Someone designs a new greedy strategy that constructs the tree in a "top down" manner as follows, starting from a sorted list in decreasing order of frequency:

• If there is only one character, return that character as a single node tree.
• Otherwise (recursively) return a tree whose left child is a leaf consisting of the first (highest frequency) character, and the right child is the tree built recursively from the rest of the list.

The height of the tree is

3

2

4

5