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 28.7.2CP
Program Plan Intro
Depth-first search (DFS):
“Depth-first search” is an
- DFS of a graph will start at any vertex V, and then recursively visits remaining vertices, which is adjacent to that vertex V.
- DFS of a tree will visit the root first, and then recursively visits the subtrees of the root R.
- It searches “deeper” in the graph, because graph may contain cycles. Hence it is referred as “depth-first” search.
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Draw two different spanning trees for the graph below:
2.
5
3₂
2
5
a
6
For the graph shown below:
a. Draw all the possible spanning trees.
b. Draw the minimum spanning tree.
Weighted Graph Applications Demonstration Java Data Structures.
Figure 29.23 illustrates a weighted graph with 6 vertices and 8 weighted edges.
Simply provide:
Minimal Spanning Tree as an illustration or a textual list of edges (in our standard vertex order).
Single-Source Shortest Path route from vertex 0 to the other 5 (described as one path/route for each).
draw the two solutions and attach the illustration or describe them in text (a list of edges for the one and the vertex to vertex path the other).
You can therefore attach proper content files with dot txt, png, jpg or jpeg extensions
Be sure the final trees or path lists are clearly visible in your solution. You don't need to show the solution development or progress, just the result.
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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- Write a program that creates the minimum spanning tree for the grapharrow_forward7. Start from vertex A, use Prim's algorithm to find a minimum spanning tree (MST) for the following weighted graph: F 3 6 E A 5 2 7 D B 2 3 C Show the weight of the MST, the sequences of the edges added to the MST during the construction and draw the MST.arrow_forwardExercise # 4: Level of each node in the graph How to determine the level of each node in the given graph? As you know, BFS involves a level-order traversal of a graph. Hence, you can use BFS to determine the level of each node as well. S Level 0 1 Level 1 Level 2 3 4 5 6. Level 3 Exercise # 4a: Write a function nodes_of_level(G, level) that takes a graph and level number as input and returns a list of all the nodes that are on the given level. Example 1: Input Adjacency list representation of graph shown above. level = 1 Output [1, 2] Example 2: Input Adjacency list representation of graph shown above. level = 2 %3D Output [3, 4, 5, 6] 9, 2.arrow_forward
- Data Structures Weighted Graph Applications Demonstration Look at Figure 29.23 which illustrates a weighted graph with 6 verticies and 8 weighted edges. Simply provide: Minimal Spanning Tree as an illustration or a textual list of edges (in our standard vertex order). Single-Source Shortest Path route from vertex 0 to the other 5 (described as one path/route for each). You may draw the two solutions and attach the illustration or describe them in text (a list of edges for the one and the vertex to vertex path the other). Be sure the final trees or path lists are clearly visible in your solution.arrow_forwardExplain what a spanning tree is: a graph with no loops.arrow_forwardConsider the graph below: A B Show the sequences of nodes that result from a depth-first traversal of the graph starting at node C. O A. Sequence is: C; G; B; A; D. B. Sequence is: C; D; F; G; A; E; B O C. Sequence is: C; D; F; A; E; G; B D. None of the abovearrow_forward
- Given a graph data structure: G = (V,E) where, V = {A, B, C, D, E } E = { (A,B), (A,D), (B,D), (B,C), (D,E) } a) Draw the graph G. b) Draw all spanning trees of the graph G, which are also “linear” (each graph node has no more than two neighbors).arrow_forwardWrite a java program Consider flight network having places of departure and destination. Flight network represent place name as a node and flight trajectories between palce names are the edges. Consider Pakistan cities as a node and show the source and destination paths, show all the paths separately with their labels and include their code as well. Analyze this scenerio that tree or graph should implement here, justify and also implement this with appropiate data structure.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_forward
- 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?arrow_forwardPlease provide all the spanning trees possible from the graph below:arrow_forwardWrite a program that creates the minimum spanning tree for the graph in Figurearrow_forward
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