Part 2: Programming Questions

Transcription

1 Part 2: Programming Questions This part of the exam is open book / open Internet, with the caveat that you must not communicate with anyone else. This means that while you are welcome to look something up in the textbook, read a webpage, or try something out in the interpreter, it is not acceptable to send a message to someone else in any manner. This prohibition includes all forms of communication by voice, text, or any other means, including talking to someone in the room, talking to someone on the phone, instant messaging, text messaging, , posting to a discussion board or forum, or otherwise soliciting help from someone other than the course instructor or one of the TAs that is supervising the exam. Put another way: while you are free to consume information that is presently available, you are not permitted to send information to anyone else, or to solicit the creation of new information that didn t exist before this exam started. Failure to abide by this non-communication requirement will be considered academic misconduct, just like talking during a traditional exam. Several of the questions in this part of the exam include some test cases for you to consider while implementing your solution. These should not be considered a complete set of test cases your solution should generate a correct result for any input provided to it. We will test your code with test cases beyond those listed on the exam. Please name your functions in the manner specified in the question, including the indicated capitalization. Please save your response to each question in a separate file, clearly numbered from 1 through 5. Provide a type signature for every function that you write except for lambda functions. Do not import any modules (other than the Prelude module, which is automatically imported). Please hand in your exam twice in case one of the electronic submission methods fails. The answers that you submit to both locations should be identical. (In the event of a discrepancy, whichever one the instructor marks will be taken to be the authoritative submission). Submit your answer to each question in a separate file. Submit all of your answers to the Midterm Exam drop box in D2L Submit all of your answers by ing them as attachments to ben.stephenson@ucalgary.ca. 6

2 Question 1: [7 marks] Write a function named percentlookup. This function will take a list and a floating point value as its two parameters. This function should be polymorphic, allowing the function to work on any type of list. The floating point value will be a percentage. Your function should return the element in the list that is the indicated percentage between its beginning and its end. For example, if the user requests the element at 0 percent then the first element in the list should be returned. Similarly, if the user requests the element at 100 percent then the last element in the list should be returned. Requesting the element at 50 percent should return the middle element from the list if the list has odd length. If the list has even length then requesting the element at 50 percent should return either the element immediately below the middle or immediately above the middle (you can choose which of the two adjacent elements should be returned when the indicated percentage is exactly on the boundary between two elements). Your function should also consider the following exceptional cases: If the list is empty then the program should terminate with an error message that indicates that percentlookup failed because it was provided with an empty list. If the floating point value is less than 0 then the first element in the list should be returned. If the percentage is greater than 100 then the last element in the list should be returned. percentlookup "asdf" (-33.0) should return 'a' percentlookup "asdf" 122 should return 'f' percentlookup [-4, 22, 12, -6] 49.9 should return 22 percentlookup [-4, 22, 12, -6] 50.1 should return 12 percentlookup [0..10] 0 should return 0 percentlookup [0..100] 100 should return 100 percentlookup [ ] 50 should return 500 7

3 Question 2: [7 marks] When the wind blows on a cold day, the air feels even colder than it actually is because the movement of the air increases the rate of cooling of warm objects, like people. This phenomenon is known as wind chill. The wind chill index can be computed from the temperature (in degrees Celsius) and the wind speed (in kilometers per hour) using the following formula: windchillindex = * temp * speed ** * temp * speed ** 0.16 Within the previous formula (and in Haskell) ** is used to denote exponentiation. The formula above is only valid when the temperature is less than or equal to 10 degrees Celsius and the wind speed is at least 4.8 kilometers per hour. Write a function named wci (short for wind chill index) that computes the wind chill for a given temperature and wind speed. If the temperature is above 10 degrees, or the wind speed is less than 4.8 kilometers per hour, then the original temperature should be returned. Otherwise the function should return the wind chill index computed using the formula noted previously. Using the wci function that you wrote previously, create a function a second function named windchills that computes the wind chill for each item in a list of temperature and speed pairs, returning a list of wind chill values that are floating point numbers. windchills [] should return [] windchills [(-25, 21.1)] should return [ ] windchills [(10, 4.8), (5, 20), (0, 0)] should return [10.0, ,0.0] windchills [(0.1, 0.1), (-9.9, 9.9)] should return [0.1, ] windchills [(19.9, 19.9)] should return [19.9] 8

4 Question 3: [7 marks] Consider a path within a Cartesian coordinate system described by a list of (x, y) values. The length of such a path is the distance from the first point to the second point, plus the length from the second point to the third point,, plus the length from point n-1 to point n. If the path is empty then its length is 0. Similarly, if the path only consists of one point the its length is 0. Write a function that computes the length of such a path using a fold. Your solution must not use recursion, list comprehensions, map or filter. You may write a helper function (or even multiple helper functions) and call other functions defined within the Prelude module. Hints: As your fold progresses you will need to both accumulate the distance travelled and keep track of the most recently visited point so that you can compute the distance to the next point. I found it easier to solve this problem with a left fold than a right fold, but both directions are possible. Recall that the distance between two points (x1, y1) and (x2, y2) is sqrt((x2-x1)**2 + (y2-y1)**2) pathlength [] should return 0.0 pathlength [(3.1, -5.2)] should return 0.0 pathlength [(1, 1), (-1, 1)] should return 2.0 pathlength [(-0.5,0.5),(-0.5,-0.5),(0.5,-0.5),(0.5,0.5),(-0.5, 0.5)] should return 4.0 pathlength [(0, 0), (1, 1), (1, 2)] should return

5 Question 4: [7 marks] The filter function provided in the Prelude module retains all items in a list for which some function evaluates to True and removes all items from the list for which that same function evaluates to False. As a result, filter can remove no items from the list, some of the items from the list, or all of the items from the list. In this question you ll write an enhanced version of filter, named filterlimit, which limits the number of items that are removed from the list. The filterlimit function will take a function, f, as its first parameter. The function f will take one parameter and return a Boolean result. The second parameter to filterlimit will be an integer, limit, which is the maximum number of items that will be removed from the list. The final parameter to filterlimit, values, will be the list of values that will be processed. The value returned by filterlimit will be a copy of values with the first limit items for which f evaluates to False removed. Your implementation of filterlimit should be polymorphic, allowing it to be applied to lists of any type. filterlimit (> 0) 10 [-3..3] should return [1,2,3] filterlimit (> 0) 0 [-5..5] should return [-5,-4,-3,-2,-1,0,1,2,3,4,5] filterlimit (> 0) 3 [-2, 2, -3, 3, -4, 4, -5, 5] should return [2,3,4,-5,5] filterlimit (== 0) 3 [] should return [] filterlimit (\x -> x `rem` 2 == 0) 2 [1..9] should return [2,4,5,6,7,8,9] 10

6 Question 5: [7 marks] Consider a program that asks the user a collection of trivia questions. Some questions are multiple choice, answered with either 'A', 'B', 'C' or 'D' while some questions are numeric, answered with a floating point number. While one could imagine having other question types, we ll confine ourselves to these two possibilities in this time-limited environment. Create a new data type named TriviaQuestion. Multiple choice questions will be created with a constructor named MCQ while numeric questions will be created with a constructor named NumericQ. Both constructors will take a string that holds the question text as their first parameter. Multiple choice questions require 5 additional parameters: 4 strings, which are the 4 possible answers to the question, and the correct answer (stored as a character). Numeric questions only require one additional parameter, which is the correct answer for the question as a floating point number. The following statements construct three questions: let q1 = NumericQ "What's 1+1?" 2.0 let q2 = MCQ "What's 1+1?" "0.0" "1.0" "2.0" "4.0" 'C' let q3 = MCQ "What's 3-1?" "0.0" "1.0" "2.0" "4.0" 'C' In addition, you should take the steps that are required so that trivia questions can be compared for equality using the == operator. Two questions are equal if they have the same question text (the multiple choice response items and correct answers should be ignored when deciding whether or not two questions are equal). For example: q1 == q2 should evaluate to True q1 == q3 should evaluate to False q2 == q1 should evaluate to True q2 == q3 should evaluate to False q3 == q1 should evaluate to False q3 == q2 should evaluate to False 11