How does the Dijkstra Algorithm handle disconnected graphs?

The Dijkstra Algorithm is primarily designed to find the shortest path between a source node and all other nodes in a connected graph. However, when it comes to handling disconnected graphs, the algorithm can be modified to handle such scenarios.

In a disconnected graph, there are multiple components or subgraphs that are not connected to each other. To handle this, we can modify the Dijkstra Algorithm by running it separately on each connected component of the graph.

Here is a step-by-step explanation of how the Dijkstra Algorithm can handle disconnected graphs:

1. Initialize the algorithm by setting the distance of the source node to 0 and all other nodes to infinity. Also, mark all nodes as unvisited.

2. Select the unvisited node with the smallest distance and mark it as visited.

3. For the selected node, update the distances of its neighboring nodes. Calculate the distance from the source node to each neighboring node by summing the distance from the source node to the selected node and the weight of the edge between the selected node and its neighbor. If this calculated distance is smaller than the current distance of the neighbor, update the neighbor's distance.

4. Repeat steps 2 and 3 until all nodes have been visited or until the destination node (if specified) has been visited.

5. If there are still unvisited nodes remaining, it means that there are disconnected components in the graph. In this case, select an unvisited node from one of the disconnected components and repeat steps 2 to 4 for that component.

6. Once all nodes have been visited or the destination node has been visited, the algorithm terminates. The distances calculated for each node represent the shortest path from the source node to that particular node.

By running the Dijkstra Algorithm separately on each connected component of a disconnected graph, we can find the shortest paths from the source node to all other nodes in each component. However, it's important to note that the algorithm will not consider paths between nodes in different components, as they are disconnected.