An evil king has n bottles of wine, and a spy has just poisoned one of them. Unfortunately, they do not know which one it is. The poison is very deadly; just one drop diluted even a billion to one will still kill. Even so, it takes a full month for the poison to take effect. Design a scheme for determining exactly which one of the wine bottles was poisoned in just one month’s time while expending O(log n) taste testers.
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Data Structures and Algorithms in Java
Additional Engineering Textbook Solutions
C How to Program (8th Edition)
C++ How to Program (10th Edition)
Java: An Introduction to Problem Solving and Programming (8th Edition)
C Programming Language
Starting Out with Java: From Control Structures through Data Structures (3rd Edition)
Management Information Systems: Managing the Digital Firm (15th Edition)
- 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 DADarrow_forwardHelp me pleasearrow_forwardA pollster obtains a list of register voters and uses a computure random number generator to choose 100 of them to ask which canidate they prefer in the upcoming electionarrow_forward
- There are a set of courses, each of them requiring a set of disjoint time intervals. For example, a course could require the time from 9am to 11am and 2pm to 3pm and 4pm to 5pm. You want to know, given a number K, if it’s possible to take at least K courses. You can only take one course at any single point in time (i.e. any two courses you choose can’t overlap). Show that the problem is NP-complete, which means that choosing courses is indeed a difficult thing in our life. Use a reduction from the Independent set problem.arrow_forwardمسئله ۱: حل مشكله التحسين الخطى التالية باستخدام طریقهٔ Large:M Max Z = x, +8x, Subject to (1) X, +3x, 56 2x, + x, = 8 X1, X, 20 نصائح: احصل على منطقة الإجابات المحتملة باستخدام طريقة الرسم. احصل أيضا على الإجابة وأجب عنها في بيئة برامج LINGO Python ,i Question 1: Solve the following linear optimization problem using the Large M methodarrow_forwardThere are m towns in a straight line, with a road joining each pair of consecutive towns. Legends say that an ordinary person in one of these towns will become a hero by completing a sequence of n quests. The first quest will be completed in their home town, but after each quest they may complete their next quest either in the same town or after moving to a neighbouring town.For example, if n = 5 and m = 4, a resident of town 2 may become a hero as follows:• begin in town 2 for quest 1,• then move to town 3 for quest 2,• stay in town 3 for quest 3,• return to town 2 for quest 4, and• move to town 1 for quest 5.Design an algorithm which runs in O(nm) time and finds the total number of waysto complete n quests.arrow_forward
- Suppose that f (n) = 0(g(n)) and f(n) = 0(h(n)), then it is ( always / sometimes / never ) the case that g(n) = 0(h(n)).arrow_forwardYou are given a collection of n bolts of different widths and n corresponding nuts. You are allowed to try a nut and bolt together, from which you can determine whether the nut is larger than the bolt, smaller than the bolt, or matches the bolt exactly. However, there is no way to compare two nuts together or two bolts together. The problem is to match each bolt to each nut. Design an algorithm for this problem with Θ(n log n) average-case complexity (in terms of nut-bolt comparisons). Explain why your algorithm has Θ(n log n) average case complexity.arrow_forwardYou are given a collection of n bolts of different widths and n corresponding nuts. You are allowed to try a nut and bolt together, from which you can determine whether the nut is larger than the bolt, smaller than the bolt, or matches the bolt exactly. However, there is no way to compare two nuts together or two bolts together. The problem is to match each bolt to each nut. Design an algorithm for this problem with Θ(n log n) average-case complexity (in terms of nut-bolt comparisons). Explain why your algorithm has Θ(n log n) average-case complexity. You may use any result without explicitly solving recurrence equations.arrow_forward
- In a candy store, there are N different types of candies available and the prices of all the N different types of candies are provided to you. You are now provided with an attractive offer. You can buy a single candy from the store and get at most K other candies ( all are different types ) for free. Now you have to answer two questions. Firstly, you have to find what is the minimum amount of money you have to spend to buy all the N different candies. Secondly, you have to find what is the maximum amount of money you have to spend to buy all the N different candies. In both the cases you must utilize the offer i.e. you buy one candy and get K other candies for free. Example 1: Input: N = 4 K = 2 %3D candies[] = {3 2 1 4} Output: 3 7arrow_forwardMr Monkey is standing in front of a row of banana trees on Skull Island which actually belong to his rival King Kong. The banana trees are unusually high on that island. He wants to steal as many bananas as possible. Here is his plan. He will climb up one of the trees and then keep jumping from one tree to the immediately next one, while collecting all the bananas from each of them. But he will not switch the direction of his jumps. No longer being the agile young monkey he once used to be, he can only jump a total distance of L, after which he will climb down and run away before Kong crushes his head. Let the trees be labelled as t1, t2, ·.· tn. Let v;, Vi = 1, 2, · ..n be the number of bananas in tree t;. Further, let l;, i = 1,2, Can you write an algorithm to help Mr. Monkey steal as many bananas as possible ? Your algorithm should be a polynomial in n, L. Please show all the steps of DP as in the sample solution - subproblem definition, recurrences, pseudocode, runtime . (Statutory…arrow_forwardAlgorithm X has a growth rate that is proportional to n ∗ n ∗ n . What is the function that represents the growth rate of algorithm X? What is the order of algorithm X?arrow_forward
- Database System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill EducationStarting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSONDigital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSON
- C How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSONDatabase Systems: Design, Implementation, & Manag...Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage LearningProgrammable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education