Algorithm Design Questions
Kruskal's algorithm is a greedy algorithm used to find a minimum spanning tree in a connected, weighted graph. The algorithm works as follows:
1. Sort all the edges of the graph in non-decreasing order of their weights.
2. Create an empty set to store the minimum spanning tree.
3. Iterate through the sorted edges and add them to the minimum spanning tree set if they do not create a cycle.
- To check for cycles, use a disjoint set data structure (e.g., union-find) to keep track of the connected components.
- If adding an edge creates a cycle, skip it and move on to the next edge.
4. Continue this process until all vertices are included in the minimum spanning tree set or until there are no more edges left.
5. The resulting set of edges forms the minimum spanning tree of the graph.
Kruskal's algorithm guarantees that the minimum spanning tree obtained will have the minimum total weight among all possible spanning trees of the graph.