CS251-SE1. Midterm 2. Tuesday 11/1 8:00pm 9:00pm. There are 16 multiple-choice questions and 6 essay questions.

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1 CS251-SE1 Midterm 2 Tuesday 11/1 8:00pm 9:00pm There are 16 multiple-choice questions and 6 essay questions. Answer the multiple choice questions on your bubble sheet. Answer the essay questions in the space provided on the exam sheet. No phones, books, notes, or programmable calculators. This exam contains 6 pages (including this cover page) Remember to fill in the following bubble card fields: Student ID (not your social security number) Last name and first name Test/Quiz: 002, Course: CS251 Instructor: Your PSO TA s last name from the table below. Section number: Your PSO Section Number from the table below. PSO Time TA Recitation Section Number P01 Wednesday, 9:30-11:20 Kevin S. Bello 0001 P03 Friday, 11:30-1:20 Kevin S. Bello 0003 P06 Wednesday, 3:30-5:20 Daniel Kumor 0006 P07 Thursday, 9:30-11:20 Ruby Tahboub 0007 P08 Wednesday, 11:30-1:20 Daniel Kumor 0008 P09 Thursday, 11:30-1:20 Gaurav Thakur 0009 Recitation Section Number: Student Last Name: Student First Name:

2 CS251-SE1 Midterm 2 - Page 2 of 6 Tuesday 11/1 8:00pm 9:00pm 1. I have correctly entered my first name, last name, and student ID. A. yes B. no 2. Which data structure is best for implementing a deque? A. singly linked list B. array C. doubly linked list D. B and C E. A, B, and C 3. The big-o notation expresses: A. the worst-case time complexity of algorithms B. the average-case space complexity of algorithms C. A and B D. lower bounds on problem complexity E. the running time of algorithms 4. Let f(n) = n 3 + n 2. A. f(n) is O(n 2 ) B. f(n) is O(n 3 ) C. f(n) is O(n 4 / log n) D. B and C E. A and B 5. How many nodes must be added to this binary tree to make it proper/complete? A. proper 2/complete 8 B. proper 1/complete 5 C. proper 2/complete 2 D. proper 5/complete 8 E. cannot be made proper/complete 8 6. A binary tree is empty or consists of a root node with left and right children that are binary trees. This definition: A. is correct, but incomplete

3 CS251-SE1 Midterm 2 - Page 3 of 6 Tuesday 11/1 8:00pm 9:00pm B. is incorrect C. is correct D. is correct for proper binary tree only E. is correct for complete binary trees only 7. Which of the following statements about 2-4 trees is false? A. Every leaf has the same depth. B. Every internal node has 2, 3, or 4 children. C. A tree with n nodes has height O(log n). D. The height of the tree only grows when the root node is split. E. None of the above. 8. How is an element z with a < z < b inserted into this 2-4 tree? 1 a b c A. Insert z into node 1 between a and b then split node 1. B. Replace a with z then recursively insert a into node 2. C. Replace b with z then recursively insert b into node 3. D. Insert z into node 2. E. Insert z into node What type of hash code is effective for character strings? A. Cast the characters to integers then sum them. B. XOR the characters in groups of 4. C. Use a polynomial hash code. D. Use a cyclic hash code. E. C and D 10. What is the MAD method? A. a method for bucketing elements in a hash table so that collisions are resolved efficiently B. a compression function that eliminates patterns in integer keys C. a hash function that efficiently hashes floating point numbers D. a probing method to find alternate locations for collisions E. an open addressing scheme that improves on linear probing 11. Which of the following statements about red-black trees is true? A. The height of a tree with n nodes is at most 2 log 2 n + 1. B. The children of a black node are red. C. The children of a red node are black.

4 CS251-SE1 Midterm 2 - Page 4 of 6 Tuesday 11/1 8:00pm 9:00pm D. Every leaf is black. E. All but one of A D. 12. In this red-black tree, the red nodes are 2, 15, 5, and 8. After inserting 4, what are the values of 1) the root and 2) the parent of the 8 node? A. 11, 7 B. 11, 14 C. 7, 11 D. 7, 14 E. 14, Which array represents a max-heap? A. 25,14,12,13,10,8,16 B. 25,14,16,13,10,8,12 C. 25,14,12,15,10,8,16 D. 25,12,16,13,10,8,14 E. None of the above 14. What is worst-case complexity of: 1) inserting an element into a min-heap of n elements, and 2) creating a min-heap from n unordered elements. A. O(log n) and O(n) B. O(log n) and O(n log n) C. O(1) and O(n) D. O(n) and O(n 2 ) E. O(log n) and O(n 2 log n) 15. Which elements of this skip list are traversed by search(99)? A.,, 38, 48, 99

5 CS251-SE1 Midterm 2 - Page 5 of 6 Tuesday 11/1 8:00pm 9:00pm B.,, 38, 38, 48, 48, 99 C.,,, 5, 38, 48, 48, 99 D.,,, 5, 5, 28, 35, 38, 43, 48, 99 E., 3, 5, 28, 35, 43, 48, Which statement is true of a skip list with n keys? A. The worst-case time complexity of insertion is O(log n). B. The average-case time complexity of insertion is O(n). C. The worst-case space complexity is O(n 2 ). D. The average-case space complexity is O(n). E. The worst-case space complexity is O(n). 17. Given an element x in a binary search tree of height h, explain how to find the the next larger element in O(h) time. Solution: If x has a right child r, return the leftmost descendant of r. If not, return the closest ancestor of x whose left child is x or is an ancestor of x. If none exists, return nil. 18. Give a recursive algorithm for printing the elements of a binary tree in reverse order. For example, the binary tree below will print as 4, 3, 2, Solution: Define print(x) for a tree node pointer x: if x is not null, call print recursively on the right child of x, print the value of x, and call print recursively on the left child of x. Call print on the root pointer. 19. What are two advantages of red-black trees over 2-4 trees? Solution: The data structure is simpler and smaller. requires dynamic memory allocation and freeing. Splitting and merging 2-4 nodes 20. What is Euler s formula for planar subdivisions? Solution: A planar subdivision with v vertices, e edges, f faces, and c components satisfies v e + f = c + 1.

6 CS251-SE1 Midterm 2 - Page 6 of 6 Tuesday 11/1 8:00pm 9:00pm 21. Why is the time complexity of the sweep algorithm on n line segments with m intersection points O((n + m) log n)? Solution: Each line segment generates two events, each intersection point generates one event, and each event takes O(log n) time to update the priority queue and the sweep list. 22. How can the running time and memory usage of skip lists be reduced by modifying the textbook insertion algorithm? Solution: Compute the number of levels for the new element and insert the element into those levels top down and left to right, thus eliminating the up and back pointers.