Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 33.4, Problem 5E
Program Plan Intro
To show thathow to determine the sets
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the closest-pair problem can be posted in the 3-dimensional space, in which the euclidean distance between two points p1(x1, y1, z1) and p2(x2, y2, z2) is defined as d = √(x1−x2)^2+(y1−y2)^2+(z1−z2)^2 what is the time-efficiency class of the brute-force algorithm for the 3-dimensional closest-pair problem?
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Give an algorithm that solves the Closest pair problem in 3D in Θ(n log n) time. (Closest pair problem in 3D: Given n points in the 3D space, find a pair with the smallest Euclidean distance between them.)
Given an abstraction of the City Tube Map where each node represents the city’s attraction, plan the trip for the tourist to visit. Start from node 1 that is their hotel, a group of tourists wants to visit all places. However, due to the time limitation, they can only visit each attraction once. To find the best order of places to visit, genetic algorithm can be used to derive the best possible solutions.
Chapter 33 Solutions
Introduction to Algorithms
Ch. 33.1 - Prob. 1ECh. 33.1 - Prob. 2ECh. 33.1 - Prob. 3ECh. 33.1 - Prob. 4ECh. 33.1 - Prob. 5ECh. 33.1 - Prob. 6ECh. 33.1 - Prob. 7ECh. 33.1 - Prob. 8ECh. 33.2 - Prob. 1ECh. 33.2 - Prob. 2E
Ch. 33.2 - Prob. 3ECh. 33.2 - Prob. 4ECh. 33.2 - Prob. 5ECh. 33.2 - Prob. 6ECh. 33.2 - Prob. 7ECh. 33.2 - Prob. 8ECh. 33.2 - Prob. 9ECh. 33.3 - Prob. 1ECh. 33.3 - Prob. 2ECh. 33.3 - Prob. 3ECh. 33.3 - Prob. 4ECh. 33.3 - Prob. 5ECh. 33.3 - Prob. 6ECh. 33.4 - Prob. 1ECh. 33.4 - Prob. 2ECh. 33.4 - Prob. 3ECh. 33.4 - Prob. 4ECh. 33.4 - Prob. 5ECh. 33.4 - Prob. 6ECh. 33 - Prob. 1PCh. 33 - Prob. 2PCh. 33 - Prob. 3PCh. 33 - Prob. 4PCh. 33 - Prob. 5P
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- Assuming that the graph G = (V, E) is represented in Adjacency List format, justify in detail the fact Greedy independent sets can be implemented in O(n 2 + m) worst-case running time, where n = |V |, m = |E|. This will require you to take real care in how the adjustment of Adj is done in line 10. The key is to only update/delete what is really necessary for the Algorithm, rather than being concerned with an accurate representation of the residual graph.arrow_forwardIf we choose to represent each genotype as a partial permutation, then provide an algebraic expression, in terms of n, for the size of the genetic search space (the number of possible valid genotypes), in terms of n. Assume that n ≥ 4.arrow_forwardSuppose that in applying the minimization algorithm in Section 2.6, weestablish some fixed order in which to process the pairs, and we follow thesame order on each pass a. What is the maximum number of passes that might be required?Describe an FA, and an ordering of the pairs, that would require thisnumber.b. Is there always a fixed order (depending on M) that would guaranteethat no pairs are marked after the first pass, so that the algorithmterminates after two passes?arrow_forward
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