CS302 Midterm Exam - October 13, 2015 - Page Two

Question 2

What are the running times of each of the following? Use the answer sheet for this. In the questions that have both m and n, assume that m is less than n, and make sure that your answer is as precise as possible. For example, if something is O(mn), then it is true that it is also O(n²); however, in that case O(mn) is the correct answer.

A. Sorting a random vector of n elements with insertion sort.
B. Creating a map from n elements.
C. The statement s2 = s1, when s1 is a string with n elements, and s2 is a string with m elements.
D. Creating a priority queue from n elements.
E. Creating a sorted vector from a map with n elements.
F. Performing n Push() operations on a priority queue with m elements.
G. The statement s2 = s1.c_str(), when s1 is a string with n elements, and s2 a (char *) that points to a C-style string with m elements.
H. Performing m Pop() operations on a priority queue with n elements.
I. Sorting a random vector of n elements with selection sort.
J. Finding the m largest elements on a map with n elements.
K. Sorting a "nearly" sorted vector of n elements with insertion sort.
L. Finding the m elements that are closest in value to a given element, on a map with n elements.
M. Performing m Push() operations on a priority queue with n elements.
N. Erasing m elements from a map with n elements.
O. Sorting a "nearly" sorted vector of n elements with selection sort.

Question 3

Part A: Which of the following vectors represent binary heaps?

A-1: { 12, 19, 24, 51, 43, 67, 31, 48, 66, 78 }
A-2: { 1, 3, 14, 5, 24, 90, 78, 77, 30, 81 }
A-3: { 18, 20, 20, 37, 41, 64, 34, 44, 38, 85 }
A-4: { 8, 25, 30, 35, 78, 70, 28, 92, 33, 83 }

Part B: Give me the vector version of the binary heap that results when you call Push(3) on the following heap: { 9, 23, 11, 57, 38, 17, 12, 86, 88, 80 }

Part C: Give me the vector version of the binary heap that results when you call Pop() on the following heap: { 6, 17, 45, 21, 26, 51, 52, 74, 67, 89 }