We are now also given an array of integers A = {a;}"-1, and some random integer k. 1. Develop an algorithm that returns an array B of all pairs of indices (i, j), such that i and j belong to {1, ...,n}, and (a; + a;)/2 = k. 2. Obtain the running time of the suggested algorithm. 3. Prove correctness of this algorithm by stating and proving a loop invariant. Exercise 3 Suppose we wish to revisit exercise 2 above, and we are given that the list A is sorted in increasing order. 1. Develop an algorithm that solves the same problem as exercise 2 above, but uses Binary search to reduce the number of comparisons needed. 2. Verify that the run-time of the proposed algorithm is indeed faster. How much is it, and why is it faster?

Q: You are given an unsorted array A[1, ..., n]. We know that the maximum (or minimum) element in the…

A: We can use Divide the array into two parts and compare the maximums and minimums of the two parts to…

Q: In Python, generate a random matrix A with 100 entries each of which is an independent…

A: The objective of the question is to generate a random matrix, perform certain operations on it, and…

Q: Write a program that, given an array of N distinct int values in ascending order, determines whether…

A: Instead of searching based on powers of two (binary search), use Fibonacci numbers (which also grow…

Q: We have two input arrays, an array A with n elements, and an array B with m elements, where m 2 n.…

A: Brute force algorithm would require us to perform linear search. Best case algorithm would require…

Q: In this exercise we are given a sequence (array) A = {a;}"-1 such that a; = 0 or a; = 1, Vi e {1,..,…

A: Hey there, I am writing the required solution based on the above given question. Please do find the…

Q: You are given an array of positive integers S[1, . . . , n]. You are initially positioned at the…

A: Naive approach: Start from the first element and recursively call for all the elements reachable…

Q: You're given an array of N integers, and a number K. The maximum K-product of the array is the…

A: Note : As the programming language is not given so i am answering it in python language. Given:…

Q: Generate random matrices of size n ×n where n = 100, 200, . . . , 1000. Also generate a random b ∈…

A: Scripting language Random Number: The stochastic component in Programming language defines a range…

Q: You are given an array of colors (reds, whites, and blues), in no particular order. Sort them into…

A: A sorting algorithm is just a series of orders or instructions. In this, an array is an input, on…

Q: Given two sorted arrays A and B, design a linear (O(|A|+|B|)) time algorithm for computing the set C…

A:

Q: Given an n-element array X of integers, Algorithm A executes an On34-time computation for each even…

A:

Q: Consider the problem of finding the distance between the two closest and y is computed as x - y.)…

A: Pseudocode is an artificial and informal language that helps programmers develop algorithms. Writing…

Q: You're given an array of N integers, and a number K. The maximum K-product of the array is the…

A: Coded using Java.

Q: Examples: Input Output: Ex 1: 55 55665 12543 27 Ex 2: 53 12345 10 9 10 10 9 39 Ex 3: 40 2243 2423 11…

A: Here I am explaining the given question: I am using a brute force approach  for solving this…

Q: Write an efficient algorithm for the following problem, and describe your reasoning. Determine the…

A: First we will count the number of zeros in whole array, which will take time complexity of O(n). If…

Q: Given an array containing integers with N elements, and the sum of consecutive elements in the array…

A: Here is the solution which is mentioned below:

Q: You are given an integer array X[1, . . . , n]. You should move each element of X[1, . . . , n] into…

A: Pseudocode is a computing tool that aids in problem-solving before a programme is written in a…

Q: Suppose we are given an array of numbers A[0], A[2], . . . , A[n - 1]. You may assume that n is a…

A: The answer is given below:-

Q: Design an algorithm to find all pairs of integers within an array which sum to a specified value…

A: 1) A brute-force solution is a straightforward, exhaustive approach to solving a problem that…

Q: Consider an n by n matrix, where each of the n² entries is a positive integer. If the entries in…

A: The statement is TRUE. With a matrix of size nxn, having integers in increasing order from left to…

Q: Array A contains positive numbers that can be smaller than 1, larger than 1, or equal to 1. Find the…

A: #include <bits/stdc++.h>using namespace std; int maxSubarrayProduct(int arr[], int n){    int…

Q: Question A: Mapping. The two-sum problem is a popular algorithm problem. Given an array of integers…

A: The Two-Sum algorithm, where you find two numbers in the array that add up to a given target.Create…

Q: Write a program that, given an array a[] of N double values, finds a closest pair : two values whose…

A: In computer science, finding the closest pair in an array of double values is a common problem. The…

Q: Given an integer n and an array a of length n, your task is to apply the following mutation to a:…

A: We need to write a program to mutate an array as per the given condition. * Language used is C

Q: Given an array A = [10, 7, 4, 2, 1], and target = 7, return the index of the target if found, else…

A: Yes, this problem can be solved in O(logN) time complexity using a binary search since the input…