Dijkstra Algorithm Questions Medium
In the Dijkstra Algorithm, the role of path modification is to update the current shortest path to a vertex if a shorter path is found.
Initially, all vertices are assigned a tentative distance value, which is set to infinity except for the source vertex, which is set to 0. The algorithm then iteratively selects the vertex with the smallest tentative distance and examines its neighboring vertices.
When examining a neighboring vertex, the algorithm checks if the path through the current vertex offers a shorter distance than the previously known distance to that neighboring vertex. If a shorter path is found, the tentative distance of the neighboring vertex is updated to the new, shorter distance.
This process continues until all vertices have been visited or until the destination vertex is reached. By modifying the path and updating the tentative distances, the algorithm gradually finds the shortest path from the source vertex to all other vertices in the graph.
In summary, path modification in the Dijkstra Algorithm is crucial for dynamically updating and refining the shortest path to each vertex as the algorithm progresses, ensuring that the final result is the shortest path from the source vertex to all other vertices in the graph.