Dijkstra Algorithm Questions Medium
In the Dijkstra Algorithm, the role of path insertion is to update the shortest path from the source node to all other nodes in the graph.
Initially, all nodes except the source node are marked with an infinite distance value. The algorithm starts by selecting the source node and setting its distance value to 0. Then, it explores the neighboring nodes of the source node and updates their distance values if a shorter path is found.
Path insertion comes into play when a shorter path to a node is discovered. When a shorter path is found, the algorithm inserts this path into the priority queue or the data structure used to store the nodes to be processed. This ensures that the algorithm continues to explore the graph and update the distances until the shortest path to all nodes is determined.
The path insertion step is crucial as it allows the algorithm to consider and update the distances of nodes that are not directly connected to the source node. By continuously inserting and updating paths, the algorithm gradually builds the shortest path tree from the source node to all other nodes in the graph.