add sheets

Exercise Sheet 1/Exercise One.txt

+double (double 2)
+double (2 + 2)
+double 4
+4 + 4
+8
\ No newline at end of file

Exercise Sheet 1/Exercise Two.txt

+sum (x:[])
+x + sum []
+x + 0
+x
\ No newline at end of file

Exercise Sheet 1/Exercise_Five.hs

+quicktros [] = []
+quicktros (x:xs) = quicktros rs ++ [x] ++ quicktros ls
+                   where 
+                     ls = [ a | a <- xs , a < x ]
+                     rs = [ a | a <- xs , a > x ]
\ No newline at end of file

Exercise Sheet 1/Exercise_Four.hs

+quicktros [] = []
+quicktros (x:xs) = quicktros rs ++ [x] ++ quicktros ls
+                   where 
+                     ls = [ a | a <- xs , a <= x ]
+                     rs = [ a | a <- xs , a > x ]
\ No newline at end of file

Exercise Sheet 1/Exercise_Seven.hs

+n = a `div` (length xs)
+        where 
+           a = 10 
+           xs = [1,2,3,4,5]
\ No newline at end of file

Exercise Sheet 1/Exercise_Three.hs

+product [] = 1
+product (x:xs) = x * (Main.product xs)
\ No newline at end of file

Exercise Sheet 2/ex1.hs

+last (x:[]) = x
+last (x:xs) = last xs
\ No newline at end of file

Exercise Sheet 2/ex2.hs

+fourth1 :: [a] -> a
+fourth1 (w:x:y:z:xs) = z
+
+fourth2 :: [a] -> a
+fourth2 xs = xs !! 3
+
+fourth3 :: [a] -> a
+fourth3 ys = head (tail (tail (tail ys)))
\ No newline at end of file

Exercise Sheet 2/ex3.hs

+safetail1 :: [a] -> [a]
+safetail1 xs =
+    if (length xs > 0) then tail xs
+    else []
+
+safetail2 :: [a] -> [a]
+safetail2 xs | length xs > 0 = tail xs
+             | otherwise = []
+
+safetail3 :: [a] -> [a]
+safetail3 [] = []
+safetail3 xs = tail xs
\ No newline at end of file

Exercise Sheet 2/ex4.hs

+halve :: [a] -> ([a],[a])
+halve xs | even listLength = splitAt (listLength `div` 2) xs
+         | otherwise = ([],[])
+    where listLength = length xs
\ No newline at end of file

Exercise Sheet 2/ex5.hs

+import Data.Char (ord)
+
+--encrypts a given string
+--returns the encrypted string and a function to decrypt the string
+encrypt :: Int -> String -> (String, String -> String)
+encrypt key str = (enc, \str -> [negate key `applyKey` x | x <- str])
+    where
+    	--applies a key to a character
+    	applyKey :: Int -> Char -> Char
+        applyKey k c | k + ord c > 122 = toEnum $ k + ord c - 26
+                     | k + ord c < 97 = toEnum $ k + ord c + 26
+                     | otherwise = toEnum $ k + ord c
+
+    	--encrypts a string with an int
+        enc :: String
+        enc = [applyKey key x | x <-str]
\ No newline at end of file

Exercise Sheet 2/ex6.hs

+--checks four bank card numbers for errors
+--returns true if valid, otherwise false
+luhn :: Int -> Int -> Int -> Int -> Bool
+luhn w x y z | total `mod` 10 == 0 = True --if the answer is divisible by 10 it is valid
+             | otherwise = False --otherwise invalid
+    where
+        --doubles a number and subtracts 9 if result > 9
+        luhnDouble :: Int -> Int
+        luhnDouble n | m > 9 = m - 9
+                     | otherwise = m
+            where m = 2 * n
+
+        total = luhnDouble w + x + luhnDouble y + z
\ No newline at end of file

Exercise Sheet 2/exA1.hs

+-- --counts the number of values within three ranges
+-- histogram :: Int -> [Int] -> [Int]
+-- histogram n xs = [x,y,z]
+--     where
+--         x = length [a | a <- xs, a >= 0, a <= n - 1] --0 <= x <= n-1
+--         y = length [a | a <- xs, a >= n, a <= 2 * n - 1] --n <= x <= 2n-1
+--         z = length [a | a <- xs, a >= 2 * n, a <= 3 * n - 1] --2n <= x <= 3n-1
+
+
+histogram :: Int -> [Int] -> [Int]
+histogram n xs | n <= 0 = error "range sizes cannot be negative or 0"                           --given range is 0 or less
+               | otherwise = [histogramCounter a | a <- [0..(maximum xs) `div` n]]              --given range is valid
+    where
+        histogramCounter :: Int -> Int
+        histogramCounter range = length [a | a <- xs, a >= range * n, a <= (range + 1) * n - 1]
\ No newline at end of file

Exercise Sheet 2/exA2.hs

+approxPi :: Int -> Double
+approxPi n | n <= 0 = error "negative numbers or 0 cannot be used for approximations of pi"
+           | otherwise = 2 * sum [product [1..a] / product [1,3..2 * a + 1] | a <- [0..fromIntegral n-1]]
\ No newline at end of file

Exercise Sheet 3/ex1.hs

+oddEvenSum :: Int
+oddEvenSum = sum [x^2 | x <- [1,3..100]] + sum [y^3 | y <- [0,2..100]]
\ No newline at end of file

Exercise Sheet 3/ex2.hs

+grid :: Int -> Int -> [(Int,Int)]
+grid m n = [(x,y) | x <- [0..m], y <- [0..n]]
+
+square :: Int -> [(Int,Int)]
+square m = [(x,y) | x <- [0..m], y <- [0..m], x /= y]
\ No newline at end of file

Exercise Sheet 3/ex3.hs

+replicate :: Int -> a -> [a]
+replicate n a = [a | x <- [1..n]]
\ No newline at end of file

Exercise Sheet 3/ex4.hs

+pyths :: Int -> [(Int,Int,Int)]
+pyths n = [(x,y,z) | x <- [1..n], y <- [1..n], z <- [1..n], x^2 + y^2 == z^2]
\ No newline at end of file

Exercise Sheet 3/ex5.hs

+perfect :: Int -> [Int]
+perfect n = [x | x <- [2..n], x == (sum . factors) x]
+    where
+    	factors :: Int -> [Int]
+    	factors v = [x | x <- [1..v], v `mod` x == 0, x /= v]
\ No newline at end of file

Exercise Sheet 3/ex6.hs

+positions :: Eq a => a -> [a] -> [Int]
+positions a as = find a $ zip as [0..]
+    where
+        find :: Eq a => a -> [ (a,b)] -> [b]
+        find k t = [ v | (k',v) <- t, k==k']
\ No newline at end of file