2. The prices for traveling between five cities in Manila by bus are given in the table. Represent the travel costs between cities using a weighted graph. Use the greedy algorithm to find a low-cost route that starts and ends in Baclaran and visits each city. Trace the route. What is the cost for taking this route?
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First, represent each problem by drawing a weighted graph. Label the vertices and indicate the weight of each edge. Then solve the problem.
Recall: Greedy
1. Choose a vertex to start at, then travel along the connected edge that has the smallest weight. (If two or more edges have the same weight, pick anyone.)
2. After arriving at the next vertex, travel along the edge of the smallest weight that connects to a vertex not yet visited. Continue this process until you have visited all vertices.
3. Return to the starting vertex.
QUESTION
2. The prices for traveling between five cities in Manila by bus are given in the table.
Represent the travel costs between cities using a weighted graph.
Use the greedy algorithm to find a low-cost route that starts and ends in Baclaran and visits each city. Trace the route. What is the cost for taking this route?
| Baclaran | Quiapo | Caloocan | Quezon City | Cubao | |
| Baclaran | 0 | 16 | 25 | 49 | 74 |
| Quiapo | 16 | 0 | 20 | 50 | 72 |
| Caloocan | 25 | 20 | 0 | 35 | 59 |
| Quezon City | 49 | 50 | 35 | 0 | 40 |
| Cubao | 74 | 72 | 59 | 40 | 0 |
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