Dijkstra Algorithm Questions Medium
In the Dijkstra Algorithm, the role of path deletion is to ensure that the algorithm finds the shortest path from a source vertex to all other vertices in a weighted graph.
During the execution of the algorithm, the shortest path to each vertex is gradually determined. When a vertex is visited, its distance from the source vertex is updated if a shorter path is found. This process continues until all vertices have been visited.
Path deletion comes into play when a shorter path to a vertex is discovered. If a vertex is already in the priority queue (which stores the vertices to be visited), the algorithm needs to update its distance value. This is done by deleting the existing path to the vertex and inserting the new, shorter path into the priority queue.
By deleting the existing path and replacing it with the shorter one, the algorithm ensures that it always considers the most up-to-date and shortest paths to each vertex. This guarantees that the algorithm will find the shortest path from the source vertex to all other vertices in the graph.