{-|
Module:      Elocrypt.Trigraph
Description: Generate a frequency trigraph based on an english dictionary
Copyright:   (c) Sean Gillespie, 2015
License:     OtherLicense
Maintainer:  Sean Gillespie <sean@mistersg.net>
Stability:   Experimental

Generate a letter frequency trigraph, based on a dictionary
-}
module Data.Elocrypt.Trigraph where

import Control.Monad
import Data.Bool
import Data.Char
import Data.List

-- |Search for the character frequencies and return a weighted list
findWeights :: String   -- ^ The two letter prefix
            -> Maybe [(Char, Rational)]
findWeights = fmap (zip ['a'..'z'] . defaultFrequencies) . findFrequency'
  where findFrequency' = findFrequency . map toLower

-- |Search for the character frequencies based on the first a two-letter string
findFrequency :: String -> Maybe [Rational]
findFrequency s = snd `liftM` find ((==) s . fst) frequencies

-- |Fix frequencies if they are all 0, since MonadRandom prohibits this.
-- In this case, use all 1s to give every item an equal weight
defaultFrequencies :: [Rational] -> [Rational]
defaultFrequencies f = bool (replicate 26 1) f (any (>0) f)

-- | A map of character frequencies, based on a dictionary.  The key is a two-letter
--   string, and the value is a list of probabilities (a-z). It's form is:
--
-- > [("aa", [2,0,3,0,0,0,1,0,0,0,0,1,1,1,0,0,0,3,2,0,0,0,0,0,0,0]),
-- > ...
-- >  ("zz", [7,0,0,0,1,0,0,0,7,0,0,17,0,0,2,0,0,0,0,0,0,0,1,0,5,0])]
frequencies :: [(String, [Rational])]
frequencies = [("aa", [2,0,3,0,0,0,1,0,0,0,0,1,1,1,0,0,0,3,2,0,0,0,0,0,0,0]),
               ("ab", [37,25,2,5,38,0,0,2,46,1,0,304,0,2,49,0,0,24,24,0,19,0,0,0,14,0]),
               ("ac", [26,1,64,2,107,0,1,94,67,0,173,13,5,1,35,1,13,32,3,114,23,0,0,0,45,0]),
               ("ad", [35,7,3,43,116,6,3,8,75,14,1,16,25,3,44,3,1,35,20,1,10,25,9,0,18,0]),
               ("ae", [2,0,2,1,0,1,3,0,0,0,0,10,0,2,3,0,0,12,6,0,2,0,0,0,0,0]),
               ("af", [5,0,0,0,14,50,2,0,3,0,2,5,0,2,7,0,0,5,1,39,1,0,0,0,1,0]),
               ("ag", [30,1,0,1,182,0,42,5,30,0,0,7,9,42,51,3,0,24,3,0,21,0,3,0,3,0]),
               ("ah", [12,0,0,0,20,0,0,0,3,0,0,5,4,2,13,0,0,2,0,0,1,0,0,0,0,0]),
               ("ai", [2,0,10,26,2,1,10,0,2,1,2,87,13,144,0,2,0,93,30,23,0,3,1,0,0,0]),
               ("aj", [4,0,0,0,3,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0]),
               ("ak", [11,0,1,1,98,1,0,1,15,0,0,3,0,0,5,1,0,3,0,1,2,0,3,0,8,0]),
               ("al", [78,20,34,45,124,21,24,5,109,0,28,237,31,3,53,23,0,7,16,69,29,26,5,0,26,2]),
               ("am", [70,57,1,1,98,3,0,1,68,0,0,3,38,2,43,69,0,3,14,3,12,0,2,0,14,0]),
               ("an", [114,6,156,359,103,8,146,12,141,2,57,4,0,89,61,1,4,1,124,443,29,6,1,3,28,9]),
               ("ao", [0,0,1,0,0,0,0,0,0,0,0,3,1,0,0,0,0,3,2,2,2,0,0,0,0,0]),
               ("ap", [29,3,0,1,59,1,0,86,25,0,1,14,1,1,37,94,0,9,22,30,8,0,0,0,9,0]),
               ("aq", [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,14,0,0,0,0,0]),
               ("ar", [124,64,101,233,115,12,47,5,188,3,61,55,68,34,46,25,6,94,48,189,5,22,5,1,172,2]),
               ("as", [19,3,32,0,71,0,1,81,49,0,22,3,19,2,19,34,4,0,152,211,12,0,1,0,17,1]),
               ("at", [50,3,41,2,863,4,0,144,352,0,5,14,6,3,144,0,0,60,13,106,57,1,5,0,8,5]),
               ("au", [0,5,23,35,5,5,38,1,0,1,3,33,4,23,0,4,1,35,52,56,0,1,0,7,0,1]),
               ("av", [35,0,0,1,108,0,0,0,49,0,0,1,0,0,19,0,0,0,0,0,3,1,0,0,6,0]),
               ("aw", [30,10,0,4,3,6,2,2,2,0,10,13,4,15,3,0,0,6,3,5,0,0,0,0,2,0]),
               ("ax", [3,0,0,0,4,0,0,0,22,0,0,1,0,0,7,2,0,0,1,1,0,0,3,0,3,0]),
               ("ay", [11,8,1,5,16,5,1,2,2,0,0,10,7,4,13,1,0,3,5,7,3,0,5,0,0,0]),
               ("az", [10,0,0,1,22,0,0,0,10,0,0,0,0,0,7,0,0,0,0,2,2,0,0,0,4,11]),
               ("ba", [0,17,74,11,1,2,19,4,8,0,10,68,7,73,1,7,0,110,54,55,9,1,3,1,12,1]),
               ("bb", [7,0,0,0,16,0,0,0,10,0,0,24,0,0,9,0,0,2,3,0,2,0,0,0,14,0]),
               ("bc", [2,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0]),
               ("bd", [2,0,0,0,2,0,0,0,2,0,0,0,0,0,3,0,0,1,0,0,3,0,0,0,0,0]),
               ("be", [51,1,14,34,18,11,16,7,9,0,1,85,5,48,2,2,2,199,36,41,0,4,5,1,6,2]),
               ("bf", [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0]),
               ("bg", [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]),
               ("bh", [0,0,0,0,1,0,0,0,0,0,0,0,0,0,5,0,0,0,0,0,1,0,0,0,0,0]),
               ("bi", [34,8,22,21,8,3,9,1,0,3,1,50,7,45,16,4,2,29,22,59,4,4,0,0,0,3]),
               ("bj", [0,0,0,0,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0]),
               ("bk", [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]),
               ("bl", [57,0,0,0,519,0,0,0,35,0,0,0,0,0,47,0,0,0,0,0,32,1,0,0,3,0]),
               ("bm", [0,0,0,0,1,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0]),
               ("bn", [1,0,0,0,2,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0]),
               ("bo", [62,7,4,21,3,2,9,3,8,1,1,46,8,63,58,2,0,55,15,20,46,6,17,10,19,0]),
               ("bp", [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0]),
               ("bq", [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]),
               ("br", [110,0,0,0,77,0,0,0,100,0,0,0,0,0,78,0,0,0,0,0,28,0,0,0,10,0]),
               ("bs", [0,0,6,0,16,0,0,0,7,0,0,0,0,0,12,0,0,0,0,27,2,0,0,0,0,0]),
               ("bt", [1,0,0,0,3,1,0,0,0,0,0,4,0,0,1,0,0,3,0,0,0,0,0,0,0,0]),
               ("bu", [0,3,21,16,3,5,14,0,12,1,2,52,7,20,2,0,1,104,44,54,0,0,0,3,1,5]),
               ("bv", [0,0,0,0,3,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]),
               ("bw", [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]),
               ("bx", [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]),
               ("by", [1,0,0,0,3,0,1,2,0,0,0,4,0,0,0,3,0,6,8,3,0,0,2,0,0,2]),
               ("bz", [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]),
               ("ca", [1,47,17,33,1,3,4,5,7,1,3,120,40,120,1,59,1,171,60,150,19,20,1,0,5,0]),
               ("cb", [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0]),
               ("cc", [23,0,0,0,22,0,0,5,13,0,0,13,0,0,26,0,0,7,0,0,27,0,0,0,0,0]),
               ("cd", [1,0,1,0,1,0,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0]),
               ("ce", [23,6,4,17,6,6,1,2,13,0,0,50,12,109,7,43,0,76,63,22,1,0,4,0,2,1]),
               ("cf", [2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]),
               ("cg", [0,0,0,0,1,0,0,0,2,0,0,0,0,0,2,0,0,4,1,0,1,0,0,0,0,0]),
               ("ch", [165,10,2,3,176,4,3,1,141,0,0,26,20,16,102,1,0,63,8,10,44,0,13,0,20,0]),
               ("ci", [76,15,8,33,24,16,3,0,0,0,0,38,5,45,50,28,0,29,38,71,6,8,0,0,0,0]),
               ("cj", [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]),
               ("ck", [17,16,2,3,90,4,1,7,20,1,1,45,8,8,12,9,0,3,32,6,6,0,13,0,22,0]),
               ("cl", [95,0,0,0,84,0,0,0,50,0,0,0,0,0,54,0,0,0,0,0,34,0,0,0,3,0]),
               ("cm", [1,0,0,0,2,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0]),
               ("cn", [2,0,0,0,1,0,0,0,4,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0]),
               ("co", [33,16,40,22,14,10,11,12,9,1,1,101,218,421,24,56,2,129,37,40,86,22,25,4,4,2]),
               ("cp", [1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0]),
               ("cq", [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,13,0,0,0,0,0]),
               ("cr", [101,0,0,0,112,0,0,0,75,0,0,0,0,0,88,0,0,0,0,1,41,0,0,0,25,0]),
               ("cs", [0,0,0,0,0,0,0,0,3,0,0,0,0,1,2,0,0,0,1,2,0,0,0,0,0,0]),
               ("ct", [44,0,0,0,12,2,0,0,113,0,0,0,2,0,94,0,0,46,0,0,42,0,1,0,3,0]),
               ("cu", [3,12,2,6,6,6,0,0,8,0,0,102,42,10,9,15,0,72,51,41,1,0,0,0,0,0]),
               ("cv", [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]),
               ("cw", [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]),
               ("cx", [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]),
               ("cy", [5,1,20,0,0,0,1,0,0,0,0,3,0,2,2,4,0,3,2,9,0,0,0,0,0,0]),
               ("cz", [2,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]),
               ("da", [0,7,16,7,1,2,13,6,18,0,3,54,23,59,0,10,0,31,6,40,8,13,3,0,32,3]),
               ("db", [9,0,0,0,7,0,0,0,3,0,0,2,0,0,8,0,0,1,0,0,8,0,0,0,2,0]),
               ("dc", [5,0,0,0,0,0,0,2,0,0,0,2,0,0,3,0,0,0,0,0,2,0,0,0,0,0]),
               ("dd", [8,0,0,0,30,0,0,3,19,0,0,38,0,0,4,0,0,4,0,0,1,0,0,0,16,0]),
               ("de", [34,37,82,14,17,41,11,4,5,2,0,88,62,170,14,40,4,183,99,39,6,20,16,6,1,2]),
               ("df", [6,0,0,0,0,0,0,0,6,0,0,2,0,0,5,0,0,2,0,0,4,0,0,0,0,0]),
               ("dg", [4,0,0,0,73,0,0,0,2,0,1,1,1,0,0,0,0,1,0,0,2,0,1,0,3,0]),
               ("dh", [8,0,0,0,9,0,0,0,4,0,0,0,0,0,10,0,0,0,0,0,0,0,0,0,0,0]),
               ("di", [100,10,104,12,33,26,31,1,1,0,1,22,22,65,57,15,0,20,138,53,20,31,1,6,0,1]),
               ("dj", [4,0,0,0,2,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,7,0,0,0,0,0]),
               ("dk", [0,0,0,0,1,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]),
               ("dl", [9,0,0,0,79,0,0,0,12,0,0,0,0,0,7,0,0,0,0,0,1,0,0,0,3,0]),
               ("dm", [13,0,0,0,3,0,0,0,21,0,0,0,0,0,11,0,0,0,0,0,1,0,0,0,0,0]),
               ("dn", [7,0,0,0,9,0,0,0,3,0,0,0,0,0,1,0,0,0,0,6,0,0,0,0,0,0]),
               ("do", [1,5,21,10,6,3,20,1,3,0,0,30,38,54,17,7,0,39,11,10,30,5,54,5,1,3]),
               ("dp", [6,0,0,0,1,0,0,1,3,0,0,1,0,0,7,0,0,1,0,0,0,0,0,0,0,0]),
               ("dq", [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0]),
               ("dr", [74,0,0,0,47,0,0,0,53,0,0,0,0,0,80,0,0,0,0,0,22,0,0,0,8,0]),
               ("ds", [1,0,3,0,10,0,0,9,5,0,1,3,10,0,16,8,0,0,0,31,1,0,2,0,0,0]),
               ("dt", [3,0,0,0,1,0,0,6,1,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0]),
               ("du", [10,7,52,2,5,3,4,0,2,0,1,33,14,15,5,11,1,19,15,8,1,0,0,0,0,1]),
               ("dv", [3,0,0,0,13,0,0,0,7,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0]),
               ("dw", [19,0,0,0,10,0,0,0,19,0,0,0,0,0,8,0,0,2,0,0,0,0,0,0,2,0]),
               ("dx", [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]),
               ("dy", [4,2,1,2,3,1,2,0,1,0,1,4,4,12,0,0,0,0,8,1,0,0,1,0,0,0]),
               ("dz", [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0]),
               ("ea", [0,39,34,110,0,12,13,3,0,0,50,68,38,71,0,13,1,117,80,112,28,19,7,0,0,1]),
               ("eb", [32,5,0,0,31,0,0,0,8,0,0,6,0,0,28,0,0,32,2,3,29,0,0,0,4,0]),
               ("ec", [33,0,9,2,51,0,0,39,49,0,47,26,0,0,59,0,0,35,2,206,42,0,0,0,2,0]),
               ("ed", [29,7,1,16,45,5,22,3,88,0,0,8,9,4,24,2,0,27,8,4,27,0,7,0,13,0]),
               ("ee", [2,4,13,63,1,6,1,4,10,0,19,23,13,66,1,42,0,43,9,34,1,4,6,0,0,8]),
               ("ef", [14,0,1,2,36,33,0,0,22,0,0,15,0,0,24,0,0,14,1,13,35,0,0,0,5,0]),
               ("eg", [48,1,0,0,36,1,15,2,38,0,0,7,4,4,26,0,0,38,0,0,19,0,0,0,4,0]),
               ("eh", [14,0,0,0,24,0,0,0,6,0,0,0,1,0,18,0,0,4,0,0,4,0,0,0,3,0]),
               ("ei", [8,0,5,13,2,1,42,0,1,1,2,13,7,59,1,1,0,10,25,22,0,7,0,0,0,2]),
               ("ej", [4,0,0,0,4,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,3,0,0,0,0,0]),
               ("ek", [2,1,0,1,6,0,0,0,4,0,0,0,0,1,1,0,0,0,2,3,0,0,0,0,1,0]),
               ("el", [76,7,6,57,131,19,7,3,125,0,4,238,22,1,48,15,0,4,27,26,17,19,2,0,7,0]),
               ("em", [87,53,1,0,84,0,0,0,102,0,0,3,8,8,56,64,0,0,4,0,19,0,1,0,8,0]),
               ("en", [78,17,68,159,128,8,35,14,96,2,2,4,5,54,57,3,2,9,127,624,33,10,8,0,11,16]),
               ("eo", [0,0,8,10,0,6,7,1,2,0,0,23,10,38,0,16,0,14,6,4,41,3,2,2,0,1]),
               ("ep", [26,1,1,0,27,0,0,32,45,0,0,21,1,0,35,9,0,35,10,65,13,0,2,0,3,0]),
               ("eq", [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,59,0,0,0,0,0]),
               ("er", [217,57,66,22,190,41,70,13,200,3,14,40,134,117,113,42,2,123,167,135,23,58,22,1,123,1]),
               ("es", [17,7,74,6,58,1,3,25,82,0,3,6,17,5,34,52,7,0,222,278,18,2,1,0,6,0]),
               ("et", [78,3,19,0,129,4,0,93,105,0,1,3,2,2,50,1,0,73,5,113,17,0,4,0,32,4]),
               ("eu", [0,4,7,6,1,0,4,0,0,0,2,3,17,4,0,15,0,46,20,18,0,2,1,0,0,0]),
               ("ev", [29,0,0,0,121,0,0,0,56,0,0,0,0,0,26,0,0,2,1,0,2,2,0,0,3,1]),
               ("ew", [33,4,3,4,16,2,0,5,24,0,0,3,3,3,23,2,0,3,15,4,0,0,1,0,2,0]),
               ("ex", [29,0,43,0,20,0,0,14,21,0,0,0,0,0,15,78,1,0,0,72,12,0,0,1,2,0]),
               ("ey", [7,3,1,4,25,2,0,2,0,0,1,4,6,4,4,1,0,2,3,0,0,1,4,0,0,0]),
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               ("zx", [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]),
               ("zy", [0,1,0,0,0,0,4,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0]),
               ("zz", [7,0,0,0,1,0,0,0,7,0,0,17,0,0,2,0,0,0,0,0,0,0,1,0,5,0])]