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 1E
Program Plan Intro
To gives the value of
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I am struggling to draw a spanning tree using a depth-first when the following graph has a vertex A as the root and using alphabetical ordering.
Apply the Breadth first traversal algorithm to the undirected graph G given in Example and replicated here for convenience. The goal is to do a Breadth first search for the key 9.
Draw the Depth-First-Search tree of the graph below, starting from node A.Show your workings.
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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- Given 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_forwardProve 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_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_forward
- Get 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_forwardSuppose that G is an unconnected graph that consists of 4 connected components. The first component is K4, the second is K2,2, the third is C4 and the fourth is a single vertex. Your job is to show how to add edges to G so that the graph has an Euler tour. Justify that your solution is the minimum number of edges added.arrow_forwardExplain 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_forward
- If removing any 3 vertices from a connected graph G keeps it connected then: A- G must be 4-vertex connected B-G must be 3-vertex connected C-The edge connectivity of G must be at least 4 D-The vertex connectivity of G must be at least 4arrow_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_forwardCharacterize the set of undirected graphs containing a vertex u, such that there exists a DFS tree T, rooted at u that is identical to a BFS tree rooted at u. Find the largest class of graphs possible.arrow_forward
- Suppose G is a connected undirected graph. An edge e whose removal disconnects the graph is called a bridge. Must every bridge e be an edge in a depth-first search tree of G? Give a proof or a counterexample.arrow_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_forward3. From the graph above determine the vertex sequence of the shortest path connecting the following pairs of vertex and give each length: a. V & W b. U & Y c. U & X d. S & V e. S & Z 4. For each pair of vertex in no. 3 give the vertex sequence of the longest path connecting them that repeat no edges. Is there a longest path connecting them?arrow_forward
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