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.
이 멘탈 모델부터 시작하세요
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.
불필요한 전문용어 없이 동작 방식 이해하기
Maintain cheapest frontier edges with a min-priority queue.
Unlike Kruskal, Prim grows a single connected tree throughout the process.
알고리즘을 연속된 의사결정으로 읽기
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Do not quote this complexity mechanically.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.
적합한 경우
- Use the algorithm only when its graph assumptions match the problem.
보통 어디에서 문제가 생기는가
- Forgetting disconnected components.
- Mixing weighted and unweighted shortest-path algorithms.
- Not protecting against revisits/cycles.
전문적인 답변 구조
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.
복잡도에 대해 무엇을 언급해야 하나요?
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.
가장 흔한 실수는 무엇인가요?
Forgetting disconnected components.