Week 3

--Assignment 1

module OneTimePad where

otp :: [Bool] -> [Bool] -> [Bool]

--a)
{-
otp m k = aux m k

aux (m:ms) (k:ks) = (xor m k) : aux ms ks 
aux [] [] = []
-}

xor False False = False
xor True True = False 
xor False True = True
xor True False = True

--implement with zip & map
{-
otp m k = aux m k

aux m k = map (\(x,y) -> xor x y ) (zip m k)
-}

-- b) use zipwith 
otp m k = zipWith (xor) m  k

--Assignment 2

module PrimeNumbers where

-- (a)
prime :: Int -> Bool
prime 0 = False
prime 1 = False
prime n = if [x | x<-[1..n], x>=1 , x<=n, mod n x ==0] == [1,n] then True else False

-- (b)
primes :: Int -> [Int]
primes n = [x | x<-[2..n], prime x == True]

-- (c)
firstPrimes :: Int -> [Int]
firstPrimes m = take m [x | x<-[2..], prime x == True]

--Assignment 3

module Palindromes where

palindromes :: [String] -> [String]
palindromes l = [v++w | v<-l, w<-l, v++w == reverse(v++w)]

--Assignment 4

module Words where

-- (a)
split :: Char -> String -> [String]
split sep s = aux sep s ""

aux sep [] w = [w]
aux sep (c:cs) w
  | c == sep  = w : aux sep cs ""
  | otherwise = aux sep cs (w ++ [c])


-- (b)
isSpace :: Char -> Bool
isSpace x
  | x == ' ' = True
  | otherwise = False


toWords :: String -> [String]
toWords s = aux' sep s ""

aux' sep [] w = []
aux' sep (c:cs) w
  | c == sep  = w : aux' sep cs ""
  | otherwise = aux' sep cs (w ++ [c])

-- (c)
countWords :: String -> Int
countWords = undefined