Problem 51 Describe a practical problem tha... [FREE SOLUTION]

Chapter 14: Problem 51

Describe a practical problem that can be solved using Kruskal's Algorithm.

Short Answer

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A practical problem such as designing a cost-effective network for a University with buildings spread throughout a city, can be solved using Kruskal's Algorithm. In this case, each building is represented by a vertex in a graph, potential connections between the buildings are represented as edges, and the cost associated with these connections is the weight on these edges. Kruskal's Algorithm is applied to find the minimum spanning tree which would indicate the optimal connections between buildings with the least overall cost.

Step by step solution

Problem Presentation

The University has several buildings spread throughout the city. Thanks to a government grant, the University has secured funding to lay high-speed fiber-optic cables between these buildings to establish a network. However, the cost of laying these cables is expensive and the funding only covers a certain amount. As a solution, the University decides to prioritize making sure every building is connected over having multiple paths between buildings. The problem, therefore, is to ensure every building is connected with the least total cost.

Converting Problem into a Graph

Every building in the city will be represented by a vertex in the graph, and every potential pair of buildings that could be connected are represented as an edge. Each edge has a weight which represents the cost of connecting two buildings.

Apply Kruskal's Algorithm

With a graph representation of the problem in place, apply Kruskal's Algorithm to find the minimum spanning tree. This is as follows: 1. Sort all the edges from low weight to high 2. Take the edge with the lowest weight and add it to the spanning tree. If adding the edge created a cycle, then reject this edge 3. Keep adding edges until all vertices are included in the spanning tree.

Solution Interpretation

The final minimum spanning tree will represent the optimal way to connect all buildings with the least total cost. The edges in the minimum spanning tree will indicate which buildings should be directly connected for the most cost-effective solution.

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91影视

Describe a practical problem that can be solved using Kruskal's Algorithm.

Short Answer

Step by step solution

Problem Presentation

Converting Problem into a Graph

Apply Kruskal's Algorithm

Solution Interpretation

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