Which of the following algorithms are based on the Breadth First Search (BFS)?

A. Prim's algorithms

B. Kruskal algorithms

C. Dijkstra algorithms

D. Greedy algorithms

E. Dynamic Programming

Choose the correct answer from the options given below:

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.