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 22.2, Problem 2E
Program Plan Intro
To gives the values of
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Draw the Depth-First-Search tree of the graph below, starting from node A.Show your workings.
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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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- Prove that every connected graph contains a vertex (together with all nearby edges) whose removal will not cause the graph to become disconnected. Then, provide a DFS technique to locate this vertex.arrow_forwardGiven the undirected graph, do the following starting from Vertex A and if needed break ties alphabetically: (1) pre-order traversal, (2) post-order traversal, and (3) breadth first search.arrow_forwardGet the bitonic shortest route from s to each of the other vertices in a given digraph (if one exists). If a path has an intermediate vertex v and the edges from s to v and from v to t are strictly rising and decreasing, the path is said to be bitonic. The way should be clear-cut.arrow_forward
- Graph Algorithm. Show the d and pi values that result from running breadth-first search on this following graph using vertex 0 as the source.arrow_forwardRun 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?arrow_forwardRecall that the degree d(u) of a node u in a graph is the number of neighbors of u. Prove the following statements. (a) In any graph, the number of nodes with odd degree must be even. (b) Every tree contains at least two nodes with degree 1. (c) If every node of a graph G has degree at least n/2, then G is connected.arrow_forward
- Explain the Kruskal’s shortest spanning tree algorithm with a suitable example by taking a graph with 7 vertices, 15 edges and with suitable weights for each edge.arrow_forwardFind the shortest path from S to other nodes, on the given directed acyclic graph.Graph: R → A : 3 S → A : 1 A → C : 6 B → D : 3 C → E : 2R → S : 2 S → B : 2 B → A : 4 C → D : 1 D → E : 1 Answer: Topological Ordering: __________________________ Node Edge Relax? Update Shortest Path from S: Length Path R S A B C D Earrow_forwardShow all the steps of Kruskal''s minimum cost spanning tree algorithm for a complete graph of 6 vertices where the weight of the edge between the distinct vertices i and j is |i-j-1|, for 1 <= i, j <= 6.arrow_forward
- Graph Transversal Simulation: For this graph write down the order of vertices encountered in a breadth-first search starting from vertex A. Break ties by picking the vertices in alphabetical order (for example, A before Z)arrow_forwardWrite Algorithm to computes SCDS of any vertex set R in a DP graph with essential dominating pair (u, v) with d(u, v) >9.arrow_forwardExplain how a vertex u of a directed graph G can end up in a depth-first tree containing only u, even though u has both incoming and outgoing edges in G.arrow_forward
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