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VOOZH | about |
Given an undirected graph with multiple connected components, the task is to clone the graph. Cloning a graph with a single connected component can be seen here.
Examples:
An example of an undirected graph with 3 connected components:
Approach: The idea is to follow the same approach posted for cloning connected graph, but with every node so that we can clone graphs with multiple connected components.
We are going to use a GraphNode class and a Graph class. The Graph class is compulsory, since we might have multiple connected components (see example above), and we cannot deal with them having only a GraphNode as an input. For the Graph class, what we actually need is a list of GraphNodes. It's also possible to make a list of nodes instead of creating a class, both ways work.
To keep track of the visited nodes, we need a data structure; a map is an appropriate one, as we can map from the "old" nodes to the "new" ones (the cloned). So, we are defining a main function, which creates the map, and uses a helper function to fill it. Once the map is created, a new graph can be created, using the cloned nodes in the map.
The helper function is going to put connections between nodes (besides filling the map). As we are dealing with a whole connected component, a similar approach to the BFS is going to be followed.
Notice that in the main function, we don't call the helper function for each node in the Graph; if the node is stored in the map, it means that we've already visited it and dealt with its connected component, so no need to repeat the steps again.
In order to check if the graph has been correctly cloned, we can print the memory addresses of the nodes, and compare them to see whether we've cloned, or we've copied them.
Below is the implementation of the above approach:
INITIAL GRAPH Node 1 - 0x1104050 Node 2 - 0x1104090 Node 3 - 0x11040d0 Node 2 - 0x1104090 Node 1 - 0x1104050 Node 4 - 0x1104110 Node 3 - 0x11040d0 Node 1 - 0x1104050 Node 4 - 0x1104110 Node 4 - 0x1104110 Node 2 - 0x1104090 Node 3 - 0x11040d0 Node 5 - 0x1104150 Node 6 - 0x1104190 Node 6 - 0x1104190 Node 5 - 0x1104150 CLONED GRAPH Node 1 - 0x1104780 Node 2 - 0x1104850 Node 3 - 0x11048d0 Node 2 - 0x1104850 Node 1 - 0x1104780 Node 4 - 0x1104970 Node 3 - 0x11048d0 Node 1 - 0x1104780 Node 4 - 0x1104970 Node 4 - 0x1104970 Node 2 - 0x1104850 Node 3 - 0x11048d0 Node 5 - 0x1104810 Node 6 - 0x1104ab0 Node 6 - 0x1104ab0 Node 5 - 0x1104810
Complexity Analysis:
