What is the runtime of Prim's algorithm?
Understand the Problem
The question is asking about the runtime complexity of Prim's algorithm, which is used for finding the minimum spanning tree of a weighted undirected graph. The high-level approach to answering this involves discussing its various implementations and their respective time complexities.
Answer
O(E log V)
The runtime of Prim's algorithm is O(V log V + E log V), which simplifies to O(E log V) where V is the number of vertices and E is the number of edges.
Answer for screen readers
The runtime of Prim's algorithm is O(V log V + E log V), which simplifies to O(E log V) where V is the number of vertices and E is the number of edges.
More Information
Prim's algorithm is efficient for dense graphs when implemented with a Fibonacci heap, achieving a time complexity of O(E + V log V).
Tips
A common mistake is confusing the time complexity with that of other algorithms like Kruskal's. Ensure to distinguish the data structures used in the implementation as they significantly impact the runtime.
Sources
- Prim's Algorithm - en.wikipedia.org
- Time Complexity of Prims Algorithm? - Stack Overflow - stackoverflow.com
- Prim's Algorithm for Minimum Spanning Tree (MST) - GeeksforGeeks - geeksforgeeks.org
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