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.
ابدأ بهذا النموذج الذهني
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.
كيف يعمل، بلا مصطلحات زائدة
Maintain cheapest frontier edges with a min-priority queue.
Unlike Kruskal, Prim grows a single connected tree throughout the process.
اقرأ الخوارزمية كسلسلة من القرارات
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Do not quote this complexity mechanically.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.
مناسب لـ
- Use the algorithm only when its graph assumptions match the problem.
ما الذي يسوء عادةً
- Forgetting disconnected components.
- Mixing weighted and unweighted shortest-path algorithms.
- Not protecting against revisits/cycles.
صيغة إجابة احترافية
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.
ماذا يجب أن أذكر عن التعقيد؟
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.
ما الخطأ الأكثر شيوعاً؟
Forgetting disconnected components.