From 0 to 1 Data Structures & Algorithms in Java - Prim's Algorithm For a Minimal Spanning Tree

The video tutorial introduces the concept of minimal spanning trees, explaining their properties and applications. It then delves into Prim's algorithm, a method for finding minimal spanning trees in undirected, connected graphs. The tutorial highlights the differences between Prim's and Dijkstra's algorithms, emphasizing Prim's focus on minimizing total edge weight. The video concludes with a step-by-step example of Prim's algorithm, illustrating its practical application in constructing a minimal spanning tree.

What is a key characteristic of a minimal spanning tree?

• It includes all edges of the graph.

• It contains cycles.

• It is a directed graph.

• It connects all vertices with the minimum total edge weight.

Why are minimal spanning trees useful in real-world applications?

• They help in finding the longest path in a graph.

• They are used to build cost-effective networks.

• They ensure maximum redundancy in networks.

• They are used to sort vertices.

What type of graph is Prim's Algorithm best suited for?

• Directed graphs

• Graphs with negative weights

• Disconnected graphs

• Undirected connected graphs

How does Prim's Algorithm differ from Dijkstra's Algorithm in terms of its objective?

• Prim's Algorithm is used for directed graphs only.

• Prim's Algorithm requires a fixed source vertex.

• Prim's Algorithm aims to minimize the total distance of connecting all vertices.

• Prim's Algorithm focuses on finding the shortest path from a single source.

In Prim's Algorithm, what is the initial state of the distance table?

• All distances are set to zero.

• All distances are set to the average edge weight.

• All distances are set to infinity except for the chosen vertex.

• All distances are set to the maximum edge weight.

What is the criterion for selecting an edge in Prim's Algorithm?

• The edge must form a cycle.

• The edge must have the highest weight.

• The edge must connect to a vertex already in the tree.

• The edge must have the lowest weight among those connecting to the tree.

Which of the following is NOT a step in Prim's Algorithm?

• Select an arbitrary starting vertex.

• Update the distance table based on edge weights.

• Ensure no cycles are formed in the spanning tree.

• Choose the highest weighted edge at each step.

What happens if two edges have the same weight in Prim's Algorithm?

• The edge with the higher vertex number is chosen.

• The algorithm fails to proceed.

• Both edges are added to the spanning tree.

• Either edge can be chosen without affecting the result.

What is the role of the distance table in Prim's Algorithm?

• It stores the cumulative distance from the source.

• It tracks the shortest path from the source to each vertex.

• It records the weight of the edge connecting to each vertex.

• It lists all possible paths in the graph.

In the execution of Prim's Algorithm, what is the significance of the vertex not being part of the spanning tree?

• It prevents the formation of cycles.

• It ensures the graph remains connected.

• It allows for multiple spanning trees.

• It increases the total cost.