Smash the 2025 HSC Standard Math Exam – Dive in and Conquer Your Calculations!

Kruskal's and Prim's algorithms are specifically designed to find a minimum spanning tree (MST) in a weighted, undirected graph.

Kruskal's algorithm works by sorting all the edges in the graph by their weights and then adding the smallest edge to the MST provided it does not form a cycle with the edges already included. This continues until there are enough edges to form a spanning tree connecting all vertices.

Prim's algorithm, on the other hand, starts with a single vertex and grows the MST by continually adding the smallest edge that connects a vertex in the growing tree to a vertex outside the tree. This method ensures that the edge chosen is always the smallest available, maintaining the properties required for a minimum spanning tree as it expands.

Both algorithms successfully construct a minimum spanning tree, albeit using different approaches. The other algorithms listed in the other answer choices serve different purposes or solve different problems; for example, Dijkstra's algorithm finds the shortest path from a source vertex to all other vertices in a graph, and Bellman-Ford is also designed for finding shortest paths but can handle graphs with negative weights. Hence, the focus on Kruskal's and Prim's is what makes the correct choice.