3.3 - Proof of Correctness of Prim's Algorithm
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Practice Questions
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What is the primary goal of Prim's Algorithm?
💡 Hint: Think about trees and connection.
What does a weighted graph represent?
💡 Hint: What can weights signify in terms of paths?
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is Prim's Algorithm primarily used for?
💡 Hint: Think about spanning and trees.
True or False: The smallest edge in a connected graph needs to be included in every minimum spanning tree.
💡 Hint: Remember what the lemma states.
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Challenge Problems
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Prove that Prim's Algorithm will not produce the correct spanning tree if the minimum separator lemma is violated (two edges of the same weight are possible).
💡 Hint: Think about edge choices and re-evaluating based on weights.
Design a graph with at least four vertices and different weights, and execute the Prim's Algorithm step-by-step to find a minimum spanning tree, detailing every decision point.
💡 Hint: Visual aids can assist in tracking your path and choices.
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