Given an unsorted array A of integers of any size, n ≥ 3, and an integer value x, write an algorithm as a pseudo code (not a program!) that would find out if there exist EXACTLY3 occurrences in the array with value x.  What is the time complexity of your algorithm, in terms of Big-O? What is the space complexity of your algorithm, in terms of Big-O? What if , the given array A is sorted. Will time complexity change from the case that A was unsorted? • If yes; give a new algorithm that achieves this better complexity (indicate the time complexity as of that algorithm). • If no, explain why such new constraints/conditions cannot lead to a better time complexity.

Consider a divide-and-conquer algorithm that calculates the sum of all elements in a set of n numbers by dividing the set into two sets of n/2 numbers each, finding the sum of each of the two subsets recursively, and then adding the result. What is the recurrence relation for the number of operations required for this algorithm?   Answer is f(n) = 2 f(n/2) + 1. Please show why this is the case.

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

Suppose you are implementing a sorting algorithm and you want to compare its performance with another algorithm. The first algorithm takes 25 seconds to sort an input of size 10,000, while the second algorithm takes 45 seconds to sort the same input size. What is the ratio of the running times of the two algorithms?

For sorting a set of items, we can employ one of these famous algorithms, merge-sort, heapsort, quicksort, and shell-sort. We can program in both Java and Python, and we have the choice of using three different computers with different instruction set architectures: x86, ARM, and MIPs. Regarding microarchitecture, for x86 we have two choices, and for ARM and MIPS we have three choices for each of them. How many choices we have to run a sort algorithm? (Draw diagram).

Below are a number of statements about sorting algorithms. Which of the above statements is correct? A. Insertion location and Mergesort are examples of comparison-based sorting algorithms.B. Quicksort is an example of the "divide-and-conquer" algorithm technique.C. Mergesort is a sorting algorithm which in both worst and average case has T (n) = 0 (n log2 n).D. Heapsort has a time complexity in the worst case that is better (faster) than the time complexity of Quicksort in the worst case.E. Selection type has the time complexity T (n) = O (n log2 n) in the worst case.F. Radixsort is not a comparison-based sorting algorithm. Group of answer options All statements are correct. No statement is correct. All statements except D are correct. All statements except E are correct. Only statements A, B, C and D are correct. Only statements A, B and F are correct.

Give an example showing that quicksort is not a stable sorting algorithm.

A sequential search of a sorted list can halt when the target is less than a givenelement in the list. Define a modified version of this algorithm and state thecomputational complexity, using big-O notation, of its best-, worst-, and average-case performances. Using this template in python: def sequential_search(input_list, target):target_index = -1#TODO: Your work here# Return target_index. If not found, -1return target_indexif __name__ == "__main__":my_list = [1, 2, 3, 4, 5]print(sequential_search(my_list, 3)) # Correct Output: 2print(sequential_search(my_list, 0)) # Correct Output: -1

Write a technique to locate the indices m and n in an array of integers such that sorting items m through n will sort the entire array. Find the smallest such sequence by minimising n - m. Example inputs: 1, 2, 4, 7, 10, 11, 7, 12, 6, 7, 16, and 19; outputs: 3 and 9.