Compare two directories.Good Design Pattern

I recently encountered an interview question."How to compare two directories".
My Answer was to use Tree Like Structure.(Generic tree).At every level,node can be a leaf or it may contain child nodes.Point Parent to first child and first child to next sibling.
The Interviewer then extended this question to "What if data is large and it cannot be in memory at once ".I could not figure answer to this question.Can someone suggest ?