In class, we discussed two quadratic sorting algorithms (Insertion-Sort and Selection-Sort) aswell 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. Igoringlower order terms and constant factors, let T1(n), T2(n), and T3(n) be the "effort" required byInsertion/Selection-Sort, Shell-sort, and Merge-Sort, respectively, to sort a list of length n. WehaveT1(n)n2T2(n)n lg? nT3(n)n lgnwhere lg n is log2 (n) and lg² n =(lg n)?.1i. On a single sheet of graph paper, plot the effort required by each of the these algorithmswhen 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 graphpaper from the PDF located at the following URL:4, 8, 16, and 32. For each algorithm, connect the plothttp://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 guaranteedto be at most 1,000.For each of the threeiii. How many times larger is the list that Merge-Sort can handle, as compared to the lists thatInsertion/Selection-Sort and Shell-sort can handle? How many times larger is the list thatShell-sort can handle, as compared to the list that Insertion/Selection-Sort can handle?

It is defined as a procedure or formula for solving a problem, based on conducting a sequence of…

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)

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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Considering the following algorithm, analyze its best case, worst case and average case time complexity in terms of a polynomial of n and the asymptotic notation of ɵ. You need to show the steps of your analysis.
1. Let S be a set of n arbitrary but distinct numbers. (a) Give a deterministic algorithm to output the largest n³/4 of the numbers in S in sorted order. Your algorithm must use O(n) comparisons. (b) Show that any deterministic comparison-based algorithm that correctly outputs the median on inputs of n distinct elements must use at least n 1 comparisons. To be completely precise, the median is defined to be the [n/2]th smallest element.
Given an unsorted array. The array has this property that every element in the array is at most k distance from its position in sorted array where k is a positive integer smaller than the size of the array. Which sorting algorithm can be easily modified for sorting this array and what is the obtainable time complexity? (A) Insertion Sort with time complexity O(kn) (B) Heap Sort with time complexity O(nLogk) (C) Quick Sort with time complexity O(kLogk) (D) Merge Sort with time complexity O(kLogk)
Comparison of the time complexity among different sorting algorithms ? (multiple choice) ^: Indicates exponent operation 單選或多選: ☐a. Worst case of Radix sort is O(n^2) Ob. Best case of Bubble sort is O(n^2) c. Worst case of Quick sort is O(n^2) Od. Best case of Selection sort is O(n^2) ☐e. Best case of Radix sort is O(nlogn) f. Average case of Shell sort is O(n) Og. Worst case of Merge sort is O(nlogn) Oh. Best case of Quick sort is O(n) ☐i. Average case of Insertion sort is O(n^2) O j. Average case of Quick sort is O(n^2) Ok. Average case of Merge sort is O(nlogn) O 1. Worst case of Selection sort is O(n^2)
Let M(n) be the minimum number of comparisons needed to sort an array A with exactly n ele- ments. For example, M(1) = 0, M(2) = 1, and M(4) = 4. If n is an even number, clearly explain why M(n) = 2M(n/2) + n/2.