The following algorithm adds all the entries in the “upper triangular” part of a square n × n array A. Consider n = 5 and the 5 × 5 array below. The work unit is the addition operation, sum = sum + A[k, j]. How many times is the sum = sum + A[k, j] operation done? sum = 0 for k = 1 to n do for j = k to n do sum = sum + A[k, j] end for end for 1 3 1 0 2 3 1 0 3 3 0 0 1 2 0 0 2 3 1 2 2 2 3 0 1

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…

Given n arrays, each array contain n positive integers. Write an O (n² log n) algorithm to find the smallest n sums out of nn possible sums that can be obtained by picking one positive integer from each of n arrays. For example, given three arrays as follows: [5, 1, 8], [5, 2,9], and [6,7, 10]. The smallest n sums of the given array is [9, 10, 12].

Python Programming