How does the Dijkstra Algorithm work?

The Dijkstra Algorithm is a graph traversal algorithm that finds the shortest path between a starting node and all other nodes in a weighted graph. It works by maintaining a priority queue of nodes, initially containing only the starting node.

The algorithm starts by assigning a distance value of 0 to the starting node and infinity to all other nodes. It then repeatedly selects the node with the smallest distance value from the priority queue and explores its neighboring nodes.

For each neighboring node, the algorithm calculates the distance from the starting node through the current node. If this distance is smaller than the previously recorded distance for that node, the distance value is updated. Additionally, the algorithm updates the previous node for the neighboring node to keep track of the shortest path.

After visiting all the neighbors of a node, it is marked as visited and removed from the priority queue. This process continues until all nodes have been visited or the destination node is reached.

Finally, the algorithm returns the shortest path from the starting node to each node, along with their respective distances.