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which DFS algorithm to follow?

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there are multiple algorithm of DFS available and i cant figure out which one to follow for solving question asking for the nodes which aren’t pushed into the stack or the nodes which are pushed more than once,

Tried to figure out from already asked question but still can’t get it,

https://gateoverflow.in/98484/dfs-using-stack

https://gateoverflow.in/161225/dfs-number-of-nodes-not-pushed-into-the-stack

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Always use the standard algorithm which uses Stack until and unless mentioned the other way around.
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