Depth-first Conversation

Depth-first search is a specific order in which the items
organized in a tree are being searched for. A tree is a way
to organize things by relating items hierarchically: a top
item leads to many items, and those in turn lead to even
more.

If you have a tree, you can follow the branches in many
different ways. Depth-first search specifies that you always
follows the leftmost branch first. At the end of a branch,
you go back to the last branch point, and explore the next
leftmost branch from there. You keep doing that until you
hit the rightmost branch.