2.2 - Spanning Trees
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Practice Questions
Test your understanding with targeted questions
What is a spanning tree?
💡 Hint: Think about what it means to connect all points without returning to the same point.
How many edges does a spanning tree with n vertices have?
💡 Hint: Relate it to the number of vertices.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the definition of a spanning tree?
💡 Hint: Consider the properties of trees in graph theory.
True or False: A minimum spanning tree for a graph can have cycles.
💡 Hint: Think about the definition of a tree.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Given a complete graph with 5 nodes and the following edge weights: (A-B: 2, A-C: 3, A-D: 1, A-E: 4, B-C: 5, B-D: 3, B-E: 2, C-D: 4, C-E: 1, D-E: 6), find the minimum spanning tree and compute its total weight.
💡 Hint: Look for the smallest edges that keep the tree connected.
Design a road restoration plan for a small town affected by a natural disaster. You have the costs of repairing each road between towns. Describe how you would apply Prim's or Kruskal's algorithm.
💡 Hint: Outline the costs and visualize the connections before applying the algorithm.
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