Solution to CIS 194 intro to functional programming (HW1)

CIS 194 HW1 (Haskell)

-- CIS 194: Homework 1 (http://www.cis.upenn.edu/~cis194/hw/01-intro.pdf)

-- Exercise 1

lastDigit :: Integer -> Integer
lastDigit n = n `mod` 10

dropLastDigit :: Integer -> Integer
dropLastDigit n = n `div` 10

-- Exercise 2

toRevDigits :: Integer -> [Integer]
toRevDigits n
    | n > 0     = lastDigit n : (toRevDigits $ dropLastDigit n)
    | otherwise = []

-- Exercise 3

doubleEveryOther :: [Integer] -> [Integer]
doubleEveryOther xs = map dbl $ zip [1..] xs
    where dbl (i, n) = if even i then 2 * n else n

-- Exercise 4

sumDigits :: [Integer] -> Integer
sumDigits xs = sum $ map (sum . toRevDigits) xs

-- Exercise 5

luhn :: Integer -> Bool
luhn n = x `mod` 10 == 0
    where x = sumDigits $ doubleEveryOther $ toRevDigits n

-- Exercise 6

type Peg = String
type Move = (Peg, Peg)

hanoi :: Integer -> Peg -> Peg -> Peg -> [Move]
hanoi 0 a b c = []
hanoi n a b c =
    hanoi (n - 1) a c b ++ [(a, b)] ++ hanoi (n - 1) c b a

CIS 194 HW1 (SML)

(* CIS 194: Homework 1 (http://www.cis.upenn.edu/~cis194/hw/01-intro.pdf) *)

infixr 0 $

fun f $ g = f g

fun sum xs = foldl (op+) 0 xs
		   
(* Exercise 1 *)

fun lastDigit n = n mod 10

fun dropLastDigit n = n div 10

(* Exercise 2 *)
				
fun toRevDigits n =
  if n > 0 then lastDigit n :: (toRevDigits $ dropLastDigit n) else []

(* Exercise 3 *)

fun doubleEveryOther xs =
  let
      fun loop [] ys _ = ys
	| loop (x::xs) ys n =
	  let
	      val y = if n mod 2 = 0 then 2 * x else x
	  in
	      loop xs (y::ys) (n + 1)
	  end
  in
      loop xs [] 1
  end

(* Exercise 4 *)

fun sumDigits xs = sum $ map (sum o toRevDigits) xs

(* Exercise 5 *)

fun luhn n =
  let
      val x = sumDigits $ doubleEveryOther $ toRevDigits n
  in
      x mod 10 = 0
  end

(* Exercise 6 *)

fun hanoi 0 a b c = []
  | hanoi n a b c =
    hanoi (n - 1) a c b @ [(a, b)] @ hanoi (n - 1) c b a