Prim's Algorithm
Prim grows one minimum spanning tree outward from a chosen start vertex, repeatedly adding the cheapest edge that connects the current tree to a new vertex.
Start with this mental model
Prim grows one minimum spanning tree outward from a chosen start vertex, repeatedly adding the cheapest edge that connects the current tree to a new vertex.
How it works, without unnecessary jargon
Maintain cheapest frontier edges with a min-priority queue.
Unlike Kruskal, Prim grows a single connected tree throughout the process.
Read the algorithm as a sequence of decisions
Define directed/undirected and weighted/unweighted assumptions.
Choose the graph representation.
Track algorithm state and handle disconnected/cyclic cases explicitly.
Read a tiny input by hand and write down the state after every important operation. For Prim's Algorithm, the goal is to make the invariant visible rather than to memorize code.
O(E log V)
Do not quote this complexity mechanically. Ask which operation or input dimension it describes, then derive the cost from the loops, recursion depth, data-structure operations and any preprocessing assumptions.
Good fit
- Use the algorithm only when its graph assumptions match the problem.
What usually goes wrong
- Forgetting disconnected components.
- Mixing weighted and unweighted shortest-path algorithms.
- Not protecting against revisits/cycles.
A professional answer shape
Compare Prim and Kruskal conceptually rather than claiming one is always faster; performance depends on graph density and representation.
What problem does Prim's Algorithm solve?
Prim grows one minimum spanning tree outward from a chosen start vertex, repeatedly adding the cheapest edge that connects the current tree to a new vertex.
What should I mention about complexity?
Its typical cost here is O(E log V), but a complete answer should connect that cost to the representation, input constraints and the dominant operations.
What is the most common mistake?
Forgetting disconnected components.