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 22.5, Problem 3E
Program Plan Intro
To show that strongly connected component
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Bellman-Ford algorithm
Draw a graph G with weights of edges ranging from 3 to 9, is it possible to calculate the LONGEST PATH without altering the algorithm at all? Justify your answer by providing solid reasons.
Run BFS algorithm on the following graph starting
with vertex s. Whenever there is a choice of vertices, choose the one that is
alphabetically first. What is the order that the vertices are visited? What is the shortest path from vertex s to vertex b?
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Chapter 22 Solutions
Introduction to Algorithms
Ch. 22.1 - Prob. 1ECh. 22.1 - Prob. 2ECh. 22.1 - Prob. 3ECh. 22.1 - Prob. 4ECh. 22.1 - Prob. 5ECh. 22.1 - Prob. 6ECh. 22.1 - Prob. 7ECh. 22.1 - Prob. 8ECh. 22.2 - Prob. 1ECh. 22.2 - Prob. 2E
Ch. 22.2 - Prob. 3ECh. 22.2 - Prob. 4ECh. 22.2 - Prob. 5ECh. 22.2 - Prob. 6ECh. 22.2 - Prob. 7ECh. 22.2 - Prob. 8ECh. 22.2 - Prob. 9ECh. 22.3 - Prob. 1ECh. 22.3 - Prob. 2ECh. 22.3 - Prob. 3ECh. 22.3 - Prob. 4ECh. 22.3 - Prob. 5ECh. 22.3 - Prob. 6ECh. 22.3 - Prob. 7ECh. 22.3 - Prob. 8ECh. 22.3 - Prob. 9ECh. 22.3 - Prob. 10ECh. 22.3 - Prob. 11ECh. 22.3 - Prob. 12ECh. 22.3 - Prob. 13ECh. 22.4 - Prob. 1ECh. 22.4 - Prob. 2ECh. 22.4 - Prob. 3ECh. 22.4 - Prob. 4ECh. 22.4 - Prob. 5ECh. 22.5 - Prob. 1ECh. 22.5 - Prob. 2ECh. 22.5 - Prob. 3ECh. 22.5 - Prob. 4ECh. 22.5 - Prob. 5ECh. 22.5 - Prob. 6ECh. 22.5 - Prob. 7ECh. 22 - Prob. 1PCh. 22 - Prob. 2PCh. 22 - Prob. 3PCh. 22 - Prob. 4P
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- Q7: Run the Ford-Fulkerson algorithm on the graph assigned to you and determine the maximum flow possible between the source (s) and destination (d) as well as determine the minimum cut of edges (set of edges with the minimum sum of the edge weights) to disconnect the source and destination. Show all the work (including the use of the residual graphs in each iteration).arrow_forwardthe simple code masks a more sophisticated computation, so studying these examples, tracing their behavior on small sample graphs, and extending them to provide a cycle or a coloring, respectively, are worthwhilearrow_forwardFor the following graph, list the vertices in the order they might be encountered in a breadth first search (BFS) starting at vertex A. No need to use any spaces, e.g., ACFGHIDBE In cases when there are multiple possibilities for the next vertex, choose them in alphabetical order (for reference: A, B, C, D, E, F, G, H, I) A B E Harrow_forward
- Answer the given question with a proper explanation and step-by-step solution. For the graph, list the first 12 edges that you would choose (in order) for Kruskal's algorithm.arrow_forwardUsing the same graph as in the previous question, list the vertices in the order thatthey will be visited by a breadth-first traversal, starting withe vertex A. Again, when there are multiple adjacent vertexes, save them alphabetically, A to G.Enter the letters with no spaces between them, in the order they would be visited.arrow_forwardRun Dijkstra's algorithm on the following graph, starting from vertex A. Whenever there are multiple choices of vertex at the same time, choose the one that is alphabetically first. You are expected to show how you initialize the graph, how you picked a vertex and update the d values at the each, and what is final shortest distance of each vertex from A. B 11 A F Earrow_forward
- If visiting every vertex is as easy as iterating through them, then why do we need graph traversal algorithms such as depth-first and breadth-first? What purpose do they serve that just iterating through the vertices one at a time, without regard for the presence of edges, wouldn't?arrow_forwardImplement a program that performs a depth-first search on the graph shown in Figure.arrow_forwardUse the algorithm below(DrawAlgo): Input: Two undirected graphs Z = (S, O) and K = (S, O') on the same set of vertices(S) DrawAlgo(Z, K): 1. for each vertex v in S 2. for each vertex w in S adjecent to v in Z 3. check if (v, w) in O' A) Both Z and K are implemented with adjecency lists. Analyze the running time of DrawAlgo, argue your answer. B) What is the best implementation of Z and K to ensure DrawAlgo has the best worst-case running time. What is the running time with this implementation. PLEASE DONT JUST COPY FROM GEEKSFORGEEKSarrow_forward
- When we learn about Graph Traversals, one question that I'm sometimes asked by students is why we need them at all. Consider the two implementation strategies for graphs that we learned about previously: an adjacency matrix and adjacency lists. Both of them include a separate array-based structure in which information about every vertex is stored. So if our only goal is to visit every vertex, we can do that by just iterating through that array-based structure. If visiting every vertex is as easy as iterating through them, then why do we need graph traversal algorithms such as depth-first and breadth-first? What purpose do they serve that just iterating through the vertices one at a time, without regard for the presence of edges, wouldn't? JAVA PROGRAMMINGarrow_forwardDraw a tree with 14 vertices Draw a directed acyclic graph with 6 vertices and 14 edges Suppose that your computer only has enough memory to store 40000 entries. Which best graph data structure(s) – you can choose more than 1 -- should you use to store a simple undirected graph with 200 vertices, 19900 edges, and the existence of edge(u,v) is frequently asked? - Adjacency Matrix - Adjacency List - Edge Listarrow_forwardWhat is the shortest path between A and Z in the graph below?(The length of a path is the sum of the numbers along the edges on the path.) Explain briefly how you have found this solution: what algorithm or solution strategy did you use? Does it work on any graph?arrow_forward
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