Dijkstra Algorithm Questions Medium
In the Dijkstra Algorithm, the role of a current vertex is to act as the starting point for the algorithm's execution and to keep track of the shortest distance from the source vertex to all other vertices in the graph.
Initially, the current vertex is set as the source vertex, and its distance from itself is considered as 0. The algorithm then explores all the neighboring vertices of the current vertex and updates their distances if a shorter path is found. This process continues until all vertices in the graph have been visited or until the shortest path to the target vertex is found.
The current vertex is crucial in determining the next vertex to be visited, as it selects the vertex with the minimum distance among the unvisited vertices. This ensures that the algorithm always explores the vertices with the shortest known distance first, gradually expanding the search outward.
By updating the distances of the neighboring vertices and selecting the next current vertex based on the minimum distance, the algorithm gradually builds the shortest path tree from the source vertex to all other vertices in the graph. The role of the current vertex is therefore essential in efficiently finding the shortest paths in a weighted graph using the Dijkstra Algorithm.