Graphs and Network Algorithms · Minimum Spanning Trees

Kruskal's Algorithm

Kruskal's algorithm builds a minimum spanning tree by taking edges in increasing weight order while avoiding cycles.

Student Focus

Students see how a greedy choice and a data structure work together.

Guided Lesson Notes

How Code Scholars teaches Kruskal's Algorithm

This guide helps students understand the idea, implement it carefully, explain the runtime, and recognize when the pattern belongs in a larger problem.

In a session, students usually start with a small trace, then write or review code, then test edge cases. The final step is a short explanation: what the structure or algorithm stores, why it is correct, and what changes when the input grows.

Key Ideas

  • Sorted edges
  • Cycle avoidance
  • Union-find support

Practice Prompts

  • Trace Kruskal on a weighted graph.
  • Explain why cycle checks are required after sorting edges.

Tutoring Connection

Turn the topic into usable problem-solving skill

Students can use this page before a lesson, after a difficult homework assignment, or while preparing for AP Computer Science A extensions, Advanced Topics in CS, USACO growth, or a college data structures course.