26.1.3. Cost of Edges in Graphs

Try these first

1. 1.

   Define a weighted graph.

   Hint

   Think about if there's a cost to travel along the edges.

2. 2.

   What is the purpose of Dijkstra's algorithm?

   Hint

   Recall which algorithm is best for non-negative weights.

3. 3.

   What is a weighted graph?

   • A graph with equal edges
   • A graph with edges having costs
   • A graph without edges

   Hint

   Think about costs associated with travel.

4. 4.

   Does Dijkstra’s algorithm work with negative weights?

   • True
   • False

   Hint

   Remember what we've discussed about algorithms.

5. 5.

   Imagine you are the logistics manager of a company. You need to create a cost-effective route to deliver items to five locations using Dijkstra’s algorithm. Draw the graph and calculate the shortest path.

   Hint

   Start at one of the locations and continually update the cost to reach other locations.

6. 6.

   Given a weighted graph with negative edge weights, demonstrate how the Bellman-Ford algorithm functions and computes shortest paths. Include a visual representation.

   Hint

   Remember, this algorithm involves systematically relaxing edges multiple times.