Weighted Graph: A graph is termed as weighted graph if each edge of the graph is assigned a weight. The weighted edges stored in the weighted graphs can be stored in adjacency lists. Weighted edges can be represented using a two-dimensional array. An weighted edge can be represented as “WeightedEdge(u,v,w)”, where “u” and “v” are edges and “w” represents the weight between them. Example of storing edge in a weighted graph: Object[][] edges = { new Integer(0), new Integer(1), new SomeTypeForWeight(8) }; Prim’s Algorithm : Prim’s Algorithm is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph by finding a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized.

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Answer 1

Question

Chapter 29.4, Problem 29.4.3CP

Program Plan Intro

Weighted Graph:

A graph is termed as weighted graph if each edge of the graph is assigned a weight. The weighted edges stored in the weighted graphs can be stored in adjacency lists.

Weighted edges can be represented using a two-dimensional array. An weighted edge can be represented as “WeightedEdge(u,v,w)”, where “u” and “v” are edges and “w” represents the weight between them.

Example of storing edge in a weighted graph:

Object[][] edges =

{ new Integer(0), new Integer(1), new SomeTypeForWeight(8) };

Prim’s Algorithm:

Prim’s Algorithm is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph by finding a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized.

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Students have asked these similar questions

If I have a large number of edges that form and undirected graph and I want to store them in an adjacency matrix, what are some techniques I can use to efficiently build the matrix without using brute force techniques?

When representing a weighted graph, are there any problems with utilizing adjacency lists?

You should consider the drawbacks of representing a weighted graph as a list of adjacencies.

Answer 2

Question

Chapter 29.4, Problem 29.4.3CP

Program Plan Intro

Weighted Graph:

A graph is termed as weighted graph if each edge of the graph is assigned a weight. The weighted edges stored in the weighted graphs can be stored in adjacency lists.

Weighted edges can be represented using a two-dimensional array. An weighted edge can be represented as “WeightedEdge(u,v,w)”, where “u” and “v” are edges and “w” represents the weight between them.

Example of storing edge in a weighted graph:

Object[][] edges =

{ new Integer(0), new Integer(1), new SomeTypeForWeight(8) };

Prim’s Algorithm:

Prim’s Algorithm is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph by finding a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 29.4, Problem 29.4.3CP

Program Plan Intro

Weighted Graph:

A graph is termed as weighted graph if each edge of the graph is assigned a weight. The weighted edges stored in the weighted graphs can be stored in adjacency lists.

Weighted edges can be represented using a two-dimensional array. An weighted edge can be represented as “WeightedEdge(u,v,w)”, where “u” and “v” are edges and “w” represents the weight between them.

Example of storing edge in a weighted graph:

Object[][] edges =

{ new Integer(0), new Integer(1), new SomeTypeForWeight(8) };

Prim’s Algorithm:

Prim’s Algorithm is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph by finding a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 29.4, Problem 29.4.3CP

Program Plan Intro

Weighted Graph:

A graph is termed as weighted graph if each edge of the graph is assigned a weight. The weighted edges stored in the weighted graphs can be stored in adjacency lists.

Weighted edges can be represented using a two-dimensional array. An weighted edge can be represented as “WeightedEdge(u,v,w)”, where “u” and “v” are edges and “w” represents the weight between them.

Example of storing edge in a weighted graph:

Object[][] edges =

{ new Integer(0), new Integer(1), new SomeTypeForWeight(8) };

Prim’s Algorithm:

Prim’s Algorithm is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph by finding a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 29.4, Problem 29.4.3CP

Program Plan Intro

Weighted Graph:

A graph is termed as weighted graph if each edge of the graph is assigned a weight. The weighted edges stored in the weighted graphs can be stored in adjacency lists.

Weighted edges can be represented using a two-dimensional array. An weighted edge can be represented as “WeightedEdge(u,v,w)”, where “u” and “v” are edges and “w” represents the weight between them.

Example of storing edge in a weighted graph:

Object[][] edges =

{ new Integer(0), new Integer(1), new SomeTypeForWeight(8) };

Prim’s Algorithm:

Prim’s Algorithm is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph by finding a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized.

Answer 6

Chapter 29.4, Problem 29.4.3CP

Program Plan Intro

Weighted Graph:

A graph is termed as weighted graph if each edge of the graph is assigned a weight. The weighted edges stored in the weighted graphs can be stored in adjacency lists.

Weighted edges can be represented using a two-dimensional array. An weighted edge can be represented as “WeightedEdge(u,v,w)”, where “u” and “v” are edges and “w” represents the weight between them.

Example of storing edge in a weighted graph:

Object[][] edges =

{ new Integer(0), new Integer(1), new SomeTypeForWeight(8) };

Prim’s Algorithm:

Prim’s Algorithm is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph by finding a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized.

Answer 7

Chapter 29.4, Problem 29.4.3CP

Program Plan Intro

Weighted Graph:

A graph is termed as weighted graph if each edge of the graph is assigned a weight. The weighted edges stored in the weighted graphs can be stored in adjacency lists.

Weighted edges can be represented using a two-dimensional array. An weighted edge can be represented as “WeightedEdge(u,v,w)”, where “u” and “v” are edges and “w” represents the weight between them.

Example of storing edge in a weighted graph:

Object[][] edges =

{ new Integer(0), new Integer(1), new SomeTypeForWeight(8) };

Prim’s Algorithm:

Prim’s Algorithm is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph by finding a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 29.2 - Prob. 29.2.1CP Ch. 29.2 - Prob. 29.2.2CP Ch. 29.3 - Prob. 29.3.1CP Ch. 29.3 - Prob. 29.3.2CP Ch. 29.3 - Show the output of the following code: public...Ch. 29.4 - Prob. 29.4.1CP Ch. 29.4 - Prob. 29.4.2CP Ch. 29.4 - Prob. 29.4.3CP Ch. 29.4 - Prob. 29.4.4CP Ch. 29.4 - Show the output of the following code: public...

Solution Summary: The author explains the time complexity of Prim's algorithm using adjacency matrix to store the weighted edges.

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Chapter 29 Solutions