10.2

route.hs

type Point = (Int, Int)
type Section = (Int, Int, Int)
data Label = A | B | C deriving Show
data Route = Route { path :: [(Label, Int)], distance :: Int } deriving Show

input :: [Section]
input = [(50, 10, 30), (5, 90, 20), (40, 2, 25), (10, 8, 0)]

zeroRoute :: Route
zeroRoute = Route { path = [], distance = 0 }

getPath :: Route -> [Label]
getPath = reverse . map fst . path

getDistance :: Route -> Int
getDistance = distance

shortestRoute :: [Section] -> Route
shortestRoute sections = let (ra, rb) = foldl next (zeroRoute, zeroRoute) sections
                         in if distance ra < distance rb then ra else rb

next :: (Route, Route) -> Section -> (Route, Route)
next (Route pa da, Route pb db) (x, y, z) = (a', b')
  where
    a' | da1 < da2 = Route ((A, x) : pa         ) da1
       | otherwise = Route ((C, z) : (B, y) : pb) da2
    b' | db1 < db2 = Route ((B, y) : pb         ) db1
       | otherwise = Route ((C, z) : (A, x) : pa) db2
    (da1, da2) = (da + x, db + y + z)
    (db1, db2) = (db + y, da + x + z)