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 33.2, Problem 5E
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To determine whether two simple polygons with a total of n vertices intersect or not.
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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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- Design an algorithm to find the shortest (directed) cycle containing a vertex v. What is the space and time complexity of your algorithm? Prove that your algorithm finds the shortest cycle.arrow_forwardCreate an algorithm that, given a directed graph g = (v e) and a distinguished vertex s v, finds the shortest path from s to v for each v v. If g contains n vertices and e edges, your method must execute in o(n + e) time.arrow_forwardComputer Science Describe, in pseudo-code, a step-by-step algorithm for computing the diameter of a graph with n vertices and m edges. Also, state the worst-case running time of your algorithm.arrow_forward
- Describe a linear-time algorithm for computing the strongconnected component containing a given vertex v. On the basis of that algorithm, describe a simple quadratic algorithm for computing the strong components of a digraph.arrow_forwardThe following table(picture) presents the implementation of the Dijkstra algorithm on the evaluated graph G with 8 vertices. How many different shortest paths exist in the graph G between the vertices a and g?arrow_forwardDesign an O(E) time algorithm for recognizing a palmpolygon P where E is the number of visible pairs of vertices in Parrow_forward
- Prove by induction that a graph with n vertices has at most n(n-1)/2arrow_forwardProvide an algorithm that given an undirected graph G with n vertices and m edges as input, finds out whether G contains a cycle. Verify that your algorithm runs in O(n + m) time and Provide an algorithm that given a directed graph G with n vertices and m edges as input, finds out whether G contains a cycle. Verify that your algorithm runs in O(n + m) timearrow_forwardDescribe a linear-time algorithm for computing the strong connected component containing a given vertex v. On the basis of that algorithm, describe a simple quadratic algorithm for computing the strong components of a digraph.arrow_forward
- Please explain 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.)arrow_forwardGive an algorithm that determines whether or not a given undirected graph G D .V; E/ contains a cycle. Your algorithm should run in O.V / time, independent of |E|.arrow_forwardSuppose you have a graph with 100 nodes and 500 edges and you want to find the shortest path between two nodes using Dijkstra's algorithm. What is the time complexity of this operation?arrow_forward
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