Let the cost of visiting a vertex be the number of
branches traversed to reach
that vertex from the last one visited.
Best case cost = 1
Worst case cost = n -1
If we amortize the cost over a traversal of the entire binary tree, then the
cost of going from each vertex to the next is less than 2. To see why, note
that every binary tree with n vertices has exactly n - 1 branches and a
complete traversal of the tree goes over each branch exactly twice. Thus the
total number of steps in a full traversal = 2(n - 1).
Amortized number of steps from one vertex to the next =