27.1.6. Lecture - 26

Try these first

1. 1.

   What does Dijkstra's algorithm aim to find?

   Hint

   Think about what the goal of defining paths is.

2. 2.

   What do we set the source vertex's distance to initially?

   Hint

   It represents the starting point.

3. 3.

   What is the primary function of Dijkstra's algorithm?

   • To find the longest path
   • To find the shortest path from a single source vertex
   • To find all paths between two vertices

   Hint

   Consider what the algorithm is frequently used for in applications.

4. 4.

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

   • True
   • False

   Hint

   Think about the assumptions the algorithm relies on regarding path costs.

5. 5.

   Given a weighted graph with both positive and negative edges, determine the shortest path from vertex A to vertex B using Dijkstra's algorithm. What challenges do you face?

   Hint

   Evaluate how negative weights affect the decisions in Dijkstra's.

6. 6.

   Create an efficient implementation of Dijkstra's algorithm using a priority queue. Discuss the time complexity of your implementation.

   Hint

   Think about the impact of using a different data structure.