Solution

The correct answer is Option 4.

Key Points

• Prim's Algorithm:
  • Prim's Algorithm is used to find the Minimum Spanning Tree (MST) for a weighted undirected graph.
  • It starts from an arbitrary node and explores all the adjacent nodes using BFS to find the edge with the smallest weight that connects the tree to a new vertex.
  • It continues this process until all vertices are included in the MST.
• Dijkstra's Algorithm:
  • Dijkstra's Algorithm is used for finding the shortest paths between nodes in a graph.
  • It starts from the source node and uses BFS to explore all possible paths to other nodes, selecting the path with the smallest cumulative weight.
  • It is particularly useful for graphs with non-negative weights.

Additional Information

• Both Prim's and Dijkstra's algorithms rely on the BFS approach to explore nodes level by level, ensuring that the shortest path or smallest weight edge is chosen at each step.
• Prim's Algorithm is specifically used for creating MSTs, whereas Dijkstra's is for shortest path problems.
• While BFS is a fundamental concept, both algorithms incorporate additional logic, such as priority queues, to optimize their respective goals.