Dijkstra Algorithm Questions Medium
In the Dijkstra Algorithm, the role of path removal is to ensure that the algorithm finds the shortest path from a source vertex to all other vertices in a weighted graph.
The algorithm starts by initializing the source vertex with a distance of 0 and all other vertices with a distance of infinity. It then explores the neighboring vertices of the source vertex and updates their distances if a shorter path is found.
After updating the distances, the algorithm selects the vertex with the minimum distance as the next current vertex and repeats the process of exploring its neighbors and updating their distances.
Path removal comes into play when a vertex is selected as the current vertex. It removes the current vertex from the set of unvisited vertices, ensuring that it will not be revisited in the future. This is important because once a vertex is visited and its shortest path is determined, there is no need to revisit it again.
By removing the current vertex from the set of unvisited vertices, the algorithm guarantees that it will only consider the remaining unvisited vertices for further exploration and distance updates. This helps in optimizing the algorithm's efficiency by avoiding unnecessary computations and reducing the overall time complexity.
In summary, path removal in the Dijkstra Algorithm ensures that each vertex is visited and its shortest path is determined only once, leading to the discovery of the shortest path from the source vertex to all other vertices in the graph.