27.2.2. Complexity Analysis

Try these first

1. 1.

   What is the first step in Dijkstra's algorithm?

   Hint

   Think about how we initialize the distances.

2. 2.

   What data structure is inefficient for Dijkstra's algorithm?

   Hint

   Consider how we store graph data and access the vertices.

3. 3.

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

   • O(n)
   • O(n log n)
   • O(n^2)

   Hint

   Think about the loops involved in finding the minimum distance.

4. 4.

   True or False: Dijkstra's algorithm can correctly determine shortest paths in a graph with negative weight edges.

   • True
   • False

   Hint

   Recall the assumptions made by Dijkstra's algorithm.

5. 5.

   Given a graph with the following weights, perform Dijkstra's algorithm from vertex A. Show all steps and final shortest paths.

   Hint

   Keep track of distances from A, marking each burnt vertex.

6. 6.

   Explain how Dijkstra's algorithm would perform on a complete graph with negative edge weights, detailing any deviations from the expected outcome.

   Hint

   Consider the implications of a negative cycle.