palindromic.hs

-- Code challenge.

{-# LANGUAGE NPlusKPatterns #-}

import Control.Monad (guard, liftM)

revert   :: Int -- | digit
         -> Int -- | with radix
         -> Int -- | reverse digit
revert d r = revert' 0 d
  where
    revert' i 0 = i
    revert' i d = let i' = mod d r + i * r
                      d' = div d r
                  in revert' i' d'

palindromic   :: Int  -- | digit
              -> Int  -- | with radix
              -> Bool -- | is palindrome
palindromic p r = p == revert p r

procRep :: (Int -> Bool)           -- | filter condition
        -> (Int -> [Int] -> [Int]) -- | processing
        -> Int                     -- | number of repetitions
        -> [Int]                   -- | list of digits
        -> [Int]                   -- | process with repetitions
procRep c s = procRep' c s $ \i l -> do
  e <- s i l
  guard $ c e
  return e

-- TODO: add multithreading
procRep' :: (Int -> Bool)           -- | filter condition
         -> (Int -> [Int] -> [Int]) -- | processing
         -> (Int -> [Int] -> [Int]) -- | condition process
         -> Int                     -- | number of repetitions
         -> [Int]                   -- | list of digits
         -> [Int]                   -- | process with repetitions
procRep' _ _ _  0           _          = [1]
procRep' _ _ _  _          []          = []
procRep' c s p n'@(n + 1) all@(x : xs) = current ++ remaining
  where
    remaining  =       procRep' c s p n' xs
    current    = p x $ procRep' c s s n all

main :: IO () -- | evaluate largest palindrome
main = print largest
  where
    digits    = 3
    radix     = 10
    count     = 2
    min       = radix ^ (digits - 1)
    max       = radix ^ digits - 1
    numbers   = [min .. max]
    process   = liftM . (*)
    condition = flip palindromic radix
    variants  = procRep condition process count numbers
    largest   = maximum variants