Consider the directed graph provided below:
Apply the first step of Kosaraju's algorithm, starting with node , and calculate the output time for each node. To maintain clarity during traversal, choose the node with the smallest label when there are several unvisited nodes available for processing at a given node. The expected output format is as follows:
3 7 5 1 4 2In this format, the first number corresponds to the output time for node , the second number corresponds to node , and so on.
Hint: When applying DFS starting from node , pay attention to nodes with multiple outgoing edges. To ensure clarity, select the edge that leads to the node with the smallest label. This choice can significantly impact the order of output times.
Additionally, keep in mind that some nodes may become unreachable from node during traversal. Treat these isolated nodes as a separate, independent graph. When working with these nodes, adjust the output time accordingly. Instead of starting from 1, initiate the output time from , where represents the maximum output time among the nodes you've already processed.