euler 28 clever

euler/28.hs

@@ -0,0 +1,25 @@
+-- Starting with the number 1 and moving to the right in a clockwise
+-- direction a 5 by 5 spiral is formed as follows:
+--
+-- 21 22 23 24 25
+-- 20  7  8  9 10
+-- 19  6  1  2 11
+-- 18  5  4  3 12
+-- 17 16 15 14 13
+--
+-- What is the sum of the numbers on the diagonals in a 1001 by 1001
+-- spiral formed in the same way?
+
+-- It is easy to notice that number in upper-right corner
+-- of each square is... odd square
+oddSqrs = [x^2 | x <- [1,3..]]
+
+-- We can copute the rest of square numbers like so
+divide (x,y) = [y - i*step | i <- [0..3]]
+	where step = (y - x) `div` 4
+
+sqrNumbers = map divide $ zip oddSqrs (tail oddSqrs)
+
+answer n = succ . sum . concat . take (n `div` 2) $ sqrNumbers
+
+main = prtin $ answer 1001