y | y <- ys] in
  filter (\x -> not (x `elem` outgoing)) xs !! 0
{-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])