## Prim’s and Kruskal’s Algorithms-

Before you go through this article, make sure that you have gone through the previous articles on Prim’s Algorithm & Kruskal’s Algorithm.

We have discussed-

• Prim’s and Kruskal’s Algorithm are the famous greedy algorithms.
• They are used for finding the Minimum Spanning Tree (MST) of a given graph.
• To apply these algorithms, the given graph must be weighted, connected and undirected.

Some important concepts based on them are-

## Concept-01:

If all the edge weights are distinct, then both the algorithms are guaranteed to find the same MST.

### Example-

Consider the following example-

Here, both the algorithms on the above given graph produces the same MST as shown.

## Concept-02:

• If all the edge weights are not distinct, then both the algorithms may not always produce the same MST.
• However, cost of both the MSTs would always be same in both the cases.

### Example-

Consider the following example-

Here, both the algorithms on the above given graph produces different MSTs as shown but the cost is same in both the cases.

## Concept-03:

Kruskal’s Algorithm is preferred when-

• The graph is sparse.
• There are less number of edges in the graph like E = O(V)
• The edges are already sorted or can be sorted in linear time.

Prim’s Algorithm is preferred when-

• The graph is dense.
• There are large number of edges in the graph like E = O(V2).

## Concept-04:

Difference between Prim’s Algorithm and Kruskal’s Algorithm-

 Prim’s Algorithm Kruskal’s Algorithm The tree that we are making or growing always remains connected. The tree that we are making or growing usually remains disconnected. Prim’s Algorithm grows a solution from a random vertex by adding the next cheapest vertex to the existing tree. Kruskal’s Algorithm grows a solution from the cheapest edge by adding the next cheapest edge to the existing tree / forest. Prim’s Algorithm is faster for dense graphs. Kruskal’s Algorithm is faster for sparse graphs.

To gain better understanding about Difference between Prim’s and Kruskal’s Algorithm,

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