Practice Correctness Of Dijkstra Algorithm (27.2.1) - Mathematical Institute

Practice: Correctness of Dijkstra Algorithm

Lesson 27.2.1Mathematical Institute

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9 questions

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6 sample questions

Question 1.
What is the primary purpose of Dijkstra's algorithm?
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Think about pathfinding in graphs.
Question 2.
Define an invariant in the context of algorithms.
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What stays fixed in an algorithm during its run?
3Question 3.
What is the time complexity of Dijkstra's algorithm when using an adjacency matrix?
- O(n)
- O(n^2)
- O(n log n)
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Consider how many comparisons are needed with a matrix representation.
4Question 4.
True or False: Dijkstra's algorithm can handle graphs with negative edge weights.
- True
- False
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Think about how negative weights impact distance calculations.
Question 5.
If the graph contains both positive and negative edge weights but no negative cycles, describe how you might adapt Dijkstra's Algorithm to work correctly.
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What alternative has been specifically designed for such cases?
Question 6.
Given a graph structure with specific distances, compute the shortest path using Dijkstra's Algorithm. Provide a step-by-step explanation.
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What systematic approach can you follow?

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