Dijkstra Algorithm Questions Long
The time complexity of the Dijkstra Algorithm is O((V + E) log V), where V represents the number of vertices and E represents the number of edges in the graph.
The algorithm works by maintaining a priority queue of vertices, where the priority is based on the shortest distance from the source vertex. It starts by initializing the distance of all vertices as infinity, except for the source vertex which is set to 0. Then, it repeatedly selects the vertex with the minimum distance from the priority queue and relaxes its adjacent vertices.
In each iteration, the algorithm performs the following steps:
1. Extract the vertex with the minimum distance from the priority queue, which takes O(log V) time.
2. Relax all the adjacent vertices of the extracted vertex, which takes O(E) time in total. Relaxing a vertex involves updating its distance if a shorter path is found.
Since each vertex is extracted from the priority queue at most once, and each edge is relaxed at most once, the total number of iterations is at most V + E. Therefore, the time complexity of the algorithm is O((V + E) log V).
It is important to note that this time complexity assumes that a suitable data structure, such as a binary heap or Fibonacci heap, is used to implement the priority queue. Using an inefficient data structure could result in a higher time complexity.