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- 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.n a sorted array, from lowest to highest, of all prime numbers less than 100 - searching for which prime numbers using linear search will be better than or equal to binary search? NOTE - in this question marking wrong answers will result in negative scoring, so be extremely careful when answering. Group of answer choices 11 41 5 23 43 29 7 17 37 13 31 2 19 3 47Java! please explain clearly with the answer by hand-writing or typing Using merge sort to sort an array of size n, then use binary search to find (1/2)n elements. Using merge sort to sort an array of size n, then run sequential search on it.
- Given an array: 5 9 7 8 10 12 11 3 1Show the array after each iteration in a selection sort (sorting from smallest largest) please help and show work !!!Use Compiler of any programming language to create array A= [n] , Generate A randomly as follows, then apply insertion and selection, bubble sort, Marge-sort, Quick sort for the same generated array. You should find the execution time for each algorithm of n items n Insertion sort Selection sort bubble sort Marge sort Quick sort 100 500 1000 5000 10000 50000 100000 1000000A. Compare insertion sort and merge sort on any aspect you can. B.For the list of numbers given below, which sort algorithm performs better, why? 110 25 40 52 65 73 84 90
- Apply Quick sort on a given sequence 7 11 14 6 9 4 3 12. What is the sequence after first phase, pivot is first element? 7 6 14 11 9 4 3 12 6 4 3 7 11 9 14 12 6 3 4 7 9 14 11 12 7 6 4 3 9 14 11 12 Quick sort follows Divide-and-Conquer strategy. True False Assume you have the array 7,9,6,10,3,5,8. What will the array look like after we call build-min-heap on the entire array? 3, 7, 5, 10, 9, 8, 6 3, 5, 6, 7, 8, 9, 10 3, 7, 5, 10, 9, 6, 8 10, 9, 8, 7, 6, 5, 3 3, 5, 7, 10, 9, 6, 8 Assume you have the following array: 30, 50, 20, 80, 10, 90, 100. Assume you were to select the quicksort pivot as the middle element of the array. What are the two sub-arrays to be sorted that result after one iteration of quicksort? 30, 50, 20, 10 | 90, 100 10, 20, 30, 50 | 90, 100 30, 50, 20, 10 | 100, 90 30, 20, 50, 10 | 100, 9Plot the result of (given) selectionsort(A) when A is a perfectly sorted and contains randoms integers ,0 to 100 inclusive, for array sizes n = 2,4,8,16,..1024. please provide code for A and generating the plot for each doubling array, as well as the resulting plot. def selectionsort(A): for i in range(len(A)): min_idx = i for j in range(i + 1, len(A)): if A[min_idx] > A[j]: min_idx = j A[i], A[min_idx] = A[min_idx], A[i] return ASuppose we want to sort the array 10, 8, 6, 13, 9, 2, 7, 14, 12, 1, 11 using QUICK SORT, and letting the last key of the array (i.e., 11) to be the pivot. Compute the array that results after the first step of the algorithm. (You do not need to explain here the details of the step, and you only need to write the resulting array.)
- Sort the following array in decreased manner using insertion sort [12, 2, 5, 10, 15, 27,4], then sort the same array another time in increased manner and compare between the number of swaps in the two casesIn the following Quick Sort algorithm, the last element in the array is selected as Pivot. We are going to select the Median of the data in the array as Pivot. Make the appropriate changes in the following algorithms. Indicate which line (line number) in each algorithm is to be modified and what are the changes. In the original algorithm, the complexity of Quick Sort is "n Log (n)". What would be the complexity with Median as Pivot? Why?Array.sort() sorts the given array in ascending order. Describe, using pseudocode, how you can use it to reconstruct a complete bst from a linear bst so it achieves O(logn) complexity for the search operation. java