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Day 16, Part 1

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Daniele Fucini
2024-12-22 15:14:20 +01:00
parent 2e6e6ac224
commit 7fb9abecb8
7 changed files with 85 additions and 24 deletions
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21
src/Graph.hs
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@@ -10,8 +10,6 @@ import Data.Hashable (Hashable)
import Data.Maybe (fromJust)
import qualified Data.PSQueue as PQ
newtype Graph a = Graph {edges :: M.HashMap a [a]} deriving (Show)
data Distance a = Dist a | Infinity deriving (Eq)
instance (Ord a) => Ord (Distance a) where
@@ -24,6 +22,8 @@ instance (Show a) => Show (Distance a) where
show Infinity = "Infinity"
show (Dist x) = show x
newtype Graph a b = Graph {edges :: M.HashMap a [(a, Distance b)]} deriving (Show)
addDistance :: (Num a) => Distance a -> Distance a -> Distance a
addDistance (Dist x) (Dist y) = Dist (x + y)
addDistance _ _ = Infinity
@@ -33,23 +33,26 @@ data DijkstraState a b = DijkstraState
distances :: M.HashMap a (Distance b)
}
updateDistances :: (Hashable a) => M.HashMap a (Distance b) -> [a] -> Distance b -> M.HashMap a (Distance b)
updateDistances :: (Hashable a, Num b) => M.HashMap a (Distance b) -> [(a, Distance b)] -> Distance b -> M.HashMap a (Distance b)
updateDistances dists [] _ = dists
updateDistances dists (n : nodes) startD =
updateDistances (M.adjust (const startD) n dists) nodes startD
let newD = addDistance startD (snd n)
in updateDistances (M.adjust (const newD) (fst n) dists) nodes startD
visit :: (Ord a, Ord b) => PQ.PSQ a (Distance b) -> a -> [a] -> Distance b -> PQ.PSQ a (Distance b)
visit :: (Ord a, Num b, Ord b) => PQ.PSQ a (Distance b) -> a -> [(a, Distance b)] -> Distance b -> PQ.PSQ a (Distance b)
visit us node [] _ = PQ.delete node us
visit us node (e : es) dist = visit (PQ.adjust (const dist) e us) node es dist
visit us node (e : es) startD =
let newD = addDistance startD (snd e)
in visit (PQ.adjust (const newD) (fst e) us) node es startD
visitNode :: (Hashable a, Ord a, Ord b) => DijkstraState a b -> Graph a -> a -> Distance b -> DijkstraState a b
visitNode :: (Hashable a, Ord a, Num b, Ord b) => DijkstraState a b -> Graph a b -> a -> Distance b -> DijkstraState a b
visitNode state graph node d =
let es = edges graph M.! node
ds = updateDistances (distances state) es d
us = visit (unvisited state) node es d
in state {unvisited = us, distances = ds}
findShortestPath :: (Hashable a, Ord a, Ord b, Num b) => Graph a -> a -> a -> Distance b
findShortestPath :: (Hashable a, Ord a, Ord b, Num b) => Graph a b -> a -> a -> Distance b
findShortestPath graph start end =
let nodesDist = (start PQ.:-> Dist 0) : [k PQ.:-> Infinity | k <- M.keys $ edges graph, k /= start]
dists = (start, Dist 0) : [(k, Infinity) | k <- M.keys $ edges graph, k /= start]
@@ -65,4 +68,4 @@ findShortestPath graph start end =
else
if d == Infinity
then Infinity
else dijkstra $ visitNode s graph n (addDistance d (Dist 1))
else dijkstra $ visitNode s graph n d