26.1.5.2. All Pairs Shortest Path Problem

Try these first

1. 1.

   Define a weighted graph and provide an example.

   Hint

   Think about graphs with costs like distances or time.

2. 2.

   What is Dijkstra’s algorithm used for?

   Hint

   Recall the scenarios discussed earlier in class.

3. 3.

   What does Dijkstra's algorithm help to compute?

   • Shortest path from one vertex to another
   • Shortest paths between all vertices
   • Total costs of all edges

   Hint

   Focus on what the algorithm's intended function is.

4. 4.

   True or False: In a weighted graph, the path with the fewest edges is always the shortest.

   • True
   • False

   Hint

   Recall examples discussed about how weights affect path selection.

5. 5.

   You are tasked with optimizing delivery routes for a city with various weights for road segments. How would you approach this problem using Dijkstra's algorithm?

   Hint

   Consider how weights affect the decisions made during each step of the algorithm.

6. 6.

   In a network of airports represented as a graph, each edge weight represents flight duration. How would you determine the fastest way to connect all airports using the All Pairs Shortest Path approach?

   Hint

   Think about how you would handle cycles and costs in the graph structure.