Introduction to Java Programming and Data Structures, Comprehensive Version (11th Edition)
11th Edition
ISBN: 9780134670942
Author: Y. Daniel Liang
Publisher: PEARSON
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Chapter 28.7, Problem 28.7.3CP
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Depth-first search (DFS):
“Depth-first search” is an
- DFS of a graph will start at any vertex V, then recursively visits remaining vertices, which is adjacent to that vertex V...
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Prove the following statement about graph theory: If a new edge (but no new vertex) is added to a tree, then the new graph will contain a circuit.
For the graph shown below:
a. Draw all the possible spanning trees.
b. Draw the minimum spanning tree.
2. Consider the graph G2(V2, E2) below.
2a. Find the MST of this graph with Kruskal’s algorithm. Draw the MST, and show the table [edge] [w(u, v)] [mark].
2b. Find the MST of this graph with Prim’s algorithm starting at vertex 'a'. Draw the MST and list the vertices in order you added them to the MST.
2c. Would you get a different MST if you repeat 2b starting at vertex 'e'? Why or why not?
Chapter 28 Solutions
Introduction to Java Programming and Data Structures, Comprehensive Version (11th Edition)
Ch. 28.2 - What is the famous Seven Bridges of Knigsberg...Ch. 28.2 - Prob. 28.2.2CPCh. 28.2 - Prob. 28.2.3CPCh. 28.2 - Prob. 28.2.4CPCh. 28.3 - Prob. 28.3.1CPCh. 28.3 - Prob. 28.3.2CPCh. 28.4 - Prob. 28.4.1CPCh. 28.4 - Prob. 28.4.2CPCh. 28.4 - Show the output of the following code: public...Ch. 28.4 - Prob. 28.4.4CP
Ch. 28.5 - Prob. 28.5.2CPCh. 28.6 - Prob. 28.6.1CPCh. 28.6 - Prob. 28.6.2CPCh. 28.7 - Prob. 28.7.1CPCh. 28.7 - Prob. 28.7.2CPCh. 28.7 - Prob. 28.7.3CPCh. 28.7 - Prob. 28.7.4CPCh. 28.7 - Prob. 28.7.5CPCh. 28.8 - Prob. 28.8.1CPCh. 28.8 - When you click the mouse inside a circle, does the...Ch. 28.8 - Prob. 28.8.3CPCh. 28.9 - Prob. 28.9.1CPCh. 28.9 - Prob. 28.9.2CPCh. 28.9 - Prob. 28.9.3CPCh. 28.9 - Prob. 28.9.4CPCh. 28.10 - Prob. 28.10.1CPCh. 28.10 - Prob. 28.10.2CPCh. 28.10 - Prob. 28.10.3CPCh. 28.10 - If lines 26 and 27 are swapped in Listing 28.13,...Ch. 28 - Prob. 28.1PECh. 28 - (Create a file for a graph) Modify Listing 28.2,...Ch. 28 - Prob. 28.3PECh. 28 - Prob. 28.4PECh. 28 - (Detect cycles) Define a new class named...Ch. 28 - Prob. 28.7PECh. 28 - Prob. 28.8PECh. 28 - Prob. 28.9PECh. 28 - Prob. 28.10PECh. 28 - (Revise Listing 28.14, NineTail.java) The program...Ch. 28 - (Variation of the nine tails problem) In the nine...Ch. 28 - (4 4 16 tails problem) Listing 28.14,...Ch. 28 - (4 4 16 tails analysis) The nine tails problem in...Ch. 28 - (4 4 16 tails GUI) Rewrite Programming Exercise...Ch. 28 - Prob. 28.16PECh. 28 - Prob. 28.17PECh. 28 - Prob. 28.19PECh. 28 - (Display a graph) Write a program that reads a...Ch. 28 - Prob. 28.21PECh. 28 - Prob. 28.22PECh. 28 - (Connected rectangles) Listing 28.10,...Ch. 28 - Prob. 28.24PECh. 28 - (Implement remove(V v)) Modify Listing 28.4,...Ch. 28 - (Implement remove(int u, int v)) Modify Listing...
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- Draw the minimum spanning tree for the following graph. Use induction to prove your result is a minimum spanning tree.arrow_forwardCompute a minimum spanning tree for the following graph, using the Prim-Jarnik algorithm, and starting from vertex a. Please illustrate all intermediate steps of the algorithm by showing the intermediate graphs and the partial minimum spanning tree obtained.arrow_forwardShow the DFS tree for the graph of Figure 11.26 starting at Vertex 1arrow_forward
- 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.arrow_forwardDiagrammatically step by step apply Prim’s algorithm to find a minimum spanning tree for the given wcightcd graph G. bt K G Choose the starting node for the algorithm based on the last digit your roll number as v Last digit of your roll number [ 0 [ 12 4]s[6[7]8]9 e Root vertex alb|e e[f[g[h]i]earrow_forwardFor a graph with 10 nodes, the minimum spanning tree should have ___ edges. Question 3 options: 10 9 8 11arrow_forward
- Explain what a spanning tree is: a graph with no loops.arrow_forwardWrite down the long codeword for the spanning tree in K10 that corresponds to the short codeword CCDCEABA. (Here the vertex set of K10 is {A,B,C,D,E,F,G,H,I,J}).arrow_forwardIf a graph G has n vertices and n−1 edges, n≥3 , then it must be that Select one: a. G cannot contain a circuit containing all of the vertices in G . b. All of the other answers are correct. c. G is a tree d. G contains at least one vertex of degree one.arrow_forward
- Given the graph below, run the Kruskal’s algorithm to find the minimum spanning tree. Show the algorithmic steps and label each edge by the order in which it was selected.arrow_forwardconstruct a bipartite graph with vertices L,M,N,O,P,Q that is a tree. what is the edge set? construct a connected bipartite graph with vertices L,M,N,O,P,Q that is not a tree. what is the edge set?arrow_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_forward
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