5. In Quick Sort algorithm, what are the key differences in performance characteristics when comparing the use of a fixed pivot (such as always choosing the first or last element) versus a pivot chosen randomly or through a median-of-three approach?
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- Question 6: Professor Holmes has come up with a new sorting algorithm. He calls it Trinary Sort and "claims" that it is asymptotically faster than Merge Sort, despite the fact both the algorithms operate using similar logic. But, unlike Merge Sort, Trinary Sort splits the input array into (roughly) 3 equal parts at each step of the recursion as long as the array is splittable (i.e., has at least 3 elements). Trinary Sort's merge subroutine, similar in principle to the one used by Merge Sort, takes 3 sorted subarrays and merges them to produce a single sorted array. Given all of this, answer the following questions. (a) In Merge Sort, the merge subroutine makes n-1 comparisons to merge 2 arrays of size n/2, which takes (n) time. How many comparisons will the merge subroutine of Trinary Sort make to merge 3 arrays of size n/3? What would be the (...) bound on the running time for this subroutine? (b) What is the (...) bound on the running time of the Trinary Sort algorithm? Come up with…Explain what linear sort is and provide an example of how it's used.Answer the question using bubble sort, enhanced bubble sort, selection sort, and insertion sort. Milo only needs the 10 highest exam scores in an array of several hundred scores. Which sort should he use that can easily be modified to accomplish the task and why?
- 4. In our linear selection algorithm, the input elements are divided into groups of 5. Would the algorithm still run in linear time we divided them into groups of 7? What about 3?I was told the answer is insertion sort, but I am not sureCompare the sorting durations of the insertion sort and QuickSort using a tiny array (less than 20). What is the time difference? Could you clarify why? Compare the sorting durations of the insertion sort and QuickSort using a tiny array (less than 20). What is the time difference? Could you clarify why?Compare the sorting durations of the insertion sort and QuickSort using a tiny array (less than 20). What is the time difference? Could you clarify why?
- What is the average-case running time for Merge Sort and Quick Sort, respectively? Why do we prefer Quick Sort algorithm in practice? Please provide at least two benefits of Quick Sort and also provide explanations for each benefit (plain language explanation is fine).3 illustrates the counting sort algorithm. For simplicity ofimplementation and understanding, the range (a, b) within which the unordered setof keys lie is assumed to be within (0, k).(b) Explain in your own words why even the more efficient versions of bubble sort are considered to be slow algorithms. Illustrate your answer using the example data: {17, 15, 11, 13}
- What are the differences between linear search and binary search algorithms, and in which scenarios is each algorithm more efficient?What is the auxiliary space complexity and average time complexity of randomized rapid sort?Consider sorting a list of items that are in reverse sorted order. If you were forced to pick between the three iterative sorting algorithms (bubble sort, selection sort, or insertion sort) to work through this set and place it into normal (ascending) sorted order, which would you pick and why?