Problem 66

66.hs

@@ -0,0 +1,26 @@
+import Data.List
+
+nextX :: (Integer, Integer, Integer, Integer, Integer) ->
+         (Integer, Integer, Integer, Integer, Integer) ->
+         Integer -> Integer
+nextX (n'', d'', c'', a'', b'')
+      (n' , d' , c' , a' , b' )
+      q = if n * n - q * d * d == 1 
+          then n
+          else nextX (n', d', c', a', b') (n, d, c, a, b) q
+          where a = (q - b' * b') `div` a'
+                c = ceiling((sqrt (fromIntegral q) + fromIntegral b') / fromIntegral a - 1)
+                b = a * c - b'
+                d = c * d' + d''
+                n = c * n' + n''
+
+
+minX :: Integer -> Integer
+minX q = let sqrtQ = floor . sqrt . fromIntegral $ q
+         in if sqrtQ * sqrtQ == q
+            then 0
+            else nextX (1, 0, 0, 0, 0) (sqrtQ, 1, sqrtQ, 1, sqrtQ) q
+
+main = print $ let mapping = map minX [1..1000]
+                   max     = maximum mapping
+               in  fmap (+1) $ elemIndex max mapping