Day 3: getDownstairs is incorrect, but the rest should be correct...

3.hs

@@ -0,0 +1,44 @@
+import qualified Data.Map.Strict as Map
+import Debug.Trace
+
+squareRoot :: Floating a => Int -> a
+squareRoot = sqrt . fromIntegral
+
+getLevel :: Int -> Int
+getLevel n = ceiling $ (squareRoot n - 1) / 2
+
+getDownstairs :: Int -> Int
+getDownstairs n =
+    let level = getLevel n
+    in  8 * level - 7 + (n - (2 * level - 1) ^ 2) `div` 2
+
+type Store = Map.Map Int Int
+
+getValue :: Int -> Store -> Int
+getValue k m = Map.findWithDefault 0 k m 
+    
+computeValue :: Int -> Store -> Store
+computeValue n m = Map.insert n value m
+    where 
+        level          = getLevel n
+        downstairs     = getDownstairs n
+        preDownstairs  = getDownstairs (n-1)
+        postDownstairs = getDownstairs (n+1)
+        lastCorner = (2 * level + 1) ^ 2
+        firstPost  = (2 * level - 1) ^ 2 + 1
+        corners    = map ((+ lastCorner) . (*(2 * level))) [(-1)..(-3)]
+        pre        = map (1-) corners
+        post       = map (1+) (lastCorner:corners)
+        value
+            | n == firstPost    =           (n-1)    + (getValue postDownstairs m)
+            | n == lastCorner   = (getValue (n-1) m) + (getValue preDownstairs  m) + (getValue (preDownstairs+1) m)
+            | n `elem` corners  = (getValue (n-1) m) + (getValue preDownstairs  m)
+            | n `elem` pre      = (getValue (n-1) m) + (getValue (downstairs-1) m) + (getValue downstairs m) 
+            | n `elem` post     = (getValue (n-1) m) + (getValue (n-2)          m) + (getValue downstairs m) + (getValue (downstairs+1) m)
+            | otherwise         = (getValue (n-1) m) + (getValue (downstairs-1) m) + (getValue downstairs m) + (getValue (downstairs+1) m)
+
+main :: IO ()
+main = do
+    let initialStore = Map.fromList $ zip [1..9] [1, 1, 2, 4, 5, 10, 11, 23, 25]
+    let infiniStore  = foldr computeValue initialStore [10..]
+    print $ computeValue 10 initialStore