26.2.4. Applications of Graphs

Try these first

1. 1.

   What is the purpose of Dijkstra's algorithm?

   Hint

   Think about how you would navigate directions.

2. 2.

   Describe what a Minimum Spanning Tree (MST) is.

   Hint

   Visualize connecting points with minimal wiring.

3. 3.

   What is the primary function of Dijkstra’s algorithm?

   • To find the maximum flow in networks
   • To find the shortest path in graphs
   • To detect cycles in graphs

   Hint

   Recall its application in navigation systems.

4. 4.

   True or False: The Bellman-Ford algorithm can deal with negative weights.

   • True
   • False

   Hint

   Think about possible real world scenarios where costs can decrease.

5. 5.

   You are given a weighted graph representing a network. Implement Dijkstra's algorithm and calculate the shortest path from vertex A to all other vertices.

   Hint

   Use a map or table to visualize distances during the process.

6. 6.

   In a directed graph, identify if there are any cycles using DFS or another method. Explain your approach.

   Hint

   Keep track of your traversal path to detect loops effectively.