Greedy Algorithms Questions Medium
Kruskal's algorithm is a greedy algorithm used to find a minimum spanning tree in a weighted connected graph. It works by considering the edges of the graph in ascending order of their weights and adding them to the spanning tree if they do not create a cycle.
Here is a step-by-step explanation of how Kruskal's algorithm works:
1. Sort all the edges of the graph in non-decreasing order of their weights.
2. Initialize an empty set called the "spanning tree" to store the final minimum spanning tree.
3. Iterate through each edge in the sorted order:
a. Check if adding the current edge to the spanning tree creates a cycle. This can be done by checking if the two vertices of the edge already belong to the same connected component in the spanning tree. If adding the edge creates a cycle, skip it and move on to the next edge.
b. If adding the current edge does not create a cycle, add it to the spanning tree.
4. Repeat step 3 until all the edges have been considered or the spanning tree contains (V-1) edges, where V is the number of vertices in the graph.
5. The resulting spanning tree is the minimum spanning tree of the original graph.
Kruskal's algorithm works on the principle of adding edges with the smallest weight first, ensuring that the resulting spanning tree has the minimum total weight. By avoiding cycles, it guarantees that the spanning tree is acyclic and connects all the vertices of the graph.