module Exercise_5 where

import Test.QuickCheck
import Data.List

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

longestPathHelp :: Graph -> Vertex -> Vertex -> Int
longestPathHelp g target currNode = let tList = [fst to | to <- edges, snd to == currNode, snd to /= target] in
  if null tList then 0 else maximum [longestPathHelp g target (tList !! i) + 1 | i <- [0..length tList - 1]]
    where
      vertices = fst g
      edges = snd g

longestPath :: Graph -> Vertex -> Int
longestPath g target = longestPathHelp g (starting g) target
  where
    vertices = fst g
    edges = snd g
    nodesIn = snd (unzip edges)
    starting g = [node | node <- vertices, not (elem node nodesIn)] !! 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])