27.2.4 - Negative Cycles
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Practice Questions
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What is the primary purpose of Dijkstra's algorithm?
💡 Hint: Think of how a navigator finds the quickest route.
What do we call the local choices made in greedy algorithms?
💡 Hint: Consider what happens when you always pick the smallest option.
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Interactive Quizzes
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What does Dijkstra's algorithm primarily find?
💡 Hint: Recall which vertex serves as the starting point.
True or False: Negative cycles can exist without negative edges.
💡 Hint: Think about the costs involved in each cycle.
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Challenge Problems
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Create a directed graph with 5 vertices and establish both positive and negative weights. Identify if the graph contains a negative cycle, and apply Dijkstra’s algorithm to see how it handles paths.
💡 Hint: Trace paths and calculate costs to either reveal a negative cycle or establish valid shortest paths.
Design an example illustrating how Dijkstra's algorithm efficiently manages a scenario without negative weights and compare the result when negative weights are added.
💡 Hint: Keep track of which edges optimize paths best.
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