Consider a scenario where you have a large network of interconnected nodes representing cities in a transportation system. You need to find the shortest paths between all pairs of cities. Discuss the most efficient algorithm to use in this situation and justify your choice.
- Bellman-Ford Algorithm
- Dijkstra's Algorithm
- Floyd-Warshall Algorithm
- Prim's Algorithm
The Floyd-Warshall Algorithm is the most efficient choice in this scenario. It can find the shortest paths between all pairs of cities in a graph, regardless of negative or positive edge weights. Although it has a higher time complexity, it is suitable for cases where the complete shortest path matrix is needed, making it optimal for this large network scenario.
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