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Haskell Quiz/Cryptograms/Solution Abhinav

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{-
  Decrypts a cryptogram (a substitution cypher).
  A solution to rubyquiz 13 (http://rubyquiz.com/quiz13.html).
  Usage: ./Cryptograms dictionary_file encrypted_file num_max_mappings
 
  Copyright 2012 Abhinav Sarkar <abhinav@abhinavsarkar.net>
-}
 
{-# LANGUAGE BangPatterns #-}
 
module Cryptograms where
 
import qualified Data.Map as M
import qualified Data.Set as S
import Control.Monad (foldM)
import Data.Char (toLower, isAlpha)
import Data.List (foldl', find, sortBy, nub)
import Data.Maybe (isJust, fromJust, mapMaybe, catMaybes, fromMaybe)
import Data.Ord (comparing)
import System.Environment (getArgs)
import Text.Printf (printf)
-- import Debug.Trace (trace)
 
trace :: String -> a -> a
trace _ x = x
 
type Mapping = M.Map Char Char
 
type Dict = M.Map Int (S.Set String)
 
-- reads the dictionary from the given file. must contain one word per line.
readDict :: FilePath -> IO Dict
readDict filePath = do
  !dictWords <- fmap (filter (all isAlpha) . map (map toLower) . lines)
                  $ readFile filePath
  return $
    foldl' (\dict w -> M.insertWith S.union (length w) (S.singleton w) dict)
          M.empty dictWords
 
-- translates the token using the given mapping.
-- return Nothing if unable to translate.
translateToken :: Mapping -> String -> Maybe String
translateToken mapping = fmap reverse
  . foldM (\acc char -> M.lookup char mapping >>= Just . (:acc)) ""
 
-- translates all tokens using the given mapping.
-- translates the token to '---' if unable to translate.
translateTokens :: Mapping -> [String] -> [String]
translateTokens mapping =
  map (\token ->
        fromMaybe (replicate (length token ) '-') . translateToken mapping $ token)
 
-- checks if the given word is in the dictionary.
inDict :: Dict -> String -> Bool
inDict dict word =
  case M.lookup (length word) dict of
    Nothing -> False
    Just ws -> word `S.member` ws
 
-- scores a mapping by counting the number of translated tokens that are
-- in the dictionary.
scoreMapping :: Dict -> Mapping -> [String] -> Int
scoreMapping dict mapping =
  length . filter (inDict dict) . mapMaybe (translateToken mapping)
 
-- scores multiple mappings and returns an assoc list sorted by descending score.
scoreMappings :: Dict -> [String] -> [Mapping] -> [(Mapping, Int)]
scoreMappings dict tokens =
  reverse . sortBy (comparing snd)
  . map (\mapping -> (mapping, scoreMapping dict mapping tokens))
 
-- finds maximum num mappings which have best scores for the given tokens.
findBestMappings :: Dict -> Int -> [String] -> [Mapping]
findBestMappings dict num tokens = let
  mappings = scoreMappings dict tokens
             . S.toList
             . foldl' (\mappings -> -- find the best num mappings
                        S.fromList . take num
                        . map fst . scoreMappings dict tokens . S.toList
                        . findMappingsForToken dict mappings)
                      S.empty
             . nub . reverse . sortBy (comparing (\x -> (length x, x)))
             $ tokens
  maxScore = if not (null mappings) then snd . head $ mappings else 0
  in map fst . takeWhile ((== maxScore) . snd) $ mappings
 
-- finds the merged mappings for a token
findMappingsForToken :: Dict -> S.Set Mapping -> String  -> S.Set Mapping
findMappingsForToken dict mappings token =
  case find (inDict dict) . mapMaybe (flip translateToken token)
       . reverse . sortBy (comparing M.size)
       . S.toList $ mappings of
    -- the token is already translatable. return current mappings.
    Just dtoken -> trace (printf "Translated %s -> %s" token dtoken) mappings
 
    -- the token is not translatable yet. return current mappings merged
    -- with the mappings for the token.
    Nothing -> mergeMappingLists mappings (createMappingsForToken dict token)
 
-- merges mapping lists. discards conflicting mappings while merging.
mergeMappingLists :: S.Set Mapping -> S.Set Mapping -> S.Set Mapping
mergeMappingLists mappings1 mappings2
  | mappings1 == S.empty = mappings2
  | mappings2 == S.empty = mappings1
  | otherwise =
      trace (printf "Merging %s x %s mappings" (show . S.size $ mappings1) (show . S.size $ mappings2)) $
        let
          merged = -- union current mappings and their merged result mappings
            S.unions [mappings1, mappings2,
              S.fromList . catMaybes $
                [mergeMappings m1 m2 | m1 <- S.toList mappings1, m2 <- S.toList mappings2]]
        in trace (printf "Merged to %s mappings" (show $ S.size merged)) merged
 
-- merges two mappings. returns Nothing if mappings conflict.
mergeMappings :: Mapping -> Mapping -> Maybe Mapping
mergeMappings mapping1 mapping2 =
  foldM
    (\acc (k, v) ->
      if M.member k acc
        then if (fromJust . M.lookup k $ acc) == v then Just acc else Nothing
        else Just $ M.insert k v acc)
    mapping1 $ M.toList mapping2
 
-- creates mappings for a token by finding words of same form from the dictionary.
createMappingsForToken :: Dict -> String -> S.Set Mapping
createMappingsForToken dict token =
  case M.lookup (length token) dict of
    Nothing -> S.empty
    Just words -> let
      tokenF = tokenForm token
      matches = S.fromList . map (getMapping token)
                . filter ((== tokenF) . tokenForm) . S.toList $ words
      in trace (printf "%s -> %s matches" token (show . S.size $ matches)) matches
 
-- returns form of a token. for example, the form of "abc" is [1,2,3]
-- while the form of "aba" is [1,2,1].
tokenForm :: String -> [Int]
tokenForm token = let
  (_, form, _) =
    foldl' (\(formMap, form, lf) char ->
             case M.lookup char formMap of
               Nothing -> (M.insert char (lf + 1) formMap, (lf + 1) : form, lf + 1)
               Just f -> (formMap, f : form, lf))
           (M.empty, [], 0) token
  in reverse form
 
-- creates the mapping between two strings of same length.
getMapping :: String -> String -> Mapping
getMapping t1 t2 = M.fromList $ zip t1 t2
 
-- returns text representation of a mapping.
showMapping :: Mapping -> String
showMapping mapping =
  map snd . sortBy (comparing fst) . M.toList
  . foldl' (\acc c -> M.insertWith (\_ l -> l) c '.' acc) mapping $ ['a'..'z']
 
main :: IO()
main = do
  (dictFile : cryptTextFile : num : _) <- getArgs
  -- read the dictionary
  !dict <- readDict dictFile
  -- read the encrypted tokens
  !tokens <- fmap (map (map toLower) . lines) $ readFile cryptTextFile
 
  let mappings = findBestMappings dict (read num) tokens
 
  if not (null mappings)
    then do
      putStrLn $ printf "%s best mappings found with score %s/%s"
        (show $ length mappings)
        (show $ scoreMapping dict (head mappings) tokens)
        (show $ length tokens)
      putStrLn . unlines $
        map (\mapping -> printf "%s -> %s"
              (showMapping mapping)
              (unwords . translateTokens mapping $ tokens))
            mappings
    else
      putStrLn "No mappings found"

Description: The program decrypts the cryptogram by finding all the possible mappings by matching the encrypted tokens with words of same form from the dictionary and merging the resulting mappings.

Source: https://github.com/abhin4v/rubyquiz/blob/master/Cryptograms.hs