2.2-2 Consider sorting n numbers stored in array A by first finding the smallest element of A and exchanging it with the element in A[1]. Then find the second smallest element of A, and exchange it with A[2]. Continue in this manner for the first n - 1 elements of A. Write pseudocode for this algorithm, which is known as selection sort. What loop invariant does this algorithm maintain? Why does it need to run for only the first n − 1 elements, rather than for all n elements? Give the best-case and worst-case running times of selection sort in O-notation.

Consider an array of integers. Write the pseudocode in Java for either the selection sort, insertion sort, or bubble sort algorithm. Include loop invariants in your pseudocode.   I need help with the above instruction for the bubble sort algorithm, please.  I appreciate your help. Thank you.

Determine how many times the innermost loop will be iterated when the following algorithm segment is implemented and run. (Assume that m and n are positive integers.) for j:=1 to m for k:=1 to n [Statements in body of inner loop. None contain branching statements that lead outside the loop.] next k next j (Hint: See Example 9.2.5 in the "Read It" link.) For each iteration of the outer loop there are X iterations of the inner loop. Therefore, the answer is H X

Given an array of positive and negative integers, write the main ideas of an algorithm to segregate them without changing the relative order of elements. The output should contain all positive numbers follow negative numbers while maintaining the same relative ordering. Example: Input: [9, -3, 5, -2, -8, -6, 1, 3] Output: [-3, -2, -8, -6, 9, 5, 1, 3]  Determine the running time complexity of this algorithm

Prime numbers can also be generated by an algorithm known as the Sieve of Eratosthenes . The algorithm for this procedure is presented here. Write a program that implements this algorithm so as to find all prime numbers up to n = 150. Sieve of Eratosthenes Algorithm To Display All Prime Numbers Between 1 and n Step 1: Define an array of integers P . Set all elements P i to 0, 2 <= i <= n. Step 2: Set i to 2. Step 3: If i > n , the algorithm terminates. Step 4: If P i is 0 (value i is a prime number), then i is prime and display its value. Step 5: For all positive integer values of j , such that i * j ≤ n , set P i ∗ j to 1 (non - prime). Step 6: Add 1 to i and go to step 3

in java

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.

Consider sorting n numbers stored in array A[1:n] by first finding the smallestelement of A[1:n] and exchanging it with the element in A[1]. Then find thesmallest element of A[2:n], and exchange it with A[2]. Then find the smallestelement of A[3:n], and exchange it with A[3]. Continue in this manner for thefirst n-1 elements of A. Write pseudocode for this algorithm, which is knownas selection sort. What loop invariant does this algorithm maintain? Why does itneed to run for only the first n-1 elements, rather than for all n elements? Give theworst-case running time of selection sort in big theta notation. Is the best-case runningtime any better?

Regarding familiarity with operating systems, what benefits does understanding assembly language provide?

Write a program to sort an array of random elements using quicksort as follows: Sort the arrays using pivot as the first element of the array Sort the arrays using pivot as the median of the first, last, and middle elements of the array Sort the arrays using pivot as the first element of the array. However,, when the size of any sub-list reduces to less than 20, sort the sub-list using insertion sort. Sort the array using pivot as the median of the first, last and middle elements of the array. When the size of any sub-list reduces to less than 20, sort the sub-list using insertion sort. Calculate and display the CPU time for each of the preceding four steps. Example of the median of the first, last and middle elements: 1 2 3 4 5 6 7 8 0 (median of 1, 5, 0 is 1) 8 0 1 2 3 4 5 6 7 (median of 8, 3, 7 is 7) To calculate the CPU time, use the header , and clock_t type. You need to cast the duration to float and divide it by CLOCKS_PER_SEC. Depends on the CPU of your computer, your…