module LeastReachableCity(dijkstra, leastReachableCity) where

import Types 
import qualified Data.Map as Map
import qualified Data.Set as Set

-- Well, it's just a magic number, because it's too much hassle to implement type like "Len val | Infinity" 
-- TODO: get graph radius and use this number as infinity
infinity :: Len
infinity = 999999 :: Len

leastReachableCity :: Graph -> Len -> (Point, Int)
leastReachableCity graph mileage = foldl (\(p, n) (p', n') -> 
        if n' < n then (p',n') 
        else (p, n)) 
    (-1, infinity) [(city, countReachableCities $ dijkstra city graph) | city <- Set.toList $ fst $ countVertices graph] where
        countReachableCities :: Distances -> Int
        countReachableCities distances = Map.foldl (\n val -> if (val <= mileage) && (val /= 0) then n + 1 else n) 0 distances 

dijkstra :: Point -> Graph -> Distances
dijkstra start graph = dijkstra' start graph visited_init to_visit_init distances_init where
    -- Helper (so we don' need to call dijkstra initializing empty visited, to_visit etc)
    dijkstra' :: Point -> Graph -> Vertices -> Vertices -> Distances -> Distances 
    dijkstra' start graph visited to_visit distances = if Set.null to_visit 
        then 
            distances
        else
            dijkstra' 
                (findMinNotVisited to_visit distances) 
                graph 
                (Set.insert start visited) 
                (Set.union (Set.delete start to_visit) $ findNotVisitedNeighbours graph visited start) 
                (updateDistances graph start distances)
    -- Other
    to_visit_init = (Set.insert start $ Set.empty :: Vertices)
    distances_init = (infinityDistances start $ snd $ countVertices graph)
    visited_init = (Set.empty :: Vertices) 

updateDistances :: Graph -> Point -> Distances -> Distances
updateDistances graph point distances = snd $ Map.foldrWithKey decideMin ((point, Map.findWithDefault (-1) point distances), Map.empty :: Distances) distances where
    decideMin ::  Point -> Len -> ((Point, Len), Distances) -> ((Point, Len), Distances)
    decideMin p' l' ((p, l), dist) = if findDistance graph p p' + l < l' then 
        ((p, l), Map.insert p' (l + findDistance graph p p') dist) else
        ((p, l), Map.insert p' l' dist)

findDistance :: Graph -> Point -> Point -> Len
findDistance ((Node (a, b, len)) : graph) p p' = if ((a == p) && (b == p') || (b == p) && (a == p')) then len else findDistance graph p p'  
findDistance _ _ _ = infinity

findMinNotVisited :: Vertices -> Distances -> Point  
findMinNotVisited to_visit distances = fst $ Set.foldl (\(p, l) p' -> case Map.lookup p' distances of 
    (Just l') -> if l' < l then 
            (p', l') 
        else (p,l)) 
    (-1, infinity) to_visit 

infinityDistances :: Point -> Int -> Distances
infinityDistances point n = Map.fromList $ (point, 0) : [(x, infinity) | x <- [1..n], x /= point] 

countVertices :: Graph -> (Vertices, Int)
countVertices graph = foldl f (Set.empty :: Vertices, 0) graph where
    f :: (Vertices, Int) -> Node -> (Vertices, Int)
    f (vertices, n) (Node (a, b, _)) = 
        let aIsNotMember = not $ Set.member a vertices 
            bIsNotMember = not $ Set.member b vertices in if (aIsNotMember && bIsNotMember) then (Set.insert a $ Set.insert b vertices, n + 2) 
                else if (aIsNotMember) then (Set.insert a vertices, n + 1) 
                    else if (bIsNotMember) then (Set.insert b vertices, n + 1) 
                        else (vertices, n)

findNotVisitedNeighbours :: Graph -> Vertices -> Point -> Vertices 
findNotVisitedNeighbours graph visited point = foldl f (Set.empty :: Vertices) graph where
    f :: Vertices -> Node -> Vertices 
    f vertices (Node (a, b, _)) = if ((a == point) && (not $ Set.member b visited)) then Set.insert b vertices 
        else if ((b == point) && (not $ Set.member a visited)) then Set.insert a vertices
            else vertices