Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 23.2, Problem 5E
Program Plan Intro
To find the run time of Prim’s
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Suppose you have a graph G with 6 vertices and 7 edges, and you are given the following information:
The degree of vertex 1 is 3.
The degree of vertex 2 is 4.
The degree of vertex 3 is 2.
The degree of vertex 4 is 3.
The degree of vertex 5 is 2.
The degree of vertex 6 is 2.
What is the minimum possible number of cycles in the graph G?
Give an algorithm to detect whether a given undirected graph contains a cycle. If the graph contains a cycle, then your algorithm should output one. (It should not output all cycles in the graph, just one of them.) The running time of your algorithm should be O(m+n) for a graph with n nodes and m edges.
Implement Dijkstra's algorithm to find the shortest path between two nodes in a graph.
What is the time complexity of your solution?
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
- True or false: For graphs with negative weights, one workaround to be able to use Dijkstra’s algorithm (instead of Bellman-Ford) would be to simply make all edge weights positive; for example, if the most negative weight in a graph is -8, then we can simply add +8 to all weights, compute the shortest path, then decrease all weights by -8 to return to the original graph. Select one: True Falsearrow_forwardGiven the following Graphs: Graph A: В 12c 1 4. E F G- H 4 J K 3 Graph B: Graph B is the undirected version of Graph A. 3.arrow_forwardOne can manually count path lengths in a graph using adjacency matrices. Using the simple example below, produces the following adjacency matrix: A B A 1 1 B 1 0 This matrix means that given two vertices A and B in the graph above, there is a connection from A back to itself, and a two-way connection from A to B. To count the number of paths of length one, or direct connections in the graph, all one must do is count the number of 1s in the graph, three in this case, represented in letter notation as AA, AB, and BA. AA means that the connection starts and ends at A, AB means it starts at A and ends at B, and so on. However, counting the number of two-hop paths is a little more involved. The possibilities are AAA, ABA, and BAB, AAB, and BAA, making a total of five 2-hop paths. The 3-hop paths starting from A would be AAAA, AAAB, AABA, ABAA, and ABAB. Starting from B, the 3-hop paths are BAAA, BAAB, and BABA. Altogether, that would be eight 3-hop paths within this graph. Write a program…arrow_forward
- Consider the line from (5, 5) to (13, 9).Use the Bresenham’s line drawing algorithm to draw this line. You are expected to find out all the pixels of the line and draw it on a graph paperarrow_forwardGiven a graph G, check whether can we color the vertices of a graph G using two colors such that no two adjacent vertices have the same color. Which algorithm will you apply for this problem and what would be the complexity?arrow_forwardConsider the following graph G. Which vertices of G have degree equal to 2. 0 0 A A B C D E F G t u B V с W D E X TI F y N Garrow_forward
- I have a directed graph with N nodes. How can I tell if the graph has a cycle? Your answer should be an algorithm in English. It is nice but not essential for you to give the name of the algorithm. You should describe how the algorithm works.arrow_forwardBrad is provided with a graph containing X branches. And it's given that the xth branch has a weight of Px. And for the given condition y-I + Py-Px there exits an edge connecting the branches. You have to develop a Python code that finds the number of connected components in this graph. Example Input: 1 3 152 Result: 1arrow_forward........arrow_forward
- Be a connected, undirected graph, G D.V; E/. To calculate a path across G that precisely travels each edge in E once in each direction, provide an O.V C E/-time method. Give you a lot of pennies; explain how you can navigate a maze using them.arrow_forwardIn the figure below there is a weighted graph, dots represent vertices, links represent edges, and numbers represent edge weights. S 2 1 2 1 2 3 T 1 1 2 4 (a) Find the shortest path from vertex S to vertex T, i.e., the path of minimum weight between S and T. (b) Find the minimum subgraph (set of edges) that connects all vertices in the graph and has the smallest total weight (sum of edge weights). 2. 3.arrow_forwardConsider a graph with five nodes labeled A, B, C, D, and E. Let's say we have the following edges with their weights: A to B with weight 3 A to C with weight 1 B to C with weight 3 B to D with weight 1 C to E with weight 4 D to E with weight 2 a. Find the shortest path from A to E using Dijkstra's algorithm (Would anything change if B to C weight was changed from 3 to 4? To 1? What about 5?)arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Database System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill Education
Starting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSON
Digital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSON
C How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSON
Database Systems: Design, Implementation, & Manag...Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage Learning
Programmable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
Database System Concepts
Computer Science
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:9780134444321
Author:Tony Gaddis
Publisher:PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:9780132737968
Author:Thomas L. Floyd
Publisher:PEARSON
C How to Program (8th Edition)
Computer Science
ISBN:9780133976892
Author:Paul J. Deitel, Harvey Deitel
Publisher:PEARSON
Database Systems: Design, Implementation, & Manag...
Computer Science
ISBN:9781337627900
Author:Carlos Coronel, Steven Morris
Publisher:Cengage Learning
Programmable Logic Controllers
Computer Science
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education