Greedy Algorithms Questions Medium
Prim's algorithm is a greedy algorithm used to find the minimum spanning tree (MST) of a connected weighted graph. The algorithm starts by selecting an arbitrary vertex as the starting point and gradually expands the MST by adding the minimum weight edge that connects the current MST to a vertex not yet included in the MST. This process continues until all vertices are included in the MST.
Here is a step-by-step explanation of how Prim's algorithm works:
1. Initialize an empty MST and a set of visited vertices.
2. Choose an arbitrary vertex as the starting point and add it to the MST.
3. Mark the chosen vertex as visited.
4. Repeat the following steps until all vertices are visited:
a. For each visited vertex, find the minimum weight edge that connects it to an unvisited vertex.
b. Select the edge with the minimum weight and add it to the MST.
c. Mark the unvisited vertex connected by the selected edge as visited.
5. Once all vertices are visited, the MST is complete.
The algorithm continues to select the minimum weight edges until all vertices are included in the MST, ensuring that the resulting tree has the minimum total weight among all possible spanning trees. The key idea behind Prim's algorithm is to always select the edge with the minimum weight that connects the current MST to an unvisited vertex, ensuring that the MST grows in a way that minimizes the total weight.