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import Data.Maybe
import Data.List
data Dir = R | D | L | U deriving (Show, Eq, Enum)
type Spiral = ([[Int]], Int, Dir) -- (rows, current row, next direction)
rows :: Spiral -> [[Int]]
rows (rs, i, d) = rs
currentrow :: Spiral -> Int
currentrow (rs, i, d) = i
nextdir :: Spiral -> Dir
nextdir (rs, i, d) = d
getrow :: Int -> [[Int]] -> Maybe [Int]
getrow i sp = if i < 0 || i >= length sp then Nothing else Just (sp!!i)
ndir :: Dir -> Dir
ndir d = if d == U then R else succ d
newsp :: Spiral
newsp = ([[1]], 0, R)
makeSpiral :: Int -> Spiral
makeSpiral i = makeSpiral' 2 newsp
where makeSpiral' j sp = if j > i
then sp
else makeSpiral' (j+1) (update j sp)
update :: Int -> Spiral -> Spiral
update i (sp, cr, d) = (sp', cr', d')
where oldrow = if (d == U && cr' == cr && cr == 0) ||
(d == D && cr' == length sp)
then []
else fromJust $ getrow cr' sp
cr' | d == L || d == R = cr
| d == U = if cr == 0 then 0 else cr-1
| otherwise = cr+1
cr'' = if d == U && cr == 0 then -1 else cr'
sp' = insertrow cr'' newrow sp
newrow = case d of
R -> oldrow++[i]
D -> oldrow++[i]
L -> i:oldrow
U -> i:oldrow
d' | d == R || d == L = if length oldrow == maximum (map length sp)
then ndir d
else d
| d == U = if cr'' == -1 then ndir d else d
| otherwise = if cr' == length sp then ndir d else d
insertrow :: Int -> [Int] -> [[Int]] -> [[Int]]
insertrow i r rs = if i == -1 then r:rs else front++[r]++back
where (front, rest) = splitAt i rs
back = if null rest then [] else tail rest
printSpiral :: Spiral -> IO ()
printSpiral (sp, i, d) = putStrLn (concat $ intersperse "\n" (map show sp))
sumdiags :: Spiral -> Int
sumdiags (sp, i, d) = (sumdiags' 0 0 (+1)) + (sumdiags' 0 end (subtract 1)) - centre
where row1 = sp!!0
end = length row1 - 1
halfx = (length row1 `div` 2)
halfy = (length sp `div` 2)
centre = (sp!!halfy)!!halfx
sumdiags' row col f = if row == length sp
then 0
else (sp!!row)!!col + sumdiags' (row+1) (f col) f
main = print (makeSpiral 10000)
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