Dijkstra Algorithm Questions Medium
In the Dijkstra Algorithm, the path length plays a crucial role in determining the shortest path from a source vertex to all other vertices in a weighted graph. The algorithm aims to find the shortest path by iteratively selecting the vertex with the minimum path length from the source vertex and updating the path lengths of its adjacent vertices.
Initially, all vertices are assigned a tentative path length of infinity, except for the source vertex which is assigned a path length of 0. As the algorithm progresses, it continuously updates the path lengths of the vertices based on the edges' weights.
The path length represents the total weight or cost of reaching a particular vertex from the source vertex through a specific path. The algorithm compares the current path length of a vertex with the sum of the path length of its adjacent vertex and the weight of the connecting edge. If the sum is smaller, it means a shorter path has been found, and the path length of the vertex is updated accordingly.
By keeping track of the path lengths, the Dijkstra Algorithm ensures that it always selects the vertex with the minimum path length in each iteration. This guarantees that the algorithm explores the graph in a systematic manner, gradually finding the shortest path to all other vertices from the source vertex.
In summary, the role of the path length in the Dijkstra Algorithm is to determine the shortest path by continuously updating and comparing the tentative path lengths of the vertices, ultimately leading to the discovery of the shortest path from the source vertex to all other vertices in the graph.