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Does Dijkstra's algorithm work for negative weights in graphs?
No, Dijkstra's algorithm does not work for graphs with negative weights.
Does Dijkstra's algorithm work with negative weights in graphs?
No, Dijkstra's algorithm does not work with negative weights in graphs because it assumes that all edge weights are non-negative.
Why does Dijkstra's algorithm fail for negative weights in graphs?
Dijkstra's algorithm fails for negative weights in graphs because it assumes that the shortest path is always the one with the smallest total weight. When negative weights are present, this assumption may not hold true, leading to incorrect results.
How does the Bellman-Ford algorithm work to find the shortest path in a graph?
The Bellman-Ford algorithm works by repeatedly relaxing the edges of the graph, updating the shortest path estimates until the optimal shortest path is found. It can handle graphs with negative edge weights, unlike Dijkstra's algorithm.
What are the key differences between the Floyd-Warshall and Bellman-Ford algorithms for finding the shortest paths in a graph?
The key differences between the Floyd-Warshall and Bellman-Ford algorithms are in their approach and efficiency. The Floyd-Warshall algorithm is a dynamic programming algorithm that finds the shortest paths between all pairs of vertices in a graph. It is more efficient for dense graphs with many edges. The Bellman-Ford algorithm is a single-source shortest path algorithm that finds the shortest path from a single source vertex to all other vertices in a graph. It is more suitable for graphs with negative edge weights. In summary, Floyd-Warshall is better for finding shortest paths between all pairs of vertices in dense graphs, while Bellman-Ford is more suitable for graphs with negative edge weights and finding shortest paths from a single source vertex.
