Duration: 90 minutes. Page 1 of 14 Q2: /13 Q3: /13 TOTAL: /38. Bonus /1

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1 CSCA48 Winter 2018 Term Test #2 Duration: 90 minutes Aids Allowed: none First Name: Student Number: Markus Login: Last Name: Carefully read and follow all instructions on this page, and fill in all fields. Write all answers neatly in the space provided, or indicate clearly where your question continues. Please place a checkmark beside your tutorial session Tutorial # Date/Time Room TA Name Check Tut 0001 TUESDAY 16:00-17:00 HW214 Mohammad Tut 0003 WEDNESDAY 16:00-17:00 BV264 William Tut 0006 THURSDAY 09:00-10:00 HW215 Kevin Tut 0008 WEDNESDAY 16:00-17:00 IC120 Mohammad Tut 0009 TUESDAY 10:00-11:00 MW110 Aiyaz Tut 0011 THURSDAY 10:00-11:00 IC120 Prantar Tut 0012 THURSDAY 12:00-13:00 AA207 Priscilla Tut 0015 FRIDAY 10:00-11:00 IC320 Maria Tut 0017 FRIDAY 14:00-15:00 BV363 Maria Tut 0018 TUESDAY 11:00-12:00 MW262 Kevin Tut 0020 TUESDAY 18:00-19:00 IC204 Rohini Tut 0021 TUESDAY 12:00-13:00 HW308 Harshil Tut 0022 FRIDAY 11:00-12:00 IC326 Yufei Cui Tut 0023 WEDNESDAY 13:00-14:00 HW308 Ralph Tut 0025 THURSDAY 10:00-11:00 HW215 Jason Tut 0026 THURSDAY 14:00-15:00 AA206 Eric Do not turn this page until you have received the signal to start. This exam consists of 3 questions plus 1 bonus question in 14 pages. When you receive the signal to start, please make sure that your copy is complete. If you use any space for rough work, indicate clearly what you want marked. Please read all questions thoroughly before starting on any work. The University of Toronto's Code of Behaviour on Academic Matters applies to all University of Toronto Scarborough students. The Code prohibits all forms of academic dishonesty including, but not limited to, cheating, plagiarism, and the use of unauthorized aids. Students violating the Code may be subject to penalties up to and including suspension or expulsion from the University. Q1: /12 Q2: /13 Q3: /13 TOTAL: /38 Bonus /1 Page 1 of 14

2 Use the space below for rough work. This page will not be marked unless you clearly indicate the part of your work that you want us to mark. Page 2 of 14

3 1. [12 marks total] In case you need it, here are the letters of the alphabet in increasing order. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Consider the following binary search tree (BST), which we call plucky. A P L U C O T Y B K M D G E I (a) [2 marks] Complete the following sentence so that we would get plucky if we were to insert the letters from it in the order they appear. Put one letter over each underscore (_). _ P L U C K Y. The sentence must be grammatically correct and meaningful. Assume that BST insertions are done according to the algorithm shown in class. Hint: Each word contains a vowel. (b) [2 marks] Give the order of nodes visited in a post-order traversal of plucky. (c) [2 marks] Give the order of nodes visited in an in-order traversal of plucky. Page 3 of 14

4 (d) [3 marks] Draw a binary search tree that contains the same letters as plucky but has minimum possible height. (e) [3 marks] Draw the resultant tree after the deletion of the letter C from plucky. Assume that BST deletions are done according to the algorithm shown in class. Page 4 of 14

5 Use the space below for rough work. This page will not be marked unless you clearly indicate the part of your work that you want us to mark. Page 5 of 14

6 2. [13 marks total] Consider the following functions. def fun(s): """ (str) -> str """ if len(s) == 0: result = s else: result = fun_helper(s, 0, 2, "") return result def fun_helper(s, i, d, t): """ (str, int, int, str) -> str """ t = t + s[i] i = i + d if i >= len(s): d = -2 i = i - 1 if i >= len(s): i = i - 2 if i < 0: result = t else: result = fun_helper(s, i, d, t) return result Page 6 of 14

7 (a) [3 marks] Trace fun("gnu"). Do your trace as shown in class. Page 7 of 14

8 (b) [5 marks] Trace fun("friend"). Do your trace as shown in class. Page 8 of 14

9 (c) [5 marks] Nick wrote a function that returns exactly what fun(s)returns, but without the use of loops or helper functions. The only function it calls is itself. Unfortunately, the Code Stealer stole parts of Nick s function. Please help Nick restore his function by filling in the blanks as indicated. def rec_fun(s): if : result = else: result = return result 3. [13 marks total] For this question we assume the existence of a binary tree node class called BTNode, with attributes left and right, for the pointers to the roots of its left and right subtrees respectively. We also assume that BTNode has getters get_left() and get_right(). We define a binary tree to be height balanced if and only if for every node (in the tree), the heights of its left and right subtrees differ by at most one. Put another way, the height of every left subtree is one less than, the same as, or one more than the height of its corresponding right subtree. We want to write a function that takes (a pointer to) the root of a binary tree and returns whether the given tree is height balanced. (a) [2 marks] Write a function header for this function along its docstring. You may omit the examples. Page 9 of 14

10 Use the space below for rough work. This page will not be marked unless you clearly indicate the part of your work that you want us to mark. Page 10 of 14

11 (b) [2 marks] Explain why using direct recursion (i.e., why recursion without a helper function) would not work here. (c) [2 marks] Write a function header for a useful helper function along with its docstring. You may omit the examples. Page 11 of 14

12 Use the space below for rough work. This page will not be marked unless you clearly indicate the part of your work that you want us to mark. Page 12 of 14

13 (c) [5 marks] Complete the body of your helper function by filling in the blanks below. # if smallest possible tree if : result = else: # find solutions for left and right subtrees, and # combine them to form solution for current tree = = result = return result (d) [2 marks] Write the body of the function whose header you gave in part (a). Page 13 of 14

14 4. [Bonus] We want you to predict how well you scored on this test in comparison to your classmates. Suppose we placed all the test marks from those who wrote this test in a list, then sorted the list so that the highest test mark is at the start of the list, and the lowest is at the end. As we scan this list from start to end, where do you think we would first encounter the test mark you got? Please check one box. (a) in the first 20% of the list (among the highest marks). (b) in the second 20% of the list. (c) in the third 20% of the list. (d) in the fourth 20% of the list. (e) in the last 20% of the list (among the lowest marks). Page 14 of 14