Prim’s Algorithm: One Step at a Time

Shreyas Naphad
Jul 2
2 min read

Imagine you're building roads to connect a group of villages. You want to make sure every village is connected without spending more money than needed.

That’s exactly what Prim’s Algorithm helps you do.

It finds a Minimum Spanning Tree (MST) — a way to connect all points in a graph using the smallest possible total cost, without forming any loops.

🧠 What's the Idea Behind It?

Start small and grow the network step by step, always picking the cheapest option available to expand.

🔧 How Prim’s Algorithm Works

Pick any starting node (village).
Look at all the edges (roads) coming out of your current network.
Choose the edge with the lowest weight that connects to a new node.
Add that node and edge to your growing network..
Repeat until all nodes are connected.

Think of it as building a tree. One branch at a time. Always choosing the cheapest new connection.

💡 Simple Analogy

You're decorating a Christmas tree 🎄 with lights. You start from the top and carefully connect each new branch, always using the shortest wire available. You never circle back (no loops), and in the end, the whole tree lights up with the least wire used.

👨‍💻 Where Is It Used?

Network design (Wi-Fi, cable, roads)
Clustering in machine learning
Designing circuits
Building maps or game worlds

🏁 Quick Example

Let’s say you have 4 cities and the roads between them have costs:

A --5-- B

| /

2 1

| /

C --3-- D

Prim’s algorithm would start at, say, A:

A → C (cost 2)
C → D (cost 3)
D → B (cost 1)

Total Cost = 6

That’s your Minimum Spanning Tree!

✨ Conclusion

Prim’s Algorithm is like being smart with your money. Always pick the cheapest new connection, grow gradually, and don’t waste anything on loops.