u have a mixed pile of N nuts and N bolts and need to quickly find the corresponding pairs of nuts and bolts. Each nut matches exactly one bolt, and each bolt matches exactly one nut. You can see which is larger by fitting a nut and bolt together, but it is not possible to directly compare two nuts or two bolts.

u have a mixed pile of N nuts and N bolts and need to quickly find the corresponding pairs of nuts and bolts. Each nut matches exactly one bolt, and each bolt matches exactly one nut. You can see which is larger by fitting a nut and bolt together, but it is not possible to directly compare two nuts or two bolts.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter17: Markov Chains

Section: Chapter Questions

Problem 12RP

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You have a mixed pile of N nuts and N bolts and need to quickly find the corresponding pairs of nuts and bolts. Each nut matches exactly one bolt, and each bolt matches exactly one nut. By fitting a nut and bolt together, you can see which is bigger, but it is not possible to directly compare two nuts or two bolts. Give an efficient method for solving the problem.
You are given an instance of a problem where you have an n x n grid of squares. Each square can be unpainted or can have a hole, so you cannot go on the square with a hole. The objective is to paint all the squares that do not have a hole. You start in the square (0,0) which is unpainted. The actions you can do are: (1) paint the square you are on if it is not painted; (2) move, either vertically or horizontally, to an adjacent square inside the grid that is not painted and does not have a hole. a. Describe a state-space representation for the problem, specifying the state representation, the initial state, the goal condition, and the actions. b. Is the state space finite? Is it a tree or a graph? c. Propose a heuristic for the problem. Is your heuristics admissible or not? Explain briefly your answer
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Suppose, you have been given a non-negative integer which is the height of a ‘house of cards’. To build such a house you at-least require 8 cards. To increase the level (or height) of that house, you would require four sides and a base for each level. Therefore, for the top level, you would require 8 cards and for each of the rest of the levels below you would require 5 extra cards. If you were asked to build level one only, you would require just 8 cards. Of course, the input can be zero; in that case, you do not build a house at all. Complete the recursive method below to calculate the number of cards required to build a ‘house of cards’ of specific height given by the parameter. public int hocBuilder (int height){ // TO DO } OR def hocBuilder(height):
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You are given a grid of size n ×m and within that grid there is a horizontal rod (arbitrary widthbut height of 1). You aim is to locate it. The only thing you can use to find the location of the rod is makequeries of the form IsPresent (x1, y1, x2, y2) where x1 ≤x2, y1 ≤y2. This returns True if part of the rod ispresent in the grid from (x1, y1) to (x2, y2) and False if not. See figures below. Design an algorithm whichuses queries O(log(n +m)) times to find the location of the rod, i.e., the leftmost coordinates and rightmostcoordinates. Hint: consider using binary search in your algorithm.
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You have n widgets, each of which is of a certain type. You want to determine whether there is a majority type; i.e., if there is a type t such that the number of widgets of type t is greater than n/2. For instance, the set of 7 widgets with types A, A, B,C, A, C, A, respectively has a majority type A since there are 4 widgets of that type. On the other hand, the set of 6 widgets with types A, A, B, C, D, A has no majority type. Unfortunately, you are unable to determine the type of any given widget. Instead, the only operation available to you is to call a subroutine Equality Test that takes two widgets as input and returns True if both are of the same type and False otherwise. Give a divide-and-conquer algorithm for determining if there is a majority type in a given set of n widgets. The running time of your algorithm is the number of calls made by your algorithm to Equality Test. Analyze the running time of your algorithm. Ideally, the running time of your algorithm should be…