Shell sort is an in-place comparison-based sorting algorithm which is based on insertion sort algorithm. It works as follow : It breaks the original list into a number of smaller sublists, each of which is sorted using an insertion sort. The unique way that these sublists are chosen is the key to the shell sort. Instead of breaking the list into sublists of contiguous items, the shell sort uses an increment i, sometimes called the gap, to create a sublist by choosing all items that are i items apart. n п a) We say that the our initial gap is floor when we divide our sequence into sublists where 2k 2k k>0 be the number of passes that can be increment until the denominator not greater than n, and then sorting the elements which are position away with insertion sort. We have three passes for an array size of 8 to 15. Demonstrate the Shell algorithm on the input array A = [35,33,42,10,14,19,27,44] showing how even- п tually the algorithm outputs the sorted array [10,14,19,27,33,35,42,44] with initial gap k: Clearly show all of your steps.

The bubble sort algorithm discussed in class is used to sort the following sequence of integers: 2 16 38 9 4 14 How many passes must the algorithm perform to guarantee the entire sequence is sorted? What is the list obtained after the first pass? What is the list obtained after the third pass? What is the list obtained after the final pass?

The best case behaviour occurs for quick sort when the partition function splits the sequence of size n into subarrays of size: Select one: a.n/4 : 3n/4 b.n/4 : 3n/2 c.3n/8 : (5n/8) d.n/2 : (n/2)-1 e.n/2 : n/3

Binary search can only be performed on a/an …………     Sorted array/list     Random array/list     Any array/list     Disordered array/list

Write the state of the elements of the vector below after each of the first 4 passes of the outermost loop of the insertion sort algorithm. (After the first pass, 2 elements should be sorted. After the second pass, 3 elements should be sorted. And so on.) // index 0 1 2 3 4 5 6 7 vector<int> numbers{29, 17, 3, 94, 46, 8, -4, 12}; insertionSort(numbers); NOTE: Write your answer inside curly braces with numbers separated by commas {29, 17, 3, 94, 46, 8, -4, 12}   after pass 1   after pass 2   after pass 3   after pass 4

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Quicksort is a powerful divide-and-conquer sorting algorithm that can be described in just four lines ofpseudocode. The key to Quicksort is the PARTITION(A, p, r) procedure, which inputs elementsptorof array A,and chooses the final element x = A[r] as the pivot element. The output is an array where all elementsto the left ofxare less thanx, and all elements to the right of x are greater than x. In this question, we will use the Lomuto Partition Method from class and assume that the pivot isalwaysthe last (right-most) element of the input array. Question: Let A be an array withn= 2k−1 elements, where k is some positive integer. Determine a formula (in terms of n) for the minimum possible number of total comparisons required by Quicksort, as well as a formula for the maximum possible number of total comparisons required by Quicksort. Use your formulas to show that the running time of Quicksort is O(nlogn) in the best case and O(n2) in the worst case.

Assume that we have a sorted list in an array: Index:         0       1       2         3       4        5      6      7      8       9        10        11 numbers:   12     15     17      19     22      26    28   30    32     34       36       38 we want to use the binary search algorithm to find the value 19 in the list. What would be the indexes of the array that the binary search would check to find the value 19  the indexes and not the actual numbers in the list otherwise

3. Given the following list: 9 4 2 6 7 5 3 8 Identify the state of the list while being sorted using the selection sort algorithm.

Select all the statements that are false, bubble sort is defined below:*             Quicksort is the fastest sorting algorithm         If you are lucky, you can get O(n) time complexity in Mergesort         On the worst case, Bubble sort will give you O(n logn) time complexity         Average time complexity of insertion sort is much better than bubble sort         Selection sort has the worst space complexity among all the sorting algorithm