Using the binary tree ADT 
(such as numChildren, inherited from the tree ADT, and left, 
right, hasLeft, hasRight, etc.), provide a recursive method 
isProper(root) to test whether the binary tree root is proper.

Algorithm isProper(root: BT)
Input: root: binary tree.
Output: result: boolean, true iff root is a proper BT.

-- initial conditions
[1] if root == null return true;
[2] if ((!root.hasLeft()) and (!root.hasRight())) return true; -- no child.
[3] if ((root.hasLeft()) and (!root.hasRight())) return false;-- left child only.
[4] if ((!root.hasLeft()) and (root.hasRight())) return false; -- right child only.

-- recursive conditions: root has both left and right children.
[5] return isProper(root.left()) and isProper(root.right());