1. (34 points) Suppose that the following definitions are made: (a) (22 points) Give the values of the following expressions.

Transcription

1 1. (34 points) Suppose that the following definitions are made: import Data.Char field :: [(Char,Integer)] field = [( e,12), ( a,3), ( k,5),( t,2)] huck :: [a] -> Int huck [] = 55 huck (x:z) = 81 huck (w:y:ts) = 97 mark :: a -> (Float,a) mark x = (1.0,x) stall :: Integer -> [(Char,Integer)] -> String stall i [] = [] stall i ((w,p):rest) i == p = w : stall i rest otherwise = "!!" flick :: Int -> Bool flick v = v > 100 even v (a) (22 points) Give the values of the following expressions. (i). 9:3:2:[] [9,3,2] (ii). div (iii). huck [3,30,300] 81 (iv). flick 18 True (v). [70,74..80] [70,74,78] (vi). isupper # False (vii). length [[2,4],[7],[],[8,6]] 4 (viii). [ r (r,m) <- field, odd m] "ak" (ix). stall 12 field "e!!" (x). zip [3,6,10,12] [20,30,40] [(3,20),(6,30),(10,40)] (xi). concat [[2,7],[],[31,8,2]] [2,7,31,8,2] (b) (12 points) Give the types of the following expressions (e.g., the type of [False] is [Bool]).

2 (i). mark Q (Float,Char) (ii). (odd 6, length [3.5]) (Bool,Int) (iii). unzip field ([Char],[Integer]) (iv). fst (flick 13,"moon") Bool (v). ["almost","spring"]:[] [[String]] (vi). [ mark b (a,b) <- field] [(Float,Integer)] 2. (16 points) Consider the following (partial) file system hierarchy, where the numeric labels associated with directories are intended merely as identification for the questions that follow: 1 / 2 dei/ 3 missions/ 4 owca/ 5 doof/ 6 norm/ 7 carl/ 8 mm/ 9 perry/ 17 silentg/ 10 backstory/ 11 inators/ 12 plans/ 13 family/ 14 gear/ 15 missions/ 16 plans/ For each question that follows, suppose that Perry s home directory is directory #9 and that his current working directory is directory #12. (a) If Perry executed the Unix command pwd, what would be the system s response? /dei/doof/plans (b) If Perry executed the Unix command cd.., which directory would become his current working directory? (Give the number of the directory, not the name.) #5 (c) If Perry executed the Unix command cd ~/.., which directory would become his current working directory? (Give the number of the directory, not the name.) #4

3 As before, suppose that Perry s home directory is directory #9 and that his current working directory is directory #12. For each of the following tasks, give a single Unix command would allow Perry to complete the task. You should assume that each task is completed independently of the others (i.e., changes made in one task do not affect other tasks). (d) Delete the file vacation (located in directory #16) rm ~/plans/vacation (e) Move the file seattle (located in directory #15) to directory #17 mv ~/missions/seattle /owca/silentg (f) Create a subdirectory in directory #3 called canada mkdir /missions/canada (g) Make a copy of the file watch.pdf (located in directory #7), placing it in directory #14 with the name new.pdf cp /owca/carl/watch.pdf ~/gear/new.pdf (h) List all files (including hidden files) in directory #11, but do not include info about file permissions and creation dates ls -a../inators 3. (16 points) A gourmet pizza shops sells pizzas with a variety of premium and regular toppings: The base price for a large pizza is $20; the base price for a small pizza is $12. Each premium topping costs $4 for a large pizza and $3 for a small pizza. Each regular topping costs $3 for a large pizza and $2 for a small pizza. To attract new customers, the shop is currently running a special promotion: the first three toppings on large pizzas are free, but additional toppings are charged at the usual prices. Under this deal, premium toppings are discounted first (see examples below). Here are examples of how the pricing works: Ana orders a small pizza with two premium toppings and five regular toppings. She pays $28 ($12 for small pizza, $6 for the premium toppings, and $10 for the regular toppings). Blake buys a large pizza with two premium toppings and five regular toppings. The special promotion makes three toppings (two premium and one regular) free. The remaining four regular toppings cost $12, and hence he pays $32 in total. Cora buys a large pizza with four premium toppings and one regular topping. Because of the special promotion, she receives three premium toppings for free. Thus, she pays $27 ($20 for large pizza, $4 for one premium topping, and $3 for one regular topping). Dale buys a large pizza with one premium topping. Because of the special promotion, the topping is free. Thus, he pays $20. Your task: Write a Haskell function

4 cost :: Integer -> Integer -> Bool -> Integer such that cost prem reg small calculates the cost (in dollars) of a customer s pizza purchase, where prem indicates the number of premium toppings, reg indicates the number of regular toppings, and small is true precisely when a small pizza is ordered. If either prem or reg is negative, the function should return 0. For example, your function should have the following behavior: *Main> cost 2 5 True 28 *Main> cost 2 5 False 32 *Main> cost 4 1 False 27 Sample solution: cost prem reg small prem < 0 reg < 0 = 0 small = 12 + prem*3 + reg*2 prem >= 3 = 20 + (prem-3)*4 + reg*3 otherwise = 20 + newreg*3 where newreg = max 0 (reg - (3-prem)) 4. (10 points) Write a Haskell function enmesh :: [Int] -> [Int] -> [Int] such that enmesh xs ys returns the list obtained by interleaving the elements of xs and ys; the resulting list should be twice the length of the shorter of the two lists. For example, the function should have the following behavior: *Main> enmesh [1,2] [50,60,70,80] [1,50,2,60] *Main> enmesh [0,0,0,0] [2,4,6] [0,2,0,4,0,6] Sample solution #1: enmesh (x:xs) (y:ys) = x: y: enmesh xs ys enmesh = [] Sample solution #2: enmesh xs ys = concat [ [x,y] (x,y) <- zip xs ys ] 5. (12 points) Write a Haskell function compress :: String -> String

5 such that compress cs returns the list obtained by removing all consecutive duplicate entries in the string cs; non-consecutive duplicates are left alone. For example, the function should have the following behavior: *Main> compress "abbbbccaaabaa" "abcaba" Sample solution: compress (x:y:zs) x == y = compress (y:zs) otherwise = x: compress (y:zs) compress xs = xs -- handles empty and singleton lists 6. (12 points) Write a Haskell function findnth :: Int -> a -> [a] -> a such that findnth k backup xs returns the k-th element of xs; if the list does not have a k-th element (either because the list is too short or k is nonpositive), then backup is returned instead. Do not use the built-in operator!! for this question. For example: *Main> findnth 3 A "cis 252" s *Main> findnth 13 A "cis 252" A *Main> findnth (-2) A "cis 252" A Sample solution #1: findnth k backup [] = backup findnth k backup (x:xs) k <= 0 = backup k == 1 = x otherwise = findnth (k-1) backup xs Sample solution #2: findnth k backup xs = head ([ x (i,x) <- zip [1..] xs, i == k] ++ [backup])