The height of the binary search tree characterizes the runtime of some of the methods of the structure. Recall that the height of a node is the length of the longest path from the node to a descendent leaf. The height of a tree is the height of its root.

Consider the BSTree structure from $3$

$$Add a method to BSTree that computes the height of the BSTree object. Note that the height

of an empty tree is $0.$

$$Test that method by inserting array $4,7,3,9,1,2,10,5,6,5,8$ and then compute the height of the resulting tree.

$$Test that method by inserting array $1,2,3,4,5,5,6,7,8,9,10$ and then compute the height of the resulting tree.