Problem 83: Partially implemented priority queue implementation of Dijkstra's for finding shortest path.

83.hs

@@ -16,8 +16,8 @@ instance Monoid Element where
         case getMin v1 v2 of 
             0  -> mempty
             v -> if v == v1 
-                then Element v1 Visited p1
+                 then Element v1 Visited p1
-                else Element v2 Visited p2
+                 else Element v2 Visited p2
 
 getMin :: Value -> Value -> Value
 getMin v1 0  = v1

83_alt.hs

@@ -0,0 +1,62 @@
+import Data.List.Split
+import Data.Matrix
+import Data.Maybe
+import Data.Foldable
+import Data.PQueue.Min
+
+type Value = Integer
+type Distance = Maybe Integer  -- Nothing represents infinity
+type Position = (Int, Int)
+data Element = Element {
+    value :: Value,
+    distance :: Distance,
+    position :: Position
+ } deriving (Eq, Show)
+data PQE = PQE Element Distance deriving (Eq, Show)
+
+instance Ord PQE where
+    PQE _ Nothing <= _ = False
+    _ <= PQE _ Nothing = True
+    PQE _ (Just d1) <= PQE _ (Just d2) = d1 <= d2
+
+dijkstra :: Matrix Element -> MinQueue PQE -> Position -> Distance
+dijkstra m q p =
+    let PQE minElement minDistance = findMin q
+    in  if position minElement == p
+        then distance minElement
+        else undefined --TODO
+
+
+findShortestPathLength :: Matrix Element -> Distance
+findShortestPathLength m =
+    let initialElement = m ! (1, 1)
+        initialMinQ = singleton $ PQE initialElement $ distance initialElement
+        lastPos = (nrows m, ncols m)
+    in  dijkstra m initialMinQ lastPos
+
+
+setInitial :: Matrix Element -> Matrix Element
+setInitial m =
+    let v = value $ m ! (1, 1)
+        maybeMatrix = safeSet (Element v (Just v) (1, 1)) (1, 1) m
+    in  case maybeMatrix of 
+        Just mm -> mm 
+        Nothing -> m
+
+initElement :: Matrix Integer -> Position -> Element
+initElement m p =
+    let value = m ! p
+    in  Element value Nothing p
+
+toElementMatrix :: Matrix Integer -> Matrix Element
+toElementMatrix m =
+    matrix (nrows m) (ncols m) (initElement m)
+
+main :: IO ()
+main = do
+    contents <- readFile "p083_matrix.txt"
+    let listsMatrix = fmap (fmap read . (splitOn ",")) $ lines contents :: [[Integer]]
+        valueMatrix = fromLists listsMatrix
+        unvisitedMatrix = toElementMatrix valueMatrix
+        mtrx = setInitial unvisitedMatrix
+    print $ findShortestPathLength mtrx