module Exercise_5 where
import Test.QuickCheck
import Data.List

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

{-
dfs :: Graph -> [Vertex]
dfs (vs,es) = reverse $ visit [] (head vs)
  where
    visit :: [Vertex] -> Vertex -> [Vertex]
    visit visited n
      | elem n visited = visited
      | otherwise = foldl visit (n:visited) [m | (n,m) <- es]
-}

longestPath :: Graph -> Vertex -> Int
longestPath (vs,es) t = go [n | (n,m) <- es, m == t] 0
  where
    go :: [Vertex] -> Int -> Int
    go [] len = len
    go nodes len = maximum [go [a | (a,b) <- es, b == n] (len+1) | n <- nodes]
{-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])