Practice Exploration of Graphs - 26.1.2 | 26. Shortest Paths in Weighted Graphs | Design & Analysis of Algorithms - Vol 1
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26.1.2 - Exploration of Graphs

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is a weighted graph?

💡 Hint: Think about how costs could represent real-world scenarios like distance or price.

Question 2

Easy

Can you explain what Dijkstra's algorithm does?

💡 Hint: Consider how you’d navigate from one point to many others while minimizing cost.

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 a weighted graph have that an unweighted graph doesn't?

  • No edges
  • Associated costs with edges
  • More vertices

💡 Hint: Think about how costs represent additional information.

Question 2

True or False: Dijkstra's algorithm can be used for graphs with negative edge weights.

  • True
  • False

💡 Hint: Recall the properties required for Dijkstra's to work effectively.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Create a weighted graph based on a map of your city. Label the edge weights based on travel time. After that, calculate the shortest path using Dijkstra's algorithm and provide your results.

💡 Hint: Pay close attention to the edge weights during calculations to ensure accuracy.

Question 2

Given a matrix representation of a weighted graph with several vertices, identify negative cycles and discuss the suitability of Dijkstra’s algorithm for this scenario.

💡 Hint: Review properties of negative cycles and their implications on graphs.

Challenge and get performance evaluation