Depth-first search algorithm is applied to a full binary tree of height k. Assume that the edges are directed from parents to children.

Depth-first search algorithm is applied to a full binary tree of height k. Assume that the edges are directed from parents to children. What is the maximal number of vertices occurring inside the stack during the execution? How many times is this maximal size repeated? Assume that the vertices are ordered level-by-level from top to bottom and from left to right inside each level.