Practice Mathematical Institute - 27.1.1 | 27. Mathematical Institute | Design & Analysis of Algorithms - Vol 1
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27.1.1 - Mathematical Institute

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What algorithm is used to find the shortest path in a graph with non-negative weights?

💡 Hint: Think about algorithms for graph traversal.

Question 2

Easy

What do you set the source vertex distance to at the beginning of Dijkstra's algorithm?

💡 Hint: It reflects the start point in terms of distance.

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 is the primary function of Dijkstra's Algorithm?

  • Finding the longest path
  • Finding shortest paths
  • Sorting vertices

💡 Hint: Focus on the word 'shortest' in pathfinding.

Question 2

Dijkstra's Algorithm works best with which type of graph?

  • True
  • False

💡 Hint: Consider the assumptions of the algorithm.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given a graph with vertices A, B, C, and D, with edges AB (1), AC (4), BD (3), and CD (2), apply Dijkstra's algorithm starting from A. What is the shortest path to D?

💡 Hint: Remember to track the distances and choose the least costly path at each step.

Question 2

Consider a graph with a negative edge weight. Explain how this could alter the results of Dijkstra's algorithm and suggest an alternative algorithm that can handle such a case.

💡 Hint: Think about what happens when a vertex is burnt and how negative cycles can influence overall costs.

Challenge and get performance evaluation