27.2. Dijkstra’s Algorithm for Single Source Shortest Path Problem

Try these first

1. 1.

   What does Dijkstra's algorithm calculate?

   Hint

   Think about path lengths in a graph.

2. 2.

   What is the initial distance set for the source vertex?

   Hint

   It's the starting point for distance calculations.

3. 3.

   What is the time complexity of Dijkstra's algorithm using an adjacency list?

   • O(n^2)
   • O(n + m log n)
   • O(log n)

   Hint

   Think about how many operations are involved in finding the minimum.

4. 4.

   True or False: Dijkstra's algorithm works for graphs with negative edge weights.

   • True
   • False

   Hint

   Consider the implications of negative costs on path calculations.

5. 5.

   Consider the following graph represented as an adjacency matrix. Calculate the shortest path from vertex A to all other vertices. Ensure to handle the vertices in a range of distances correctly.

   Hint

   Apply the algorithm step-by-step and confirm the distances.

6. 6.

   If you found a negative cycle in a graph, how would it impact your approach? Can Dijkstra's algorithm be adjusted to handle it?

   Hint

   Think about the principles behind Dijkstra's greedy strategy.