CIS 252 Introduction to Computer Science Section M013: Exam 3 (Blue) April 26, Points Possible

Transcription

1 Name: CIS 252 Introduction to Computer Science Section M013: April 26, 2018 Question Points Possible Points Received Total 100 Instructions: 1. This exam is a closed-book (and closed-notes) exam. 2. Legibility counts! Make sure we can read (and find!) your answers. If you need more room for an answer than that given, use the back side of the pages. Be sure to leave a note indicating where the answer is. 3. This test should have 9 pages (including this cover sheet). Let us know now if your copy does not have the correct number of pages. 4. Unless specified otherwise, you may use any built-in Haskell function you want, as long as you use it correctly (including using its correct name). The last page includes Turing machine representations and also lists some common Haskell functions and their types.

2 1. (18 points) Suppose that the following definitions are made: data Fun a = Travel Bool Game a [a] Sport (Float, a, Int) laugh :: (Float,Integer) -> Bool laugh (z,m) = even m z > 500 frolic :: a -> IO [a] frolic w = do putstrln "ready" return (replicate 5 w) Give the types of the following expressions (e.g., the type of [False] is [Bool]). (a) (\ q -> length (q : [False,True,True])) (b) getchar >>= frolic (c) filter laugh [] (d) Sport (e) Game True (f) sequence [getline, getcontents, getline ] (g) map length (h) return ("trip", False) (i) curry laugh

3 2. (20 points) For each of the following tasks, assume that you start out in your home directory, and assume that all files are located there unless otherwise indicated. (Thus, each task is completely independent of the others.) What one-line Unix command (possibly involving pipes or redirection) should you type to perform each of the following tasks? The result for any count task should be a single number. Recall: /usr/share/dict/words is a special file that has exactly one word per line. (a) Find all of the words in the file /usr/share/dict/words that start with the letter d (independent of case) (b) Find all of the words in the file /usr/share/dict/words that contain at most two occurrences of the letter m (c) Create a file called chars.txt that contains the number of characters in the file wonders.txt (d) Get a listing of the nonhidden files in the current working directory whose names do not contain the lowercase letter w (e) Count the number of lines in the file lab3.hs that contain both the substring Int and the substring Bool (the substrings may appear in either order)

4 3. (12 points) Consider the following Turing Machine: mytm :: Prog mytm = [ (("U", w ),( p,rght,"s")), (("U", p ),( #,Rght,"T")), (("Q", p ),( p,rght,"q")), (("Q", # ),( w,rght,"s")), (("T", w ),( p,rght,"q")), (("T", p ),( #,Rght,"S")), (("S", w ),( p,rght,"u")), (("S", p ),( w,lft,"t")) ] (a) Suppose the Turing machine is run with an initial input string of wwwwpppp, with the tape head initially on the leftmost symbol of the string. Determine the final string (including the final position of tape head) on the tape, along with the machine s final state. Final string (including position of tape head): Final state: (b) Suppose the Turing machine is run with an initial input string of ppwwppp, with the tape head initially on the leftmost symbol of the string. Determine the final string (including the final position of tape head) on the tape, along with the machine s final state. Final string (including position of tape head): Final state:

5 4. (14 points) Write a Turing machine that takes a (possibly empty) string containing qs and es, and determines whether the string is an even-lengthed palindrome (i.e., the same frontwards and backwards). Upon termination of the machine, the tape should contain a single symbol: Y if the initial input string was an even-lengthed palindrome, and N otherwise. For example, if the initial input is qqeqqeqq or ee, then the result should be Y. If the original input is qqeeeq (not a palindrome) or eqqqe (palindrome, but not of even length), then the result should be N. You should assume that the tape head is initially set on the leftmost symbol of the string. You may have the final tape head rest wherever you want. Give your answer either as a state-transition (bubble) diagram or as a table, whichever you prefer, but give only one representation. Make sure all necessary information (including the start state) is included in whichever format you use. For your convenience, the last page of this exam includes an example of each format.

6 5. (24 points) A binary tree is either an empty tree or a node with two children, each of which is also a binary tree. In lecture and on homework, we defined (polymorphic) binary trees in Haskell using the following type definition: data BTree a = Empty BNode a (BTree a) (BTree a) deriving (Show) According to this definition, each node has a label: every label in a given binary tree has the same type, just as every element of a given list has the same type. As an example, here is a sample tree along with its BTree Int representation (the filled-in circles represent empty trees): BNode 35 (BNode 20 (BNode 51 Empty Empty) Empty) (BNode 43 (BNode 14 Empty (BNode 23 Empty Empty)) (BNode 26 (BNode 21 Empty Empty) Empty)) Terminology: Recall that a leaf is a node that has no children (or, in terms of our representation: it has only empty trees as children). In contrast, an interior node is a node that has at least one child (i.e., it is a node that is not a leaf). In the tree pictured above, the leaves are those nodes labeled by 51, 23, and 21; the interior nodes are those nodes labeled by 35, 20, 43, 14, and 26. (a) (12 points) Write a Haskell function interiors :: BTree a -> [a] such that interiors tr creates a list containing the labels of all the interior nodes in tr. For example, if tree1 is the tree pictured above, then interiors tree1 returns [35,20,43,14,26]. (The order in which the labels appear is not important.)

7 (b) (12 points) Write a Haskell function graft :: BTree a -> BTree a -> BTree a such that graft tr1 tr2 returns the tree obtained by replacing each empty tree in tr1 with the tree tr2. For example, if tree2 is the tree pictured at the left below and tree3 is the tree pictured in the middle, then graft tree2 tree3 produces the tree pictured on the right:

8 6. (12 points) Write a Haskell program stats :: IO (Float,Float) that performs the following actions in order: (i) prompts the user to enter three floating-point numbers, (ii) reads in three floating-point numbers, and then (iii) returns a pair containing their average and the minimum value among the three numbers. Here s a sample interaction (text typed by the user appears in bold, and the value returned is underlined): *Main> stats Please enter three floats: (7.5,1.3) Important note: For this question, you may assume the existence of a program getfloat :: IO Float that reads a Float value from standard input.

9 Appendix 1: Sample Turing Machines Here is an example of a Turing machine, given as a state-transition (bubble) diagram, as a state table, and as an executable table. Of course, this Turing machine doesn t do much of anything useful. (Note: the symbol below denotes a blank symbol.) A 1/0 L 0/1 R /1 R C B 1/1 R 0 1 A 1, R, B 0, L, C B 1, R, C C 1, R, B sampletm :: Prog sampletm = [ (("A", 0 ),( 1,Rght,"B")), (("A", 1 ),( 0,Lft,"C")), (("B", 1 ),( 1,Rght,"C")), (("C", ),( 1,Rght,"B")) ] Appendix 2: Types of some standard Haskell functions/actions (:) :: a -> [a] -> [a] (++) :: [a] -> [a] -> [a] isupper, islower :: Char -> Bool even, odd :: Integral a => a -> Bool maximum, minimum :: Ord a => [a] -> a length :: [a] -> Int map :: (a -> b) -> [a] -> [b] filter :: (a -> Bool) -> [a] -> [a] curry :: ((a,b) -> c) -> a -> b -> c uncurry :: (a -> b -> c) -> (a,b) -> c (>>=) :: IO a -> (a -> IO b) -> IO b (>>) :: IO a -> IO b -> IO b getchar :: IO Char getline, getcontents :: IO String putchar :: Char -> IO () putstr, putstrln :: String -> IO () return :: a -> IO a print :: Show a => a -> IO () show :: Show a => a -> String sequence :: [IO a] -> IO [a] sequence_ :: [IO a] -> IO ()