Minimum Spanning Tree Algorithm Demo

Minimum Spanning Tree Algorithm Demo
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2018-10-02 04:50
In collections Matrices & MST Algorithms
This example demonstrates how to construct a minimum spanning tree in a weighted graph. The minimum spanning tree is a classic optimization problem in graph theory, aiming to find a tree that connects all vertices with the minimum total edge weight. Construction highlights: Using Segment command to draw line segments connecting vertices A through F and other objects, applying MinimumSpanningTree command to automatically calculate and highlight the spanning tree with minimum total weight. The diagram shows the selection process for different edge weights (marked as f, g, h, etc.), intuitively presenting the core ideas of Kruskal or Prim algorithms. Suitable for high school mathematics extension, algorithm competition introduction, and university discrete mathematics graph theory chapters, helping students understand optimization concepts in discrete mathematics.

GeoGebra Commands & Parameters

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

AI Drawing Prompt Reference

Draw a schematic diagram of a weighted graph with points A, B, C, D, E, F, and G connected by line segments. The line segments represent different weights, and the goal is to find a minimum spanning tree that connects all points with the smallest total weight. Show how to select appropriate line segments to construct this tree, illustrating optimization concepts.
The prompt above was compiled from the original drawing commands and is for reference only.