You are given an array A of n integers (they can also be negative). Describe an algorithm that determines the maximum sum of numbers in any subarray A[i: j]. The complexity of the algorithm should be O(n log n)
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- 1.Write a Θ(n) algorithm that sorts n distinct integers, ranging in size between 1 and kn inclusive, where k is a constant positive integer. (Hint: Use a knelement array.) 2.Algorithm A performs 10n 2 basic operations, and algorithm B performs 300 ln n basic operations. For what value of n does algorithm B start to show its better performance? 3. There are two algorithms called Alg1 and Alg2 for a problem of size n. Alg1 runs in n 2 microseconds and Alg2 runs in 100n log n microseconds. Alg1 can be implemented using 4 hours of programmer time and needs 2 minutes of CPU time. On the other hand, Alg2 requires 15 hours of programmer time and 6 minutes of CPU time. If programmers are paid 20 dollars per hour and CPU time costs 50 dollars per minute, how many times must a problem instance of size 500 be solved using Alg2 in order to justify its developmentIn searching an element in an array, linear search can be used, even though simple to implement, but not efficient, with only O(n) time complexity. Assuming the array is already in sorted order, modify the search function below, using a better algorithm, so the average time complexity for the search function is O(log n). include <iostream> using namespace std; int search(int al), int s, int v) { 1/ Modify below codes. for (int i = 0; i <s; i++) { if (a[i] = v) return i; return -1; int main() { int intArray:10] = { 5, 7, 8, 9, 10, 12, 13, 15, 20, 34); // Search for element '12' in 10-elements integer array. cout << search(intArray, 10, 12); // '5' will be printed out. // Search for element '35' in 10-elements integer array. cout << search(intArray, 10, 35); // '-1' will be printed out. // Index '-l' means that the element is not found. return 0;Given an array A of integer type of length n (n > 7), write a pseudocode of an efficient algorithm for finding the seven smallest elements in A. What is the running time of your algorithm?
- Design an algorithm that takes an array containing n distinct natural numbers. A number k ≤ n and calculates the sum of the k largest numbers in the array. For example, if the array is {3, 7, 5, 12, 6} and k = 3, then the algorithm should return 25 (12+7+6). You may freely use standard data structure/s and algorithms from the course in your solutionAn array A contains n - 1 unique integers in the range [0, n - 11; that is, there is one number from this range that is not in A. Design an O(n)- time algorithm (write a pseudo-code, Python function or Java method) for finding that number. You can use only 0(1) additional space beside array A.Design a dynamic programming algorithm for solving the problem of finding if there are exactly K entries in array 'A' whose sum is equal to a given integer 'T'
- 16. Given an n-element array with n > 100, is it possible to find an algorithm that can find an element that is neither the maximum nor the minimum with fewer than 10 comparisons? (a) yes (b) noConsider the problem of finding the distance between the two closest numbers in an array of n and y is computed as x - y.) numbers. (The distance between two numbers x Design a presorting-based algorithm in pseudo code for solving this problem and determine its efficiency class. Answer: // your algorithm goes here Provide the the algorithm efficiency analysis here:In a sequence, numbers decrease up to a point and then increase. Example: A=[10,9,8,7,6,5,13,14,15] Write an algorithm with O(logn) time complexity that finds the smallest element in such an array. (can be pseudocode.)
- Given an array A and a positive integer k, the selection problem amounts to finding the largestelement x ∈ A such that at most k elements of A are less than or equal to x, or nil if no suchelement exists. A simple way to implement it is as follows:SimpleSelection(A, k)1 if k > A.length2 return nil3 else sort A in ascending order4 return A[k]Example A = (29, 28, 35, 20, 9, 33, 8, 9, 11, 6, 21, 28, 18, 36, 1) k = 6You are given an array of n integers, and a target sum S. Give an algorithm that determines if there are two elements in the array (may be the same one) whose sum is S. Your algorithm should have a complexity less than Θ(n^2).asap