Suppose that each person in a group of n people votes for exactly two people from a slate of candidates to fill two positions on a committee. The top two finishers both win positions as long as each receives more than n /2 votes. a) Devise a divide-and-conquer algorithm that determines whether the two candidates who received the most votes each received at least n /2 votes and, if so, determine who these two candidates are. b) Use the Master Theorem to estimate the number of comparisons needed by the algorithm you devised in part (a)

Suppose that each person in a group of n people votes for exactly two people from a slate of candidates to fill two positions on a committee. The top two finishers both win positions as long as each receives more than n /2 votes. a) Devise a divide-and-conquer algorithm that determines whether the two candidates who received the most votes each received at least n /2 votes and, if so, determine who these two candidates are. b) Use the Master Theorem to estimate the number of comparisons needed by the algorithm you devised in part (a)

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter15: Recursion

Section: Chapter Questions

Problem 18SA

See similar textbooks

Related questions

Q: Suppose you begin with one pair of newborn rabbits. At the end of the third month, and at the end of…

A: Dear learner, hope you are doing well, I will try my best to answer this question. Thank You!!

Q: Now suppose that n is not 2i for any integer i. How would we change the algorithm so that it handles…

A: If you are wondering just how slowly a program can run, consider the algorithm below. Assume the…

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: Gildong has a square board comprising of n lines and n sections of square cells, each comprising of…

A: Here have to determine about the Triangles programming problem statement.

Q: 9. Voting Suppose that the votes of n people for different candidates (where there can be more than…

Q: The search algorithm developed will be used for users to search the catalog for all items matching…

A: Let us first see what exactly is happening here. Assume that you are searching for something on a…

Q: Consider the problem of making change for n cents using the fewest number of coins. Assume that we…

A: Recursive Backtracking Algorithm: Function CoinChange(n, coins) return CoinChangeRecursive(n,…

Q: Today is Max's birthday. He has ordered a rectangular fruit cake which is divided into N x M pieces.…

A: This program deals with a situation where Max receives a rectangle fruit cake divided into N x M…

Q: Could we use the ideas of the Closest Pair of Points Algorithm to solve the following problem?…

A: The idea of closest pair of points algorithm can be used here, closest pair of points involves…

Q: 2. Honest Goblins are Easy to Find At Hogwarts a new shipment of n goblins has arrived. To be of any…

A: Assume that more than half of the given n goblins are truth tellers. Pairing the goblins and…

Q: Consider the problem of making change for n cents using the fewest number of coins. Assume that we…

A: Instead of starting with the larger problem and breaking it down into smaller subproblems…

Q: Alice and Bob got n confections from their folks. Each candy weighs either 1 gram or 2 grams.…

A: Here have to determine about the candy weighs programming problem statement.

Q: An electrician has wired n lights, all initially on, so that: 1) light 1 can always be turned…

A: IMPLEMENTATION: The algorithm works from left to right implementing individual bits. First bit can…

Q: If five integers are chosen from the set {1, 2, 3, 4, 5, 6, 7, 8}, must there be at least two…

A: Initially, the set X can be partitioned into four subsets: {1, 3}, {2, 4}, {5, 7}, {6, 8}. We…

Q: There are n students who studied at a late-night study for final exam. The time has come to order…

A: When ordering pizzas for a group of students studying for their final exams, it's essential to…

Q: Considering the function f(x) = x – cos(x), what is the value of x7 after performing fixed point…

A: The fixed point iteration method is method for finding the real root of the non-linear equations by…

Q: Correct answer will be upvoted else downvoted. Computer science. Polycarp recalled the 2020-th…

A: Here, we have to find the solution to the above problem. I wrote the program in Python programming…

Q: Consider a modified Borda count where a first-place vote is worth F points (F > N where N denotes…

A: The question seeks the determination of the smallest value of F (expressed in terms of N) in a…

Q: Al and Bob are arguing about their algorithms. Al claims his O(n logn)-time method is always faster…

A: f(n) = O(g(n)) if there exists a positive integer n1 and a positive constant C, such that…

Q: Given A = {1,2,3} and B={u,v}, determine. a. A X B b. B X B

A: Cartesian Product: Let us consider A and B to be two non-empty sets, then cartesian product A × B is…

Q: uppose that f(n) = 0(g(n)) and f(n) = 0(h(n)), then it is ( always / sometimes / never) the case…

A: Defined the given statement always, sometimes or never

Q: This problem is taken from the delightful book "Problems for Mathematicians, Young and Old" by Paul…

A: Note: C programming language is used to solve the problem Algorithm: Resultant algorithm for given…

Q: A ancient magnate is failing. His want is to have solely ONE of his descendant’s receive ALL of his…

A: Java code import java.util.Scanner; public class Decendent { public static void main(String…

Q: Which of the following best describes the useful criterion for comparing the efficiency of…

A: Which of the following best describes the useful criteria for comparing the efficiency of…

Q: Consider the problem of making change for n cents using the fewest number of coins. Assume that we…

A: 1) A bottom-up (non-recursive) O(nk)-time algorithm refers to an algorithmic approach that builds…

Q: There are n people who want to carpool during m days. On day i, some subset si of people want to…

A: The above question is solved in step 2:-

Q: Consider the argument form pvr .: p→r Is this argument form valid? Prove that your answer is…

A: Logical argument is a claim that set of premises support a conclusion. There are 2 types of…

Q: Imagine there are N teams competing in a tournament, and that each team plays each of the other…

A: INTRODUCTION: Each team plays every other in a round-robin competition. Each team in an eight-team…

Concept explainers

Polynomial Time

The problems for which the deterministic polynomial-time algorithm exists belong to the complexity class (p) and it is central in the field of computational complexity theory. According to Cobham’s thesis, polynomial time is a synonym for “feasible”, “fast”, and “efficient”.

Question

Suppose that each person in a group of n people votes
for exactly two people from a slate of candidates to fill
two positions on a committee. The top two finishers both
win positions as long as each receives more than n /2
votes.
a) Devise a divide-and-conquer algorithm that determines whether the two candidates who received the
most votes each received at least n /2 votes and, if so,
determine who these two candidates are.
b) Use the Master Theorem to estimate the number of
comparisons needed by the algorithm you devised in
part (a)

Process or set of rules that allow for the solving of specific, well-defined computational problems through a specific series of commands. This topic is fundamental in computer science, especially with regard to artificial intelligence, databases, graphics, networking, operating systems, and security.

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: Sollution a:

VIEW

Step 2: implementation of the algorithm in Python:

VIEW

Step 3: Sollution b:

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 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

This problem is taken from the delightful book "Problems for Mathematicians, Young and Old" by Paul R. Halmos. Suppose that 931 tennis players want to play an elimination tournament. That means: they pair up, at random, for each round; if the number of players before the round begins is odd, one of them, chosen at random, sits out that round. The winners of each round, and the odd one who sat it out (if there was an odd one), play in the next round, till, finally, there is only one winner, the champion. What is the total number of matches to be played altogether, in all the rounds of the tournament? Your answer: Hint: This is much simpler than you think. When you see the answer you will say "of course".
2. Honest Goblins are Easy to Find At Hogwarts a new shipment of n goblins has arrived. To be of any use, a goblin must be completely truthful (never lies). Unfortunately, not all of the n goblins in the shipment are truth tellers. Only some are truth-tellers, and some are deceivers. It is your task to design an algorithm to separate the truth-teller goblins from the deceiver goblins. To do this, you have one tool available: You may combine any two goblins and have them state whether the other goblin is a truth-teller or a deceiver. A truth-teller will always say correctly what the other goblin is, but a deceiver may lie (but also may sometimes tell the truth to REALLY confuse you). For any two goblins that you test, the following can be concluded from the goblin responses: Goblin A says Goblin B says Conclusion B is a truth-teller A is a truth-teller both are truth-tellers or both are deceivers B is a truth-teller A is a deceiver at least one is a deceiver B is a deceiver A is a…
Imagine there are N teams competing in a tournament, and that each team plays each of the other teams once. If a tournament were to take place, it should be demonstrated (using an example) that every team would lose to at least one other team in the tournament.
The search algorithm developed will be used for users to search the catalog for all items matching the search keyword(s), and there are a total of 15000 items in the catalog. During development, three different algorithms were created. • Algorithm A runs in constant time, with a maximum runtime of 1.10 seconds and returns all matching results. ● Algorithm B runs in logarithmic time, with a maximum runtime of 0.3 seconds, and returns only the first result. ● Algorithm C runs in linear time, with a maximum runtime of 1.50 seconds and returns all matching results. Which algorithm would be the least suitable for the requirements stated? In your answer, justify your choice by explaining why you picked that algorithm, and why you did not pick the other two algorithms.OND OND OND DAD
Voting Suppose that the votes of n people for different candidates (where there can be more than two candidates) for a particular office are the elements of a sequence. A person wins the election if this person receives a majority of the votes. 9. (a) Devise a divide-and-conquer algorithm that determines whether a candidate received a majority and, if so, determine who this candidate is. (b) Devise a divide-and-conquer algorithm that determines whether the two candidates who received the most votes each received at least n/4 votes and, if so, determine who these two candidates are. (c) Give a big-O estimate for the number of comparisons needed by the algorithm you devised in part (a).
(Note: Please do not copy the answer from Bartleby, Chegg, or from the internet. I request you to elaborate the answer with an example.)
Considering the function f(x) = x – cos(x), what is the value of x7 after performing fixed point iteration. Assume an initial guess of 1. Use the equation form that will seem fit according to the choices provided.Group of answer choices 0.72210 0.71537 0.76396 0.72236
Consider a modified Borda count where a first-place vote is worth F points (F > N where N denotes the numberof candidates) and all other places in the ballot are the same as in the ordinary Borda count: N − 1 points for second place, N − 2 points for third place, . . . , 1 point for last place. By choosing F large enough, we can make this variation of the Borda count method satisfy the majority criterion. Find the smallest value of F (expressed in terms of N ) for which this happens.
Today is Max's birthday. He has ordered a rectangular fruit cake which is divided into N x M pieces. Each piece of the cake contains a different fruit numbered from 1 to N*M. He has invited K friends, each of whom have brought a list of their favorite fruit choices. A friend goes home happy if the piece he receives is of his favorite fruit. Note that each friend can receive only one piece of cake. Design a way for Max to find the maximum number of friends he can make happy. Input The first line of the input consists of an integer - numOfFriends, representing the number of friends(k). The next Klines consist of X+1 space-separated integers, where the first integer represents the count of choices of the th friend followed by X space-separated integers representing the fruits he likes. The next line of the input consists of an integer - numN, representing the number of rows. The next line of the input consists of an integer - numM, representing the number of columns. Output Print an…
Could we use the ideas of the Closest Pair of Points Algorithm to solve the following problem? Given n points on the plane. Each point pi is defined by its coordinates (xi,yi). It is required to find a triangle (defined by a set of three points) with minimal perimeter. Justify the answer.
Which of the following best describes the useful criterion for comparing the efficiency of algorithms? None of the above Memory Time Both Time and Memory
CT ser.