You 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).

Q: Implement a Binary Search algorithm, and using the results from Exercise 5, show how long the Binary…

A: Here's an implementation of the Binary Search algorithm in Python:- def binary_search(arr, target):…

Q: Given an array of integers, return the largest gap between the sorted elements of the array. For…

A: Algorithm -   Create a new class with the name main.  Now create a method with the name largest gap…

Q: Please try the Give solution whose Time Complexity is O Write a Java Program to find the average…

A: class Solution {    public double average(int[] salary) {        final int N = salary.length;…

Q: We want to determine if an unsorted array A of n entries has duplicates. These integers are 1,...,…

A: To determine if an unsorted array A of n entries has duplicates, we can use a simple approach based…

Q: Let B be an array of n >= 6 numbers ranging from 1 to n-5, inclusive, with precisely five…

A: Following is the pseudo-code.Note, in the below code, any array of size x has index from 1 to x. Not…

Q: Using the algorithm in the image, please answer the following: a. what does the algorithm compute?…

A:

Q: Write a O(n) algorithm that sorts n distinct integers, ranging in size between 1 and kn inclusive,…

A: You can use the counting sort algorithm with a slight alteration to obtain O(n) time complexity for…

Q: Given n positive integers, partition them into two disjoint subsets with the same sum of their…

A: Disjoint Subsets : Disjoint subsets are two or more sets that have no elements in common. In other…

Q: You are given a one-dimensional array of n integer numbers. What is the worst-case time complexity…

A: Solution - In the given question we have to find the worst case time complexity of finding the…

Q: Perform an experimental analysis to test the hypothesis that Java's Array.sort method runs in O(n…

A: Let us take the best example of merge sort in this case to prove the average running time O(n log…

Q: We are going to create a poorly efficient sort which we will call Sort. This algorithm will arrange…

A: Algorithm are refers to the set of the instructions or the rules that are used for the solving of…

Q: Using Java, Write an algorithm that finds both the smallest and largest numbers in a list of n…

A: The question has been solved in step2:

Q: In this programming, you learn more about efficiency of algorithms based upon run time. Hence you…

A: Solution:   In this code, the binarySearch function performs a recursive binary search on the given…

Q: array k has m elements k[0],….,k[m-1], and the elements have disntict values.You are asked to design…

A: One possible parallel algorithm to find the 2nd largest element in the array k with m elements is as…

Q: We have k sorted arrays, and we know in total there are n elements in these k arrays. Design an…

A: Given k sorted arrays, we know in total there are n elements in these k arrays. Design an algorithm…

Q: Create an array of size one million (1,000,019). Fill it in reverse sequentially with values (e.g.…

A: Initialize an array of size 1,000,019 and fill it with numbers in reverse order. Select a random…

Counting sort

The counting sort algorithm sorts an array’s contents by counting the repetition of each element that occurs in the array. A counting sort algorithm is a stable algorithm that works the best when the range of elements in the array is small, say for example from 0 to 9. The count which is the number of repetitions of an element in the array is mapped to an index of an auxiliary array, which is then saved in an auxiliary array. The counting sort algorithm has a stable time complexity of the order of O(size of array + size of auxiliary array). Let’s discuss the algorithm in detail as follows.