Dijkstra Algorithm Questions Medium
In the Dijkstra Algorithm, the path weight 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 path with the minimum total weight.
The path weight represents the cumulative cost or distance associated with traversing a particular path. It is the sum of the weights of all the edges along the path. The algorithm uses this path weight to make decisions on which paths to explore and update.
Initially, all vertices are assigned a tentative distance value, which is set to infinity except for the source vertex, which is set to 0. As the algorithm progresses, it continuously updates the tentative distance values of the vertices based on the path weight.
At each iteration, the algorithm selects the vertex with the smallest tentative distance as the current vertex. It then examines all its neighboring vertices and calculates the path weight from the current vertex to each neighbor. If this newly calculated path weight is smaller than the current tentative distance of the neighbor, the tentative distance is updated to the new path weight.
By iteratively selecting the vertex with the smallest tentative distance and updating the tentative distances of its neighbors, the algorithm gradually explores and evaluates all possible paths from the source vertex to all other vertices. This process continues until all vertices have been visited or until the destination vertex is reached.
Ultimately, the path weight allows the Dijkstra Algorithm to determine the shortest path by considering the cumulative weights of the edges. It ensures that the algorithm finds the path with the minimum total weight, providing an optimal solution for finding the shortest path in a weighted graph.