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rell as one n lgn sorting algorithm (Merge-Sort). Dozens, if not hundreds, of other sorting algo- thms have been developed. Another well-known sorting algorithm is Shell – Sort whose asymp- otic running time is on the order of n lg² n, when implemented appropriately. In the problems that follow, you will compare these three algorithms for sorting. Ignoring ower order terms and constant factors, let T1(n), T2(n), and T3(n) be the "effort" required by asertion/Selection-Sort, Shell-sort, and Merge-Sort, respectively, to sort a list of length n. We ave n2 T1(n) T2(n) n lg? n T3(n) n lg n

rell as one n lgn sorting algorithm (Merge-Sort). Dozens, if not hundreds, of other sorting algo- thms have been developed. Another well-known sorting algorithm is Shell – Sort whose asymp- otic running time is on the order of n lg² n, when implemented appropriately. In the problems that follow, you will compare these three algorithms for sorting. Ignoring ower order terms and constant factors, let T1(n), T2(n), and T3(n) be the "effort" required by asertion/Selection-Sort, Shell-sort, and Merge-Sort, respectively, to sort a list of length n. We ave n2 T1(n) T2(n) n lg? n T3(n) n lg n

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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In class, we discussed two quadratic sorting algorithms (Insertion-Sort and Selection-Sort) as well as one n lgn sorting algorithm (Merge-Sort). Dozens, if not hundreds, of other sorting algo- rithms have been developed. Another well-known sorting algorithm is Shell – Sort whose asymp- totic running time is on the order of n lg? n, when implemented appropriately. In the problems that follow, you will compare these three algorithms for sorting. Igoring lower order terms and constant factors, let T1(n), T2(n), and T3(n) be the "effort" required by Insertion/Selection-Sort, Shell-sort, and Merge-Sort, respectively, to sort a list of length n. We have T1(n) n2 T2(n) n lg? n T3(n) n lgn where lg n is log2 (n) and lg² n = (lg n)?. 1 i. On a single sheet of graph paper, plot the effort required by each of the these algorithms when run on lists of length n = points with a smooth, hand-drawn curve. See the plots given in the "Exponentials and Logs" appendix of the text for examples of what you should do. You may print a piece of graph paper from the PDF located at the following URL: 4, 8, 16, and 32. For each algorithm, connect the plot http://www.printfreegraphpaper.com/ (If you view this assignment on-line, you may simply click on the above hyperlink.) ii. Suppose that you were given a budget of 1,000 units of "effort." algorithms, determine the largest list length such that the sorting effort required is guaranteed to be at most 1,000. For each of the three iii. How many times larger is the list that Merge-Sort can handle, as compared to the lists that Insertion/Selection-Sort and Shell-sort can handle? How many times larger is the list that Shell-sort can handle, as compared to the list that Insertion/Selection-Sort can handle?
Transcribed Image Text:In class, we discussed two quadratic sorting algorithms (Insertion-Sort and Selection-Sort) as well as one n lgn sorting algorithm (Merge-Sort). Dozens, if not hundreds, of other sorting algo- rithms have been developed. Another well-known sorting algorithm is Shell – Sort whose asymp- totic running time is on the order of n lg? n, when implemented appropriately. In the problems that follow, you will compare these three algorithms for sorting. Igoring lower order terms and constant factors, let T1(n), T2(n), and T3(n) be the "effort" required by Insertion/Selection-Sort, Shell-sort, and Merge-Sort, respectively, to sort a list of length n. We have T1(n) n2 T2(n) n lg? n T3(n) n lgn where lg n is log2 (n) and lg² n = (lg n)?. 1 i. On a single sheet of graph paper, plot the effort required by each of the these algorithms when run on lists of length n = points with a smooth, hand-drawn curve. See the plots given in the "Exponentials and Logs" appendix of the text for examples of what you should do. You may print a piece of graph paper from the PDF located at the following URL: 4, 8, 16, and 32. For each algorithm, connect the plot http://www.printfreegraphpaper.com/ (If you view this assignment on-line, you may simply click on the above hyperlink.) ii. Suppose that you were given a budget of 1,000 units of "effort." algorithms, determine the largest list length such that the sorting effort required is guaranteed to be at most 1,000. For each of the three iii. How many times larger is the list that Merge-Sort can handle, as compared to the lists that Insertion/Selection-Sort and Shell-sort can handle? How many times larger is the list that Shell-sort can handle, as compared to the list that Insertion/Selection-Sort can handle?
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