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 = let ts = topsort [(v,0) | v<- vs] es in
  head [c | (t',c) <- ts, t' == t]

topsort :: [(Vertex,Int)] -> [Edge] -> [(Vertex,Int)]
topsort [] es = []
topsort ((s,c):vs) es = (s,c) : topsort [(s, if elem (s,t) es then maximum (1 + c, c') else c') | (t,c') <- vs] es
{-TTEW-}