This question is concerned with your understanding of various algorithms studied in this class. You are given an implementation of a sorting algorithm written by someone else. You know that the algorithm being implemented is either Insertion sort, Quicksort, or Heapsort. You need to identify the implemented sorting algorithm by running it on carefully designed test cases.   (a) You use the program to sort an array A that is in sorted order. Every time you double the number of elements to be sorted, the observed running time is approximately quadrupled. Which sorting algorithm is implemented?   (b) You use the program to sort an array A that is in sorted order. Every time you double the number of elements to be sorted, the time required is slightly more than doubled, but significantly less than tripled. You then use the program to sort an array A that is in reverse sorted order. Every time you double the number of elements to be sorted, the time required is slightly more than doubled, but significantly less than tripled. Which sorting algorithm is implemented?   (c) You use the program to sort an array A that is in sorted order. Every time you double the number of elements to be sorted, the time required is approximately doubled. You then use the program to sort an array A that is in reverse sorted order. Every time you double the number of elements to be sorted, the time required is approximately quadrupled. Which sorting algorithm is implemented?

Write a brief justification to your answer to Q1-b1.

Given an unsorted array A of n distinct integers and an integer k, you need to return the k smallest integers in the array in sorted order, where k may be any integer between 1 and n. Suppose that you have the following three algorithms to solve this problem. A1: Sort the array in increasing order, then list the first k integers after sorting. A2: Build a min-heap from these n integers, then call Extract-Min k times. A3: Use the linear time selection algorithm to find the k-th smallest integer in the array, then partition the array about that number to obtain the k smallest numbers in the array, and finally sort the k smallest numbers. Assume that you are using mergesort as your sorting algorithm, and use the linear time build-heap algorithm to build the heap. Let T1(n, k) denote the worst-case running time of Algorithm A1. Let T2(n, k) denote the worst-case running time of Algorithm A2. Let T3(n, k) denote the worst-case running time of Algorithm A3. Analyze the worst-case running times of the algorithms. What is the asymptotic notation for T3(n, k)? Use the most accurate big-O notation in your answer. Note that k is between 1 and n. Hence k is nominated by n.

Write a brief justification to your answer to Q1-a1.

There are two sequences X= and Y=. You need to use the dynamic programming algorithm taught in class to compute a longest common subsequence (LCS) of X and Y. You need to compute the values of c(i, j) and b(i, j). Please note that I have used parentheses (rather than brackets) due to the Canvas syntax. Answer the following questions: (a) The value of c(5, 6) is   (b) The value of c(4, 6) is   (c) The value of c(3, 6) is   (d) The value of c(2, 6) is   (e) The value of c(1, 6) is   (f) The value of c(5, 1) is   (g) The value of c(5, 2) is   (h) The value of c(5, 3) is   (i) The value of c(5, 4) is   (j) The value of c(5, 5) is   (k) The LCS computed by the algorithm is

Look at the works-cited or bibliography below. What would the in-text citation look like in MLA?   James, Ken and Sue Apple. ( July 2020). ” The Ten Ways to Help Your Coworkers.”  International Today. www.internationaltoday.com/10ways-to-help-your-coworker

Look at the works-cited or bibliography and choose the correct in-text citation in APA format.   Campbell, Jim. “Training Top-notched Workers.”  Business & Society.  27 July 2013.  www.businessandsocietynow.com/training    

Match the following scenarios to the correct way the speaker is trying to appeal to the audiences.

Looking at this paragraph, what type of essay would this paragraph be included in?

EXTRA CREDIT 2 (5-10 points) – **Depends on the entire class’s participation!***  Please complete the Course Instructor Opinion Survey (via Canvas link or online) for the lecture component of this course (EAS 1601-A)!  If at least 67% of you complete this anonymous survey by Monday December 9, then 5 bonus points will be added to all of your Quiz 6 grades!  If at least 80% of you complete it, then 10 bonus points will be added!! **You don’t need to write anything here on the exam – this is a placeholder.** Thanks for a great semester!