JAVA: The Height of a Binary Tree

To start, a node in a binary tree looks like the following, in terms of Java:

public class BinaryTreeNode {

int key;

BinaryTreeNode left, right, parent;

public BinaryTreeNode(int key){

this.key=key;

left=right=parent=null; }

}

And a binary tree looks like the following:

public class BinaryTree {

BinaryTreeNode root;

public BinaryTree(){

root=null; }

}

Okay so WHAT TO DO:

implement at least the Insertion operation, either non-recursively or recursively.

MAIN PART: You need a method, with its signature being int treeHeight(BinaryTreeNode root), that gives the height of any tree with its top node referred by the root parameter.

Here is the recursive opertion:

Algorithm 6 TREE-INSERT-REC(yx,z) if x if z.key