26.1.5.1. Single Source Shortest Path Problem

Try these first

1. 1.

   What is a weighted graph?

   Hint

   Think about what makes them different from unweighted graphs.

2. 2.

   Define the weight function.

   Hint

   What does it help us determine in the graph?

3. 3.

   What does Dijkstra's Algorithm primarily find?

   • Shortest path from a source vertex
   • Longest path from a source vertex
   • All paths in the graph

   Hint

   Recall the main purpose of Dijkstra's Algorithm.

4. 4.

   True or False: Dijkstra's algorithm can be used for graphs with negative edge weights.

   • True
   • False

   Hint

   Consider how the algorithm evaluates edge weights.

5. 5.

   Your city has a new public transit system represented as a weighted graph. Analyze how Dijkstra's algorithm would determine the quickest route for a commuter.

   Hint

   Visualize the graph and calculate edge weights carefully.

6. 6.

   Propose an optimization to Dijkstra's algorithm that could enhance performance in large graphs.

   Hint

   Think about data structures and their impact on time complexity.