package weiss.nonstandard;

// BinarySearchTree class
//
// CONSTRUCTION: with no initializer
//
// ******************PUBLIC OPERATIONS*********************
// void insert( x )       --> Insert x
// void remove( x )       --> Remove x
// void removeMin( )      --> Remove minimum item
// Comparable find( x )   --> Return item that matches x
// Comparable findMin( )  --> Return smallest item
// Comparable findMax( )  --> Return largest item
// boolean isEmpty( )     --> Return true if empty; else false
// void makeEmpty( )      --> Remove all items
// ******************ERRORS********************************
// Exceptions are thrown by insert, remove, and removeMin if warranted

/**
 * Implements an unbalanced binary search tree.
 * Note that all "matching" is based on the compareTo method.
 * @author Mark Allen Weiss
 */
public class BinarySearchTree
{
    /**
     * Construct the tree.
     */
    public BinarySearchTree( )
    {
        root = null;
    }

    /**
     * Insert into the tree.
     * @param x the item to insert.
     * @throws DuplicateItemException if x is already present.
     */
    public void insert( Comparable x )
    {
        root = insert( x, root );
    }

    /**
     * Remove from the tree..
     * @param x the item to remove.
     * @throws ItemNotFoundException if x is not found.
     */
    public void remove( Comparable x )
    {
        root = remove( x, root );
    }

    /**
     * Remove minimum item from the tree.
     * @throws ItemNotFoundException if tree is empty.
     */
    public void removeMin( )
    {
        root = removeMin( root );
    }

    /**
     * Find the smallest item in the tree.
     * @return smallest item or null if empty.
     */
    public Comparable findMin( )
    {
        return elementAt( findMin( root ) );
    }

    /**
     * Find the largest item in the tree.
     * @return the largest item or null if empty.
     */
    public Comparable findMax( )
    {
        return elementAt( findMax( root ) );
    }

    /**
     * Find an item in the tree.
     * @param x the item to search for.
     * @return the matching item or null if not found.
     */
    public Comparable find( Comparable x )
    {
        return elementAt( find( x, root ) );
    }

    /**
     * Make the tree logically empty.
     */
    public void makeEmpty( )
    {
        root = null;
    }

    /**
     * Test if the tree is logically empty.
     * @return true if empty, false otherwise.
     */
    public boolean isEmpty( )
    {
        return root == null;
    }

    /**
     * Internal method to get element field.
     * @param t the node.
     * @return the element field or null if t is null.
     */
    private Comparable elementAt( BinaryNode t )
    {
        return t == null ? null : t.element;
    }

    /**
     * Internal method to insert into a subtree.
     * @param x the item to insert.
     * @param t the node that roots the tree.
     * @return the new root.
     * @throws DuplicateItemException if x is already present.
     */
    protected BinaryNode insert( Comparable x, BinaryNode t )
    {
        if( t == null )
            t = new BinaryNode( x );
        else if( x.compareTo( t.element ) < 0 )
            t.left = insert( x, t.left );
        else if( x.compareTo( t.element ) > 0 )
            t.right = insert( x, t.right );
        else
            throw new DuplicateItemException( x.toString( ) );  // Duplicate
        return t;
    }

    /**
     * Internal method to remove from a subtree.
     * @param x the item to remove.
     * @param t the node that roots the tree.
     * @return the new root.
     * @throws ItemNotFoundException if x is not found.
     */
    protected BinaryNode remove( Comparable x, BinaryNode t )
    {
        if( t == null )
            throw new ItemNotFoundException( x.toString( ) );
        if( x.compareTo( t.element ) < 0 )
            t.left = remove( x, t.left );
        else if( x.compareTo( t.element ) > 0 )
            t.right = remove( x, t.right );
        else if( t.left != null && t.right != null ) // Two children
        {
            t.element = findMin( t.right ).element;
            t.right = removeMin( t.right );
        }
        else
            t = ( t.left != null ) ? t.left : t.right;
        return t;
    }

    /**
     * Internal method to remove minimum item from a subtree.
     * @param t the node that roots the tree.
     * @return the new root.
     * @throws ItemNotFoundException if t is empty.
     */
    protected BinaryNode removeMin( BinaryNode t )
    {
        if( t == null )
            throw new ItemNotFoundException( );
        else if( t.left != null )
        {
            t.left = removeMin( t.left );
            return t;
        }
        else
            return t.right;
    }    

    /**
     * Internal method to find the smallest item in a subtree.
     * @param t the node that roots the tree.
     * @return node containing the smallest item.
     */
    protected BinaryNode findMin( BinaryNode t )
    {
        if( t != null )
            while( t.left != null )
                t = t.left;

        return t;
    }

    /**
     * Internal method to find the largest item in a subtree.
     * @param t the node that roots the tree.
     * @return node containing the largest item.
     */
    private BinaryNode findMax( BinaryNode t )
    {
        if( t != null )
            while( t.right != null )
                t = t.right;

        return t;
    }

    /**
     * Internal method to find an item in a subtree.
     * @param x is item to search for.
     * @param t the node that roots the tree.
     * @return node containing the matched item.
     */
    private BinaryNode find( Comparable x, BinaryNode t )
    {
        while( t != null )
        {
            if( x.compareTo( t.element ) < 0 )
                t = t.left;
            else if( x.compareTo( t.element ) > 0 )
                t = t.right;
            else
                return t;    // Match
        }
        
        return null;         // Not found
    }

      /** The tree root. */
    protected BinaryNode root;


        // Test program
    public static void main( String [ ] args )
    {
        BinarySearchTree t = new BinarySearchTree( );
        final int NUMS = 4000;
        final int GAP  =   37;

        System.out.println( "Checking... (no more output means success)" );

        for( int i = GAP; i != 0; i = ( i + GAP ) % NUMS )
            t.insert( new Integer( i ) );

        for( int i = 1; i < NUMS; i+= 2 )
            t.remove( new Integer( i ) );

        if( ((Integer)(t.findMin( ))).intValue( ) != 2 ||
            ((Integer)(t.findMax( ))).intValue( ) != NUMS - 2 )
            System.out.println( "FindMin or FindMax error!" );

        for( int i = 2; i < NUMS; i+=2 )
             if( ((Integer)(t.find( new Integer( i ) ))).intValue( ) != i )
                 System.out.println( "Find error1!" );

        for( int i = 1; i < NUMS; i+=2 )
        {
            if( t.find( new Integer( i ) ) != null )
                System.out.println( "Find error2!" );
        }
    }
}