- #1
Prove It said:
Prim's algorithm is a greedy algorithm used to find the minimum spanning tree of a weighted undirected graph. This means it finds the subset of edges that connects all vertices in a graph with the minimum total weight.
Prim's algorithm starts with a random vertex and then grows the minimum spanning tree by adding the edge with the smallest weight that connects the tree to a new vertex. This process is repeated until all vertices are connected and a minimum spanning tree is formed.
The time complexity of Prim's algorithm is O(V^2), where V is the number of vertices in the graph. This can be improved to O(ElogV) using a priority queue data structure.
Both Prim's and Kruskal's algorithm are used to find the minimum spanning tree of a graph. The main difference is that Prim's algorithm grows the tree from a starting vertex, while Kruskal's algorithm sorts all the edges and adds them to the tree in order of increasing weight.
Prim's algorithm should be used when the graph is dense (has a large number of edges) and when a starting vertex is known. It is also useful when there are multiple disconnected components in the graph, as it can find the minimum spanning tree for each component separately.
