Monad Knight's quest exercise.

category-theory/monad-knight-quest.hs

@@ -0,0 +1,40 @@
+import Control.Monad
+
+type KnightPos = (Int,Int)
+
+moveKnight :: KnightPos -> [KnightPos]  
+moveKnight (c,r) = do  
+    (c',r') <- [(c+2,r-1),(c+2,r+1),(c-2,r-1),(c-2,r+1)  
+               ,(c+1,r-2),(c+1,r+2),(c-1,r-2),(c-1,r+2)  
+               ]  
+    guard (c' `elem` [1..8] && r' `elem` [1..8])  
+    return (c',r')
+
+-- same function defined using list's filter
+moveKnightFilter :: KnightPos -> [KnightPos]  
+moveKnightFilter (c,r) = filter onBoard  
+    [(c+2,r-1),(c+2,r+1),(c-2,r-1),(c-2,r+1)  
+    ,(c+1,r-2),(c+1,r+2),(c-1,r-2),(c-1,r+2)  
+    ]  
+    where onBoard (c,r) = c `elem` [1..8] && r `elem` [1..8]
+
+a1 = moveKnight (6,2)  
+a2 = moveKnight (8,1)
+
+-- all the positions that can be reached in 3 moves
+in3 :: KnightPos -> [KnightPos]  
+in3 start = do   
+    first <- moveKnight start  
+    second <- moveKnight first  
+    moveKnight second
+
+b1 = in3 (6,2)
+
+-- defined without do notation
+--in3 start = return start >>= moveKnight >>= moveKnight >>= moveKnight
+
+canReachIn3 :: KnightPos -> KnightPos -> Bool  
+canReachIn3 start end = end `elem` in3 start
+
+c1 = (6,2) `canReachIn3` (6,1)
+c2 = (6,2) `canReachIn3` (7,3)