Dijkstra Algorithm Questions Medium
In the Dijkstra Algorithm, the role of a path update is to continuously update the shortest path from the source node to all other nodes in the graph.
Initially, all nodes except the source node are assigned a tentative distance value, which is set to infinity. The algorithm starts by selecting the source node and setting its tentative distance value to 0.
Then, it explores the neighboring nodes of the source node and updates their tentative distance values based on the weight of the edges connecting them. If the new tentative distance is smaller than the current tentative distance, the path is updated with the new shorter distance.
This process is repeated for all the nodes in the graph, always selecting the node with the smallest tentative distance as the current node. By continuously updating the path, the algorithm gradually finds the shortest path from the source node to all other nodes in the graph.
The path update step is crucial in ensuring that the algorithm converges to the correct shortest path. Without updating the path, the algorithm would not be able to find the optimal solution.