When deciding between Bellman-Ford and Dijkstra's Algorithm, think about these points:
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Negative Weights:
- Bellman-Ford can work with edges that have negative weights. This means if one path has a weight of -5, it can still find the shortest path correctly.
- On the other hand, Dijkstra's Algorithm does not handle negative weights, so it might give wrong results in such cases.
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Speed:
- Dijkstra's is usually quicker. It has a speed of O(E+VlogV), which makes it great for bigger graphs with lots of connections.
- Bellman-Ford works at O(VE), which is slower, especially for larger graphs.
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When to Use Each:
- Choose Bellman-Ford if you’re dealing with situations like currency exchange, where there might be cycles with negative weights.
- Use Dijkstra's for most other cases where edges have only positive weights and you need to find the shortest path.
In short, pick the algorithm based on what kind of graph you have and your specific needs!