Dijkstra Algorithm Questions Medium
In the Dijkstra Algorithm, the role of path comparison is to determine the shortest path from a source vertex to all other vertices in a weighted graph.
The algorithm maintains a set of vertices for which the shortest path has already been determined, and a set of vertices for which the shortest path is yet to be determined. It starts by assigning a tentative distance value to all vertices, with the source vertex having a distance of 0 and all other vertices having a distance of infinity.
At each iteration, the algorithm selects the vertex with the smallest tentative distance from the set of vertices yet to be determined. This vertex becomes the current vertex, and its neighbors are examined. For each neighbor, the algorithm calculates the distance from the source vertex through the current vertex and compares it with the tentative distance already assigned to the neighbor.
If the newly calculated distance is smaller than the tentative distance, the tentative distance is updated to the new value. This comparison ensures that the algorithm always selects the shortest path available to each vertex.
By continuously updating the tentative distances and selecting the vertex with the smallest tentative distance, the algorithm gradually explores all possible paths from the source vertex to all other vertices. Eventually, it determines the shortest path from the source vertex to each vertex in the graph.
Therefore, the path comparison plays a crucial role in the Dijkstra Algorithm by allowing the algorithm to find the shortest path by comparing and updating the tentative distances of the vertices.