27.1.2. Prof. Madhavan Mukund

Try these first

1. 1.

   What is the main goal of Dijkstra's algorithm?

   Hint

   Think about the term 'shortest path'.

2. 2.

   Define a burnt vertex in the context of Dijkstra's algorithm.

   Hint

   What happens to the distance of burnt vertices?

3. 3.

   What does Dijkstra's algorithm aim to achieve?

   • Find the shortest path from a single source
   • Find the longest path
   • Sort vertices

   Hint

   Focus on the part about the 'shortest path'.

4. 4.

   True or False: Dijkstra's algorithm can handle graphs with negative weights.

   • True
   • False

   Hint

   Recall what we discussed about negative weights.

5. 5.

   Consider a graph with vertices and edges that have both positive and negative weights, describe how Dijkstra's algorithm would handle this, and what issues might arise.

   Hint

   Reflect on the definitions and properties of negative weights.

6. 6.

   Design a modified version of Dijkstra's algorithm to account for negative weights and leverage efficient graph traversing. Explain your solution.

   Hint

   Recall the properties and functionalities of other pathfinding algorithms.