Dijkstra Algorithm Questions Long
The visited array in the Dijkstra Algorithm is used to keep track of the vertices that have been visited or explored during the algorithm's execution. It is typically implemented as a boolean array, where each element represents a vertex in the graph.
The main role of the visited array is to ensure that each vertex is visited only once and to avoid revisiting already explored vertices. This is important because the Dijkstra Algorithm aims to find the shortest path from a source vertex to all other vertices in a weighted graph. By marking a vertex as visited, we can guarantee that its shortest path has been determined and it does not need to be considered again.
Initially, all vertices are marked as unvisited except for the source vertex, which is marked as visited with a distance of 0. As the algorithm progresses, it selects the unvisited vertex with the smallest distance from the source and marks it as visited. This process continues until all vertices have been visited.
The visited array is crucial for the efficiency of the Dijkstra Algorithm. Without it, the algorithm would waste time revisiting vertices and potentially get stuck in an infinite loop. By keeping track of the visited vertices, the algorithm can focus on exploring unvisited vertices and updating their distances if a shorter path is found.
In summary, the visited array in the Dijkstra Algorithm plays a vital role in ensuring that each vertex is visited only once, avoiding unnecessary revisits, and allowing the algorithm to efficiently find the shortest path from a source vertex to all other vertices in a weighted graph.