import Data.Char -- useful for Caesar exercise
import Data.Ratio -- for Bernoulli exercise
import Data.List -- for the tests

{- Caesar cipher-}

shift :: Int -> Char -> Char
shift = undefined

encode :: Int -> String -> String
encode = undefined

freqList = [8.2, 1.5, 2.8, 4.3, 13, 2.2, 2, 6.1, 7, 0.15, 0.77, 4, 2.4, 6.7,
            7.5, 1.9, 0.095, 6, 6.3, 9.1, 2.8, 0.98, 2.4, 0.15, 2, 0.074]

count :: Char -> String -> Int
count = undefined

percent :: Int -> Int -> Float
percent = undefined

freqs :: String -> [Float]
freqs = undefined

chisqr :: [Float] -> [Float] -> Float
chisqr = undefined

rotate :: Int -> [a] -> [a]
rotate = undefined

positions :: Eq a => a -> [a] -> [Int]
positions = undefined

crack :: String -> String
crack = undefined

encString = "rkcuovv sc pex"

{--Bernoulli numbers--}

fact :: Integer -> Integer
fact = undefined

binom :: Integer -> Integer -> Integer
binom = undefined

bernoulli :: Integer -> Rational
bernoulli = undefined

bernoullis :: Integer -> [Rational]
bernoullis = undefined

check1 :: Integer -> Bool
check1 = undefined

check2 :: Integer -> Bool
check2 = undefined

{-- Tests  --}

-- The following should print the first eight rows of Pascal's triangle - try it out!
pascalTriangle = putStrLn $ unlines $ map (\n -> spaces ((m - n) * 2) ++ (intercalate " " $ map (pad 3 . show . binom n) [0..n])) [0..m]
  where m = 8
        spaces n = replicate (fromIntegral n) ' '
        pad n s = let l = length s in if l < n then s ++ spaces (n - l) else s

tests = do
  test "1.1  " "\"mjwj nx fs jcfruqj.\"" (encode 5 "here is an example.")
  test "1.2a " "2" (count 'e' "example")
  test "1.2a'" "33.333336" (percent 1 3)
  test "1.2b " "[10.0,20.0,30.000002,40.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]" (freqs "abbcccdddd")
  test "1.2c " "25.0" (chisqr [50,50,0] [40,40,20])
  test "1.2d " "[4,5,1,2,3]" (rotate 3 [1,2,3,4,5])
  test "1.2d'" "[0,2,3]" (positions 3 [3,1,3,3])
  test "1.3  " "\"test\"" (crack (encode 10 "test"))
  test "2.1a " "[1,1,2,6,24,120]" (map fact [0..5])
  test "2.1b " "[1,5,10,10,5,1]" [binom 5 k | k <- [0..5]]
  test "2.2  " "[1 % 1,(-1) % 2,1 % 6,0 % 1,(-1) % 30,0 % 1,1 % 42]" (map bernoulli [0..6])
  test "2.3  " "[1 % 1,(-1) % 2,1 % 6,0 % 1,(-1) % 30,0 % 1,1 % 42]" (bernoullis 6)
  test "2.4a " "True" (check1 10)
  test "2.4b " "True" (check2 10)

test name e c = do
  putStr ("*** " ++ name ++ ": ")
  if show c == e then putStrLn "OK"
  else putStrLn ("ERROR; expected '" ++ e ++ "', but found '" ++ show c ++ "'")