Which of the following algorithms is best suited for finding the shortest path in a weighted graph where some edges may have negative weights but no negative cycles?
The Bellman-Ford Algorithm (C) is best suited for finding the shortest path in graphs that may have negative weights but no negative cycles. It works by relaxing the edges up to (V-1) times, where V is the number of vertices, ensuring it can handle negative weights and detect negative cycles. Why Other Options Are Wrong: A) Dijkstra's Algorithm: Dijkstra’s algorithm is faster than Bellman-Ford for graphs with non-negative weights but fails when negative weights are present, as it assumes all edge weights are positive. B) Kruskal's Algorithm: This is a Minimum Spanning Tree (MST) algorithm used to connect all nodes in a graph with minimum weight, not to find the shortest path between two nodes. D) Prim’s Algorithm: Like Kruskal’s, Prim’s algorithm is used for finding an MST, not for finding the shortest path in a graph with negative weights. E) Floyd-Warshall Algorithm: This algorithm computes shortest paths between all pairs of vertices and works for both positive and negative weights, but it is not optimal for solving single-source shortest path problems.
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