Which algorithm can be used to detect cycles in a directed graph?

Which algorithm can be used to detect cycles in a directed graph?

Step 1: Start with a directed graph that you want to check for cycles.
Step 2: Use Depth-First Search (DFS) to explore the graph.
Step 3: Keep track of nodes that you have visited to avoid revisiting them.
Step 4: Maintain a recursion stack to keep track of the nodes in the current path of the DFS.
Step 5: As you visit each node, mark it as visited and add it to the recursion stack.
Step 6: For each adjacent node of the current node, check if it is already in the recursion stack.
Step 7: If you find an adjacent node that is already in the recursion stack, a cycle exists.
Step 8: If you finish exploring all nodes without finding a cycle, then the graph is acyclic.

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