Write an algorithm for a divide-and-conquer algorithm for finding values of both the largest and smallest elements in an array of n numbers. Implement the above-designed algorithm using Java Programming Language. How does this algorithm compare with the brute-force algorithm for this problem?

develop an implementation TwoSumFaster thatuses a linear algorithm to count the pairs that sum to zero after the array is sorted (instead of the binary-search-based linearithmic algorithm). Then apply a similar idea todevelop a quadratic algorithm for the 3-sum problem.

algorithms are solely theoretical for a and b. please number the steps of the algorithm, thank you

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Describe an algorithm for finding the 10 largest elements in an array of size n. What is the running time of your algorithm?

Write a version of the bubble sort algorithm that sorts a list of integers in descending order. Namely, change the bubble sort method to sort the parameter array in descending order. Hint: Bubble sort: void bubbleSort(int array(1) { int size = array.length; boolean isChanged = false; for (int i = 0; i < size - 1; i++) isChanged = false; for (int j = 0; j < size . 1 . 1; j++) if (array(s) > array() + 1]) { int temp = array(s); array[3] . arrays + 1); array() + 1] = temp; is Changed = true; } if (isChanged) break;

Write algorithm method code that demonstrates the Fibonacci search process. The amount of data elements in this case, n, is such that: i) Fk+1 > (n+1); andii) Fk + m = (n +1) for some m ≥ 0, where Fk+1 and Fk are two consecutiveFibonacci numbers.

Write a java code to implement binary search on a sorted array of size 15. Use random values(integers

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?