Which algorithm is known for solving the single-source shortest paths problem?

Which algorithm is known for solving the single-source shortest paths problem?

• A. Prim's Algorithm
• B. Dijkstra's Algorithm
• C. Kruskal's Algorithm
• D. A* Algorithm

Answer: (B)

Dijkstra's Algorithm is specifically designed for solving the single-source shortest paths problem in a weighted graph where all weights are non-negative. This means that given a starting vertex, it can efficiently calculate the shortest path to all other vertices within the graph. The algorithm operates by maintaining a priority queue of vertices, where it repeatedly selects the vertex with the smallest known distance, and then relaxes all its adjacent vertices, updating their distances if a shorter path is found. In contrast, Prim's Algorithm and Kruskal's Algorithm are used for finding minimum spanning trees, which is a different problem altogether. The A* Algorithm, while also related to pathfinding, incorporates heuristics to find the shortest path in a way that can be more efficient than Dijkstra's in certain scenarios, but it does not specialize in the single-source shortest path for graphs with non-negative weights. Thus, Dijkstra's Algorithm stands out as the correct choice for the specific problem of single-source shortest paths.

Dijkstra's Algorithm is specifically designed for solving the single-source shortest paths problem in a weighted graph where all weights are non-negative. This means that given a starting vertex, it can efficiently calculate the shortest path to all other vertices within the graph. The algorithm operates by maintaining a priority queue of vertices, where it repeatedly selects the vertex with the smallest known distance, and then relaxes all its adjacent vertices, updating their distances if a shorter path is found.

In contrast, Prim's Algorithm and Kruskal's Algorithm are used for finding minimum spanning trees, which is a different problem altogether. The A* Algorithm, while also related to pathfinding, incorporates heuristics to find the shortest path in a way that can be more efficient than Dijkstra's in certain scenarios, but it does not specialize in the single-source shortest path for graphs with non-negative weights. Thus, Dijkstra's Algorithm stands out as the correct choice for the specific problem of single-source shortest paths.