Dijkstra, Bellman-Ford, Floyd-Warshall, Prim, Kruskal, union-find, topological sort and max flow.
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- What is Dijkstra's algorithm?
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A greedy algorithm for finding the shortest path from a source vertex to all other vertices in a weighted graph with non-negative edge weights.- What is the time complexity of Dijkstra's algorithm with a binary min-heap?
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O((V + E) log V), where V is the number of vertices and E is the number of edges.- Why does Dijkstra's algorithm use a greedy strategy?
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It always selects the unvisited vertex with the smallest known distance, which guarantees the shortest path to that vertex.- Can Dijkstra's algorithm handle negative edge weights?
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No, it fails with negative weights because the greedy choice of the minimum distance vertex may not lead to the true shortest path.- What is relaxation in Dijkstra's algorithm?
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The process of updating a vertex's distance if a shorter path is found through another vertex.- What is the Bellman-Ford algorithm?
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An algorithm that computes shortest paths from a source vertex to all other vertices in a weighted graph, even with negative edge weights.- What is the time complexity of the Bellman-Ford algorithm?
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O(VE), where V is the number of vertices and E is the number of edges.- What is a key advantage of Bellman-Ford over Dijkstra?
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Bellman-Ford can handle graphs with negative edge weights.- How does Bellman-Ford detect negative cycles?
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By running one additional relaxation pass after V - 1 passes; if any distance improves, a negative cycle exists.- How many relaxation passes does Bellman-Ford perform to guarantee shortest paths?
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V - 1 passes, where V is the number of vertices.- What is the Floyd-Warshall algorithm?
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A dynamic programming algorithm that computes the shortest paths between all pairs of vertices in a weighted graph.- What is the time complexity of Floyd-Warshall?
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O(V^3), where V is the number of vertices.- Why is Floyd-Warshall called an all-pairs shortest path algorithm?
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It computes the shortest distance between every pair of vertices in the graph.- What does the intermediate vertex k represent in Floyd-Warshall's recurrence?
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The algorithm considers paths from vertex i to vertex j that pass through only vertices 0 to k.- Can Floyd-Warshall detect negative cycles?
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Yes, by checking if any diagonal element in the final distance matrix is negative.
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