Practice Negative Cycles - 27.2.4 | 27. Mathematical Institute | Design & Analysis of Algorithms - Vol 1
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27.2.4 - Negative Cycles

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the primary purpose of Dijkstra's algorithm?

💡 Hint: Think of how a navigator finds the quickest route.

Question 2

Easy

What do we call the local choices made in greedy algorithms?

💡 Hint: Consider what happens when you always pick the smallest option.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What does Dijkstra's algorithm primarily find?

  • Shortest paths from multiple sources
  • Shortest paths from one source
  • All paths in a graph

💡 Hint: Recall which vertex serves as the starting point.

Question 2

True or False: Negative cycles can exist without negative edges.

  • True
  • False

💡 Hint: Think about the costs involved in each cycle.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

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.

Question 2

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.

Challenge and get performance evaluation