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Kruskal's Algorithm

Kruskal's Algorithm
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2020-11-15 03:45
FunctionOptimizationGeometric Construction
This example demonstrates how Kruskal's algorithm constructs a minimum spanning tree. Key mathematical concepts include minimum spanning trees in graph theory. Using GeoGebra commands such as Length, Segment, Shuffle, etc., users can visually understand the algorithm's steps. Suitable for high school and above students learning graph theory and algorithms.

GeoGebra Commands & Parameters

  1. Length(Unique[Flatten[vertsofedge]]) → numberOfNodes
  2. Length(vertsofedge) → numberOfEdges
  3. Segment(A, B) → e1
  4. Segment(B, C) → e2
  5. Segment(D, A) → e3
  6. Shuffle(WtsOrdered) → Wts, {4, 12, 16, 7, 3, 14, 19, 18, 17, 13, 2, 8, 11, 5, 15, 9, 10, 6, 1}
  7. KeepIf(componentOfNode(vertsofedge(j, 1)) ≠ componentOfNode(vertsofedge(j, 2)), j, 1…numberOfEdges) → CandidateEdges
  8. Min(Zip[Wts(j), j, CandidateEdges]) → nextminweight
  9. Segment(A, F) → e4
  10. Segment(B, F) → e5
  11. Segment(B, G) → e6
  12. Segment(C, G) → e7
  13. Segment(C, H) → e8
  14. Segment(D, F) → e9
  15. Segment(F, G) → e10
  16. Segment(G, H) → e11
  17. Segment(D, I) → e12
  18. Segment(I, F) → e13
  19. Segment(F, J) → e14
  20. Segment(J, G) → e15
  21. Segment(G, K) → e16
  22. Segment(K, H) → e17
  23. Segment(I, J) → e18
  24. Segment(J, K) → e19
  25. If(E ≟ {}, {}, Unique[Flatten[Zip[vertsofedge(j), j, E]]]) → V

AI Drawing Prompt Reference

Visualize Kruskal's algorithm constructing a minimum spanning tree with multiple nodes and edges, using different colors or thicknesses to represent edge weights, progressively adding edges until forming an acyclic graph covering all nodes, highlighting the features of the minimum spanning tree for students learning graph theory and algorithms.
The prompt above was compiled from the original drawing commands and is for reference only.