Dijkstra Algorithm Questions Medium
The role of path selection in the Dijkstra Algorithm is to determine the shortest path from a starting node to all other nodes in a weighted graph. The algorithm iteratively selects the node with the smallest distance from the starting node and explores its neighboring nodes. By comparing the distances of the current node with the distances of its neighbors, the algorithm updates the shortest path to each node.
During each iteration, the algorithm selects the node with the smallest distance as the current node. This ensures that the algorithm always explores the nodes with the shortest known distance first. By doing so, it guarantees that the shortest path to each node is found progressively.
The path selection process involves examining the distances of the current node's neighbors and updating them if a shorter path is found. This is done by comparing the sum of the current node's distance and the weight of the edge connecting it to its neighbor with the neighbor's current distance. If the sum is smaller, the neighbor's distance is updated, and the current node becomes the previous node for the neighbor.
By continuously selecting the node with the smallest distance and updating the distances of its neighbors, the Dijkstra Algorithm gradually builds the shortest path tree. This tree represents the shortest paths from the starting node to all other nodes in the graph.
In summary, the role of path selection in the Dijkstra Algorithm is to determine the shortest path by iteratively selecting the node with the smallest distance and updating the distances of its neighbors. This process ensures that the algorithm finds the shortest path to each node progressively.