You are given an array A of n>1 integers (not necessarily sorted) and your goal is togiven an efficient divide and conquer algorithm for the following problem. Note thatyour divide and conquer algorithm should not use sorting as a subroutine (see questionsbelow).(a) To find if there are two integers in A whose product is exactly t. If so, return True,otherwise return False. For your assigned problem, answer the following:(i) Explain your algorithm clearly in plain language (pseudocode is not required).(ii) Argue its correctness.(iii) Analyze the running time of your algorithm.(iv) Explain how you can solve your problem in O(n log n) time using MergeSort as asubroutine (or as a black box) algorithm.(v) One disadvantage of using MergeSort as a subroutine is that it takes e(n log n) timein the best case (i.e., for every input). On the other hand, your divide and conqueralgorithm can take O(n) time in the best case. Explain why and give an exampleinput where your algorithm exhibits 0(n) runtime.

Actually, given question regarding divide and conquer.

You are given an array A of n> 1 integers (not necessarily sorted) and your goal is to iven an efficient divide and conquer algorithm for the following problem. Note that our divide and conquer algorithm should not use sorting as a subroutine (soe questions melow). (a) To find if there are two integers in A whose product is exactly t. If so, return True, otherwise return False.

You are given an array A of n> 1 integers (not necessarily sorted) and your goal is to iven an efficient divide and conquer algorithm for the following problem. Note that our divide and conquer algorithm should not use sorting as a subroutine (soe questions melow). (a) To find if there are two integers in A whose product is exactly t. If so, return True, otherwise return False.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Related questions

Q: For the problems given below, determine whether it is more efficient to use a divide and conquer…

A: memFib(n) { if (mem[n] is undefined) if (n < 2) result = n else result =…

Q: Given an array of numbers X₁ = {x₁, x2, ..., n } an exchanged pair in X is a pair xi, xj such that i…

A: The objective of the question is to design a divide-and-conquer algorithm that counts the number of…

Q: Let m be a randomly chosen non-negative integer having at most n decimal digits, i.e. an integer in…

A: Let m be randomly chosen non-negative integer having at most n digits, i.e.,an integer in the…

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: Problem 5. Let S be a perhaps multi-set of n integers. Give an algorithm to determine whether 5 has…

A: Task : Given the multiset S and value k. The task is to find the algorithm to determine whether S…

Q: In n queens problem, n queens should be placed on an n × n chessboard so that they do not threaten…

A: In queens problem n queen should be placed on an n x n chessboard so that they do not threaten each…

Q: - You are given two sorted arrays of integers A and B of size m and n respectively. Describe a…

A: The objective of the question is to find an efficient algorithm to find the kth smallest element in…

Q: Describe a Branch & Bound algorithm to solve the employee to project assignment reward problem. You…

A: Branch and Bound algorithm Branch and bound algorithm design paradigm which is used for solving the…

Q: Consider an n x n array ARR stored in memory consisting of 0’s and 1’s such that, in a row of ARR,…

Q: A team sport game has m players in a team and a tournament can have n competing teams. Team T1 ranks…

A: The question is asking to design an algorithm to determine if two teams can be ranked based on their…

Q: You wish to find duplicates in an unsorted n-element array A. 1,..., 2n integers. Give this…

A: The worst case time complexity for the elements 1 to 2n is O(n^2) . This time complexity is when we…

Q: The Chinese Remainder Theorem is often used as a way to speed up modular exponentiation. In this…

A: Fermat's Little Theorem states that if p is a prime number, then for any integer a not divisible by…

Q: Lets say we have an array of n items that we need to sort. Lets say that there is a sorting…

A: - We need to talk about the worst case time complexity in at least Ω(n2 / log n).

Concept explainers

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.

Question

You are given an array A of n>1 integers (not necessarily sorted) and your goal is to
given an efficient divide and conquer algorithm for the following problem. Note that
your divide and conquer algorithm should not use sorting as a subroutine (see questions
below).
(a) To find if there are two integers in A whose product is exactly t. If so, return True,
otherwise return False.

For your assigned problem, answer the following:
(i) Explain your algorithm clearly in plain language (pseudocode is not required).
(ii) Argue its correctness.
(iii) Analyze the running time of your algorithm.
(iv) Explain how you can solve your problem in O(n log n) time using MergeSort as a
subroutine (or as a black box) algorithm.
(v) One disadvantage of using MergeSort as a subroutine is that it takes e(n log n) time
in the best case (i.e., for every input). On the other hand, your divide and conquer
algorithm can take O(n) time in the best case. Explain why and give an example
input where your algorithm exhibits 0(n) runtime.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.

Similar questions

Please write it on paper
Please answer completely
We want to determine whether an unsorted array A of n entries has duplicates. These integers are 1,..., 2n. Give this solution's worst-case running time asymptotic order T(n). Find an efficient algorithm.
1. Let S be a set of n arbitrary but distinct numbers. (a) Give a deterministic algorithm to output the largest n³/4 of the numbers in S in sorted order. Your algorithm must use O(n) comparisons. (b) Show that any deterministic comparison-based algorithm that correctly outputs the median on inputs of n distinct elements must use at least n 1 comparisons. To be completely precise, the median is defined to be the [n/2]th smallest element.
Problem 1. Assume we have an array A = {a1,...,an) of n elements, where it is guaranteed a majority element exists. For example, (2, 1, 1) has a majority element 1. a. Describe a divide and conquer method to solve this problem. b. Write the run time as a recurrence sequence. c. Solve this recurrence sequence using any method introduced so far (expansion, generative function, master theorem).
Problem 2: Finding an element.(i) Let n be an even positive integer. Let A be an array containing n not necessarydifferent integers. Elements in A are not necessary sorted. Describe an algorithmwhich in time O(n) tests whether there exists an element x in A that appears in Aat least n/2 times.(ii) Let S be a set containing n integers. An element x ∈ S is an approximate median ofS, if|{y ∈ S | y < x}| ≥ n/4and |{y ∈ S | y > x}| ≥ n/4Given an array A containing n different integers, not necessary sorted, describe analgorithm which in time O(n) finds all approximate medians of the set {A[i] | i =1, 2, . . . , n}.