Question
Does Dijkstra's algorithm work for graphs with both
negative and positive edge weights?Solution
Dijkstra's algorithm is a well-known algorithm for finding the shortest paths from a single source vertex to all other vertices in a graph. However, it assumes that all edge weights are non-negative. This is because Dijkstra's algorithm relies on the fact that once a vertex's shortest path is determined, it will not change. If there were negative weights, a shorter path might be found later, invalidating the correctness of the algorithm. For example, if a graph has a negative weight edge, Dijkstra's algorithm might incorrectly calculate the shortest path by not considering a path that includes the negative edge. This limitation is why Dijkstra’s algorithm is not suitable for graphs with negative edge weights. Instead, algorithms like Bellman-Ford are used for graphs where negative weights are present, as they can correctly handle such situations.
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