26.1.6. Algorithm Analogy

Try these first

1. 1.

   What is a weighted graph?

   Hint

   Think about graphs with costs like distances.

2. 2.

   Name one application of weighted graphs.

   Hint

   Think about systems where some paths may cost more than others.

3. 3.

   What characterizes a weighted graph?

   • Each vertex has a cost
   • Each edge has an associated cost
   • The graph is circular

   Hint

   Focus on what the edges imply in terms of graph representation.

4. 4.

   True or False: Dijkstra's algorithm can be used effectively on unweighted graphs.

   • True
   • False

   Hint

   Think about how edge weights affect the algorithm.

5. 5.

   Given a weighted graph with vertices representing cities and edges as roads with costs, outline how you would employ Dijkstra’s algorithm to find the least expensive route from City A to City C.

   Hint

   Visualize the graph and track costs methodically.

6. 6.

   Create a unique scenario with a weighted graph where Dijkstra’s algorithm may produce different outcomes when edge weights are modified.

   Hint

   Think about real-life implications, like changing speed limits affecting travel time.