[[ProjectEular]]

 -- Problem 27
 
 module Main (main) where
 
 import Array
 import qualified Common as C (is_prime)
 
 main :: IO ()
 main = print $ problem27
 
 problem27 :: Int
 problem27 = (fst idx) * (snd idx)
     where
         idx = find_max_idx arr
         arr = listArray ((-999,-999),(999,999))
                         [ num_primes a b | a <- [-999..999], b <- [-999..999] ]
 
 find_max_idx :: Array (Int,Int) Int -> (Int,Int)
 find_max_idx arr = find_max_idx_iter arr idcs idx
     where (idx:idcs) = indices arr
 
 find_max_idx_iter :: Array (Int,Int) Int -> [(Int,Int)] -> (Int,Int) -> (Int,Int)
 find_max_idx_iter arr idcs max_idx
     | null idcs             = max_idx
     | arr!idx > arr!max_idx = find_max_idx_iter arr idcs' idx
     | otherwise             = find_max_idx_iter arr idcs' max_idx
     where (idx:idcs') = idcs
 
 num_primes :: Int -> Int -> Int
 num_primes a b = num_primes_iter 0 a b
 
 num_primes_iter :: Int -> Int -> Int -> Int
 num_primes_iter n a b
     | C.is_prime (n^2 + a*n + b) = 1 + (num_primes_iter (n+1) a b)
     | otherwise                  = 0
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