26.1.8. Dijkstra's Algorithm

Try these first

1. 1.

   What is a weighted graph?

   Hint

   Think about what each edge in the graph represents.

2. 2.

   What is the purpose of Dijkstra's Algorithm?

   Hint

   Consider what problems it might solve in real life.

3. 3.

   What is the main goal of Dijkstra's Algorithm?

   • To find the longest path
   • To find the shortest path in a weighted graph
   • To visit every vertex

   Hint

   Think about what the 'shortest path' means in terms of weights.

4. 4.

   True or False: Dijkstra’s Algorithm can find the shortest paths in both weighted and unweighted graphs.

   • True
   • False

   Hint

   Consider how edge weights affect path calculations.

5. 5.

   Given a graph with vertices A, B, C, D, and E with specified edge weights, illustrate step-by-step how Dijkstra's Algorithm would find the shortest path from A to all other nodes.

   Hint

   Use the burn analogy to visualize the process.

6. 6.

   Analyze a real-world logistics problem where Dijkstra's Algorithm could be applied. Describe the graph, the vertices, and edge weights, then compute the shortest path from the main warehouse to various retail stores.

   Hint

   Consider practical constraints like delivery times or traffic conditions.