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 zone :: [(Int,Char)] zone = [(23, g ), (3, m ), (4, d ), (2, k ), (13, e )] poach :: [a] -> Float poach [] = 6.1 poach (x:z) = 3.2 poach (w:y:ts) = 4.0 force :: a -> (a,integer) force x = (x,17) mark :: Int -> [(Int,Char)] -> String mark r [] = [] mark r ((d,m):rest) r == d = m : mark i rest otherwise = "##" handler :: Integer -> Bool handler v = v < 7 odd v (a) (22 points) Give the values of the following expressions. (i). [1,4..9] [1,4,7] (ii). islower? False (iii). handler 2 True (iv). 7:1:9:[] [7,1,9] (v). zip [8,2,6] [400,300,200,100] [(8,400),(2,300),(6,200)] (vi). poach [3,63,12] 3.2 (vii). [ q (i,q) <- zone, even i] "dk" (viii). mark 23 zone "g##" (ix). concat [[4,],[1,2,7],[],[6,2,1]] [4,,1,2,7,6,2,1] (x). div 21 4 (xi). length [[2,4],[9,13],[7],[],[8,6]] (b) (12 points) Give the types of the following expressions (e.g., the type of [False] is [Bool]).

2 (i). (poach [3.], odd 8) (Float,Bool) (ii). force Q (Char,Integer) (iii). [ S, U ]:[] [[Char]] (iv). fst (length [2,2,2],handler 13) Int (v). [ force a (a,b) <- zone] [(Int,Integer)] (vi). unzip zone ([Int],[Char]) 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/ 8 missions/ 9 owca/ 3 doof/ 4 norm/ 10 carl/ 11 mm/ 12 perry/ 13 silentg/ backstory/ 6 inators/ 7 plans/ 14 family/ 1 gear/ 16 missions/ 17 plans/ For each question that follows, suppose that Heinz s home directory is directory #3 and that his current working directory is directory #1. (a) If Heinz executed the Unix command pwd, what would be the system s response? /owca/perry/gear (b) If Heinz executed the Unix command cd.., which directory would become his current working directory? (Give the number of the directory, not the name.) #12 (c) If Heinz executed the Unix command cd ~/.., which directory would become his current working directory? (Give the number of the directory, not the name.) #2

3 As before, suppose that Heinz s home directory is directory #3 and that his current working directory is directory #1. For each of the following tasks, give a single Unix command would allow Heinz 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) List all files (including hidden files) in directory #14, but do not include info about file permissions and creation dates ls -a../family (e) Create a subdirectory in directory #4 called tasks mkdir /dei/norm/tasks (f) Make a copy of the file agents (located in directory #13), placing it in directory #7 with the name blog cp /owca/silentg/agents ~/plans/blog (g) Delete the file duplic.pdf (located in directory #6) rm ~/inators/duplic.pdf (h) Move the file kickball (located in directory #) to directory #8 mv ~/backstory/kickball /missions 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 $18; the base price for a small pizza is $10. 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 $26 ($10 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 $30 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 $2 ($18 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 $18. Your task: Write a Haskell function

4 cost :: Bool -> Int -> Int -> Int such that cost large prem reg 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 large is true precisely when a large 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 False 2 26 *Main> cost True 2 30 *Main> cost True Sample solution: cost large prem reg prem < 0 reg < 0 = 0 not large = 10 + prem*3 + reg*2 prem >= 3 = 18 + (prem-3)*4 + reg*3 otherwise = 18 + newreg*3 where newreg = max 0 (reg - (3-prem)) 4. (10 points) Write a Haskell function interleave :: String -> String -> String such that interleave cs ds returns the string obtained by interleaving the elements of cs and ds; the resulting string should be twice the length of the shorter of the two strings. For example, the function should have the following behavior: *Main> interleave "abcde" "XYZ" "axbycz" *Main> interleave "..." "ABCDE" ".A.B.C.D" Sample solution #1: interleave (x:xs) (y:ys) = x: y: interleave xs ys interleave = [] Sample solution #2: interleave xs ys = concat [ [x,y] (x,y) <- zip xs ys ]. (12 points) Write a Haskell function condense :: [Integer] -> [Integer]

5 such that condense xs returns the list obtained by removing all consecutive duplicate entries in the list xs; non-consecutive duplicates are left alone. For example, the function should have the following behavior: *Main> condense [3,0,0,0,21,3,3,7,1,1,1,0] [3,0,21,3,7,1,0] Sample solution: condense (x:y:zs) x == y = condense (y:zs) otherwise = x: condense (y:zs) condense xs = xs -- handles empty and singleton lists 6. (12 points) Write a Haskell function getnth :: [a] -> Integer -> a -> a such that getnth xs k backup 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> getnth "cis 22" 3 A s *Main> getnth "cis 22" 13 A A *Main> getnth "cis 22" (-2) A A Sample solution #1: getnth [] k backup = backup getnth (x:xs) k backup k <= 0 = backup k == 1 = x otherwise = getnth xs (k-1) backup Sample solution #2: getnth xs k backup = head ([ x (i,x) <- zip [1..] xs, i == k] ++ [backup])