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Prim's Algorithm: Visualizing Minimum Spanning Tree Construction

Prim's Algorithm: Visualizing Minimum Spanning Tree Construction
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2018-10-02 04:46
SequenceOptimizationGeometric ConstructionSlider AnimationGraphing
In collections Matrices & MST Algorithms
This example demonstrates how Prim's algorithm progressively constructs a minimum spanning tree in a weighted connected undirected graph. The core mathematical concepts include Minimum Spanning Tree (MST) and greedy algorithm, involving graph theory and combinatorial optimization. Construction details: Using ConstructionStep command to record each construction step, Segment command to draw edges, and MinimumSpanningTree command to compute the minimum spanning tree, intuitively showing the greedy selection process expanding from the starting node to cover all nodes. Suitable for computer science students studying graph theory, high school mathematics extensions, or informatics competition training.

GeoGebra Commands & Parameters

  1. ConstructionStep() → stap
  2. Segment(A, F) → f
  3. Segment(A, B) → g
  4. Segment(A, E) → h
  5. Segment(B, C) → i
  6. Segment(B, E) → j
  7. Segment(E, C) → k
  8. Segment(C, D) → l
  9. Segment(F, B) → m
  10. Segment(C, G) → n
  11. Segment(A, G) → p
  12. Segment(G, D) → q
  13. Segment(E, G) → r
  14. MinimumSpanningTree({A, B, C, D, E, F, G}) → grafiek1
  15. Segment(B, E) → s

AI Drawing Prompt Reference

Create a weighted undirected graph demonstrating Prim's algorithm for constructing a minimum spanning tree, featuring 7 interconnected nodes. Display all possible connecting edges with their weights, and highlight the edges progressively selected by the minimum spanning tree algorithm. Show how the greedy approach expands from the starting node to cover all nodes, using distinct colors to distinguish between the original graph edges and the MST edges being constructed for educational purposes in graph theory and combinatorial optimization.
The prompt above was compiled from the original drawing commands and is for reference only.