Name two algorithms to find a Minimum Spanning Tree.

• A. Dijkstra's and Bellman-Ford
• B. Kruskal's and Prim's algorithms
• C. BFS and DFS
• D. Kruskal's algorithm only

Answer: (B)

Finding a Minimum Spanning Tree means connecting every vertex with the least possible total edge weight without creating any cycles. Two well-established ways to construct such a tree are Prim's algorithm and Kruskal's algorithm.

Prim's algorithm starts from any vertex and grows a single connected tree. At each step it adds the lightest edge that connects the current tree to a new vertex, continually expanding until all vertices are included. This approach builds a spanning tree by always extending the existing structure with the cheapest possible link to an unused vertex.

Kruskal's algorithm takes a different route: it looks at all edges in order of increasing weight and adds an edge only if it connects two previously disconnected components, avoiding cycles (typically using a union-find structure). It continues until enough edges are added to span all vertices.

The other options don’t fit because Dijkstra's and Bellman-Ford determine shortest paths, not spanning trees. BFS and DFS are graph traversals that ignore edge weights. Also, Kruskal's alone isn’t enough to satisfy “two algorithms,” since Prim's complements it to provide two valid methods.