/**
 * A public interface for Binary Trees
 * @author gtowell
 * Created: March 2020
 */
public interface BinaryTreeInterface<E> 
{
    /**
     * @return the number of items in the tree
     */
    int size();
    
    /**
     *  
     * @return the maximum number of links between 
     *  the root of the tree and the most distant leaf
     */
    int height();
    
    /**
     * @return return true if the tree has no nodes
     */
    boolean isEmpty();
    
    /**
     * @return true if the given element exists in the tree and false otherwise
     */
    boolean contains(E element);
    
    /**
     * Add an element to the tree (if the element does not already exist
     * in the tree) If the element already is in the tree, do nothing.
     * @param element the element to be added
     */
    void insert(E element);
    
    /**
     * Remove an element from the tree, if it is in the tree
     * @param element the element to be removed
     * @return element if it was in the tree, null otherwise
     */
    boolean remove(E element);

    /**
     * return a string containing the items in the tree on a single line in the natural
     * order arising from their type.  That is, numbers should be in numeric order; 
     * strings in alphabetic order.  All items should be on the same line separated by 
     * spaces. (An extra trailing space is fine.)
     * @return a string containing all of the items in the tree
     */
    String printNaturalOrder();
}