Using DFS with a Modified Stack For cycle detection using DFS in a directed graph, the basic idea is to traverse the graph and mark each node as visited. The nodes that are currently being explored (i.e., on the DFS call stack) are also marked. If we encounter a node that is already on the stack, we've detected a cycle.

However, DFS recursion can lead to stack overflow in graphs with large depths. To mitigate this:

Iterative DFS with an explicit stack: Instead of relying on recursive calls, use an explicit stack (or queue) to perform DFS iteratively. This avoids the recursion limit issue.

Optimized memory usage: Only store essential data (e.g., visitation state) and make sure to avoid storing unnecessary structures