working i think

.gitignore

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+*.swp
+spiral
+*.hi
+*.o

README.md

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+# Spiral
+
+bad attempts at solving interview questions
+
+## The Problem - Verbatim
+
+Write a small program which:
+accepts on the command line an odd number N
+outputs a sequence of numbers corresponding to the following steps:
+the numbers 1 through N^2 are written in a grid
+the first number in the sequence is the number in the center of the grid
+the subsequent numbers are found by spiraling out clockwise, starting to the right
+For example, for N = 3 we have the grid:
+1 2 3
+4 5 6
+7 8 9
+So we start with 5, head right to 6, then down to 9, left through 8 and 7, up through 4 and 1 and finally right through 2 and 3. This gives the output:
+5, 6, 9, 8, 7, 4, 1, 2, 3, end
+
+For N=5 the output should be:
+13, 14, 19, 18, 17, 12, 7, 8, 9, 10, 15, 20, 25, 24, 23, 22, 21, 16, 11, 6, 1, 2, 3, 4, 5, end
+
+IMPORTANT: your solution should not make use of arrays or matrices of numbers. If you are unable to determine a way to solve it without arrays/matrices then a solution with them is better than no solution.
+
+## Compiling and Running
+
+```
+ghc -02 -Wall Spiral.hs -o spiral
+spiral
+```

spiral.hs

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+import System.IO
+
+data Incarnation = S Bool Bool Int (Int,Int) Int Int
+
+seed :: Int -> Int
+seed n = 1 + (h * (n+1))
+   where h = (div n 2)
+
+lineage :: Int -> [Int]
+lineage n = take (n*n) $ futures (atom n)
+
+atom :: Int -> Incarnation
+atom n = S False True 1 (1,0) (seed n) n
+
+xor :: Bool -> Bool -> Bool
+xor a b = (a || b) && (not (a && b))
+
+futures :: Incarnation -> [Int]
+futures self@(S _ _ _ _ l _) =
+   (l:(futures (evolve self)))
+
+divine :: Incarnation -> Int
+divine (S v s _ _ l n) = l `sign` val
+   where
+      sign = if s then (+) else (-)
+      val = if v then n else 1
+
+evolve :: Incarnation -> Incarnation
+evolve i@(S v s cd (so,sn) _ b)
+   | cd > 1 = (S v s (cd-1) (so,sn) (divine i) b)
+   | otherwise =
+      (S (not v) (s `xor` v) (cs ns) ns (divine i) b)
+   where
+      ns = (intuit v (so,sn))
+      cs = (if v then fst else snd)
+
+intuit :: Bool -> (Int,Int) -> (Int,Int)
+intuit True (a,b) = ((a+1),b)
+intuit _ (a,b) = (a,(b+1))
+
+-- blurgh io
+-- bloating the program making me import stuff >:(
+
+main :: IO ()
+main = do
+   putStr "destinies to observe: "
+   hFlush stdout
+   args <- getLine
+   mapM_ putStrLn
+      $ map (\n -> ("n=" ++ (show n) ++ " ~ ")
+              ++ (if (aura n)
+                  then (show (lineage (read n)))
+                  else "[ soul contains invalid aura ]"))
+            (words args)
+
+aura :: String -> Bool
+aura s = foldr (&&) True
+         (map (`elem` ['0'..'9']) s)