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Kruskal’s algorithm

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Math for Non-Math Majors

Definition

Kruskal’s algorithm is a method used to find the minimum spanning tree of a connected, undirected graph. It adds edges in increasing order of weight without forming any cycles until all vertices are connected.

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5 Must Know Facts For Your Next Test

  1. Kruskal’s algorithm sorts all edges by weight and processes them in ascending order.
  2. It uses the union-find data structure to detect cycles efficiently.
  3. The algorithm ensures that no cycles are formed while adding edges to the spanning tree.
  4. Kruskal’s algorithm is particularly useful for sparse graphs with fewer edges relative to vertices.
  5. The time complexity of Kruskal's algorithm is O(E log E), where E is the number of edges.

Review Questions

  • What data structure does Kruskal's algorithm use to detect cycles?
  • How does Kruskal’s algorithm ensure it creates a minimum spanning tree?
  • What is the time complexity of Kruskal's algorithm?
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