Computer Science: An Overview (12th Edition)
12th Edition
ISBN: 9780133760064
Author: Glenn Brookshear, Dennis Brylow
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 5, Problem 50CRP
Program Plan Intro
- Consider a group of people divided into two subgroups (of any arbitrary size) with no one having same age in common such that the difference of their sum of ages of both groups is maximum.
- Now according to big-theta notation, we need to find the smallest number and separate it into one group and remaining in another group.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Consider the problem of counting, in a given text, the number of substrings that start with an A and end with a B. For example, there are four such substrings in CABAAXBYA.a. Design a brute-force algorithm for this problem and determine its efficiency class.b. Design a more efficient algorithm for this problem with complexity O (n)
Imagine a collection of nuts and bolts that are all together in one pile on a table. Describe, in pseudocode, how you would find all matching pairs of nuts and bolts. You need to find one solution for each of the problem-solving approaches given below. For each of your solutions, determine how many comparisons of pairs of nuts and bolts you might have to make in the best- and worst-case scenario. You can assume that there are complete pairs, no single nuts or bolts and that for each bolt, there is exactly one nut that fits. Describe a solution to the nuts and bolts problem (in pseudocode) using a Divide and Conquer Approach.
Imagine that you have a problem P that you know is N P-complete. For
this problem you have two algorithms to solve it. For each algorithm, some
problem instances of P run in polynomial time and others run in exponential time (there are lots of heuristic-based algorithms for real N P-complete
problems with this behavior). You can’t tell beforehand for any given problem instance whether it will run in polynomial or exponential time on either
algorithm. However, you do know that for every problem instance, at least
one of the two algorithms will solve it in polynomial time.
(a) What should you do?
(b) What is the running time of your solution?
564 Chap. 17 Limits to Computation
(c) What does it say about the question of P = N P if the conditions
described in this problem existed?
Chapter 5 Solutions
Computer Science: An Overview (12th Edition)
Ch. 5.1 - Prob. 1QECh. 5.1 - Prob. 2QECh. 5.1 - Prob. 3QECh. 5.1 - Suppose the insertion sort as presented in Figure...Ch. 5.2 - A primitive in one context might turn out to be a...Ch. 5.2 - Prob. 2QECh. 5.2 - The Euclidean algorithm finds the greatest common...Ch. 5.2 - Describe a collection of primitives that are used...Ch. 5.3 - Prob. 2QECh. 5.3 - Prob. 3QE
Ch. 5.3 - Prob. 4QECh. 5.4 - Modify the sequential search function in Figure...Ch. 5.4 - Prob. 2QECh. 5.4 - Some of the popular programming languages today...Ch. 5.4 - Suppose the insertion sort as presented in Figure...Ch. 5.4 - Prob. 5QECh. 5.4 - Prob. 6QECh. 5.4 - Prob. 7QECh. 5.5 - What names are interrogated by the binary search...Ch. 5.5 - Prob. 2QECh. 5.5 - What sequence of numbers would be printed by the...Ch. 5.5 - What is the termination condition in the recursive...Ch. 5.6 - Prob. 1QECh. 5.6 - Give an example of an algorithm in each of the...Ch. 5.6 - List the classes (n2), (log2n), (n), and (n3) in...Ch. 5.6 - Prob. 4QECh. 5.6 - Prob. 5QECh. 5.6 - Prob. 6QECh. 5.6 - Prob. 7QECh. 5.6 - Suppose that both a program and the hardware that...Ch. 5 - Prob. 1CRPCh. 5 - Prob. 2CRPCh. 5 - Prob. 3CRPCh. 5 - Select a subject with which you are familiar and...Ch. 5 - Does the following program represent an algorithm...Ch. 5 - Prob. 6CRPCh. 5 - Prob. 7CRPCh. 5 - Prob. 8CRPCh. 5 - What must be done to translate a posttest loop...Ch. 5 - Design an algorithm that when given an arrangement...Ch. 5 - Prob. 11CRPCh. 5 - Design an algorithm for determining the day of the...Ch. 5 - What is the difference between a formal...Ch. 5 - Prob. 14CRPCh. 5 - Prob. 15CRPCh. 5 - The following is a multiplication problem in...Ch. 5 - Prob. 17CRPCh. 5 - Four prospectors with only one lantern must walk...Ch. 5 - Starting with a large wine glass and a small wine...Ch. 5 - Two bees, named Romeo and Juliet, live in...Ch. 5 - What letters are interrogated by the binary search...Ch. 5 - The following algorithm is designed to print the...Ch. 5 - What sequence of numbers is printed by the...Ch. 5 - Prob. 24CRPCh. 5 - What letters are interrogated by the binary search...Ch. 5 - Prob. 26CRPCh. 5 - Identity the termination condition in each of the...Ch. 5 - Identity the body of the following loop structure...Ch. 5 - Prob. 29CRPCh. 5 - Design a recursive version of the Euclidean...Ch. 5 - Prob. 31CRPCh. 5 - Identify the important constituents of the control...Ch. 5 - Identify the termination condition in the...Ch. 5 - Call the function MysteryPrint (defined below)...Ch. 5 - Prob. 35CRPCh. 5 - Prob. 36CRPCh. 5 - Prob. 37CRPCh. 5 - The factorial of 0 is defined to be 1. The...Ch. 5 - a. Suppose you must sort a list of five names, and...Ch. 5 - The puzzle called the Towers of Hanoi consists of...Ch. 5 - Prob. 41CRPCh. 5 - Develop two algorithms, one based on a loop...Ch. 5 - Design an algorithm to find the square root of a...Ch. 5 - Prob. 44CRPCh. 5 - Prob. 45CRPCh. 5 - Design an algorithm that, given a list of five or...Ch. 5 - Prob. 47CRPCh. 5 - Prob. 48CRPCh. 5 - Prob. 49CRPCh. 5 - Prob. 50CRPCh. 5 - Prob. 51CRPCh. 5 - Does the loop in the following routine terminate?...Ch. 5 - Prob. 53CRPCh. 5 - Prob. 54CRPCh. 5 - The following program segment is designed to find...Ch. 5 - a. Identity the preconditions for the sequential...Ch. 5 - Prob. 57CRPCh. 5 - Prob. 1SICh. 5 - Prob. 2SICh. 5 - Prob. 3SICh. 5 - Prob. 4SICh. 5 - Prob. 5SICh. 5 - Is it ethical to design an algorithm for...Ch. 5 - Prob. 7SICh. 5 - Prob. 8SI
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
- Imagine a collection of nuts and bolts that are all together in one pile on a table. Describe, in pseudocode, how you would find all matching pairs of nuts and bolts. You need to find one solution for each of the problem-solving approaches given below. For each of your solution, determine how many comparisons of pairs of nuts and bolts you might have to make in the best- and worst- case scenario. You can assume that there are complete pairs, no single nuts or bolts, and that for each bolt, there is exactly one nut that fits. Describe a solution to the nuts and bolts problem (in pseudocode) using a Divide and Conquer Approach.arrow_forwardIf we want to prove P = NP, we only need to pick up any one NPC problem and design a polynomial-time algorithm for the problem. If you want to prove P = NP, select one NPC problem based on your preference and describe your idea of a polynomial-time algorithm that solves the problem. It does not have to be a formal algorithm or pseudo-code, a description of your idea of designing such an algorithm would be fine.arrow_forwardGive a clear description of an efficient algorithm for finding the k smallest elements of a very large n-element vector. Compare its running time with that of other plausible ways of achieving the same result, including that of applying k times your solution for part (a). [Note that in part (a) the result of the function consists of one element, whereas here it consists of k elements. As above, you may assume for simplicity that all the elements of the vector are different.]arrow_forward
- IN PYTHON A tridiagonal matrix is one where the only nonzero elements are the ones on the main diagonal and the ones immediately above and below it.Write a function that solves a linear system whose coefficient matrix is tridiag- onal. In this case, Gauss elimination can be made much more efficient because most elements are already zero and don't need to be modified or added. As an example, consider a linear system Ax = b with 100,000 unknowns and the same number of equations. The coefficient matrix A is tridiagonal, with all elements on the main diagonal equal to 3 and all elements on the diagonals above and below it equal to 1. The vector of constant terms b contains all ones, except that the first and last elements are zero. You can use td to find that x1= −0.10557. The following code format should help: def td(l, m, u, b): '''Solve a linear system Ax = b where A is tridiagonal Inputs: l, lower diagonal of A, n-1 vector m, main diagonal of A, n vector u,…arrow_forwardA Norman window has the shape of a rectangle surmounted by a semicircle. Suppose the outer perimeter of such a window must be 600 cm. In this problem you will find the base length x which will maximize the area of such a window. Use calculus to find an exact answer. When the base length is zero, the area of the window will be zero. There is also a limb on how large x can her when x is large enough, the rectangular portion of the window shrinks down to zero height. What is the exact largest value of x when this occurs?arrow_forwardAnalyzing the exact complexity of recursive functions can be difficult todo. Finding the Big O of them can be somewhat eyeballed by drawingout charts of how many calls are made for a recursive function to solvea problem. Take the Fibonacci sequence, which has much less repeatedwork when calculated with iteration but is very elegant to write withrecursion (without tail call optimization). (a) Using the description of Fibonacci below to draw out arecursive Fibonacci call for fibonacci(5), the 5th Fibonacci number.The actual calculated values are not as important as the numberpassed into each Fibonacci call. Just write out the call tree until thetermination of the tree down at each F(1) and F(0) leaf. (b) There are many repeated calls going down the recursiontree, especially when calculating the low Fibonacci numbers. If weused record keeping to remember what we calculated previously (of-ten called dynamic programming) then these repeated calculationsall the way down the tree would not…arrow_forward
- Information is present in the screenshot and below. Based on that need help in solving the code for this problem in python. The time complexity has to be as less as possible. Output Format For each query, output one line containing the length of the last movie Richie watches, without the credits, given the strategy described in the problem statement. If Richie can't watch any movie, output -1. Sample Input 0 8 148 116 157 100 169 15 188 98 91 68 165 70 145 2 11 6 3 2 6 52 12 2 6 13 7 0 4 2 3 Sample Output 0 90 154 -1 The actual code n = int(input())movies = []for i in range(n): r,c = list(map(int,input().rstrip().split(" "))) movies.append([r,c]) q = int(input())for cc in range(q): s,e,a,k = list(map(int,input().rstrip().split(" "))) # solve for answer herearrow_forwardImplement an algorithmic solution, indicating which states are valid and which are not, and model the space of the following problem: An interest group from a small town decided to sue a company for commercial abuse. For this, the people have organized themselves and decided to send 3 representatives, who will have to travel in a Van to the city where the lawsuit will be filed. The company to be sued, upon learning of these actions, has decided to send 3 lawyers to persuade the representatives, who will also travel in the same Van for that purpose. The community must file the class action suit under these conditions: - The three applicants must reach the destination city; - Only two people can travel per trip in the Van (small town - city, city - small town); - There can never be more lawyers than plaintiffs in any one place (either in the small town or city) because the lawyers can persuade the plaintiffs and as a consequence, the lawsuit would not be made; - The Van cannot be…arrow_forwardThe binomial coefficient C(N,k) can be defined recursively as follows: C(N,0) = 1, C(N,N) = 1, and for 0 < k < N, C(N,k) = C(N-1,k) + C(N - 1,k - 1). Write a function and give an analysis of the running time to compute the binomial coefficients as follows: A. The function is written using dynamic programming.arrow_forward
- The binomial coefficient C(N,k) can be defined recursively as follows: C(N,0) = 1, C(N,N) = 1, and for 0 < k < N, C(N,k) = C(N-1,k) + C(N - 1,k - 1). Write a function and give an analysis of the running time to compute the binomial coefficients as follows: A. The function is written recursively.arrow_forwardYou will analyze three algorithms to solve the maximum contiguous subsequence sum problem, and then evaluate the performance of instructor-supplied implementations of those three algorithms. You will compare your theoretical results to your actual results in a written report. What is the maximum contiguous subsequence sum problem? Given a sequence of integers A1, A2, ..., An (where the integers may be positive or negative), find a subsequence Aj, ... , Ak that has the maximum value of all possible subsequences. The maximum contiguous subsequence sum is defined to be zero if all of the integers in the sequence are negative. Consider the sequence shown below. A1: -2 A2: 11 A3: -4 A4: 13 A5: -5 A6: 2 The maximum contiguous subsequence sum is 20, representing the contiguous subsequence in positions 2, 3, and 4 (i.e. 11 + (-4) + 13 = 20). The sum of the values in all other contiguous subsequences is less than or equal to 20. Consider a second sequence, shown below. A1: 1…arrow_forwardDynamic Programming) Recall the rod cutting problem. We are given a non-negative integer n and an array P[1..n] of prices. We wish to cut the rod into a number of pieces whose lengths sum to n in order to sell the pieces. We are paid P[i] for selling a piece of length i. Our goal is to find the maximum total selling price for our pieces of rod. Consider a variant of the problem where we can cut the rod into at most k pieces where k ≤ n is given as part of the input. Describe an efficient algorithm for this version of the problem.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- C++ Programming: From Problem Analysis to Program...Computer ScienceISBN:9781337102087Author:D. S. MalikPublisher:Cengage Learning
C++ Programming: From Problem Analysis to Program...
Computer Science
ISBN:9781337102087
Author:D. S. Malik
Publisher:Cengage Learning