Prim's Minimum Spanning Tree
Build MST by growing a single tree from any starting vertex using greedy edge selection
Algorithm Simulator
Interactive Graph Builder
Current Mode: NODE
Click to add nodes • Drag nodes to move them
Click to add nodes • Drag nodes to move them
Graph Summary:
Nodes: None
Edges: None
MST Visualization
Click "Find MST" to see visualization
Understanding Prim's Algorithm
Key Characteristics
- •Vertex-based approach to MST construction
- •Greedy choice: minimum weight edge crossing cut
- •Maintains a single tree throughout execution
- •Works with both dense and sparse graphs
- •Can start from any vertex
Applications
- •Network design and routing
- •Circuit design optimization
- •Cluster analysis in data mining
- •Transportation network planning
- •Approximation algorithms for TSP
Exam Tips
Understand the cut property of MSTs
Practice tracing algorithm execution step by step
Know time complexity with different data structures
Compare with Kruskal's algorithm
Learn to prove correctness using cut property
University Exam Preparation
Question Types
- •Trace Prim's algorithm execution on given graph
- •Prove correctness using cut property
- •Analyze time complexity with different implementations
- •Compare Prim's vs Kruskal's algorithm
- •Design MST algorithms for specific constraints
Practice Problems
- •Find MST of weighted graph using Prim's
- •Implement Prim's with priority queue
- •Modify algorithm for maximum spanning tree
- •MST in graphs with negative weights
- •Applications in network design problems
Exam Pattern
Prim's algorithm is frequently asked in university exams (10-15 marks), focusing on algorithm tracing, complexity analysis, and comparison with Kruskal's.