// BinarySearchTree class
//
// CONSTRUCTION: with no initializer
//
// ******************PUBLIC OPERATIONS*********************
// void insert( x ) --> Insert x
// void remove( x ) --> Remove x
// boolean contains( x ) --> Return true if x is present
// Comparable findMin( ) --> Return smallest item
// Comparable findMax( ) --> Return largest item
// boolean isEmpty( ) --> Return true if empty; else false
// void makeEmpty( ) --> Remove all items
// void printTree( ) --> Print tree in sorted order
// ******************ERRORS********************************
// Throws UnderflowException as appropriate


/* * Implements an unbalanced binary search tree. * Note that all "matching" is based on the compareTo method. */

public class MyBST<AnyType extends Comparable<? super AnyType>>
{
    //@// Fields
    private BinaryNode<AnyType> root;


    //@// Constructors
    public MyBST()
    {
        root = null;
    }


    //@// Classes
    private static class BinaryNode<AnyType>
    {
        BinaryNode(AnyType theElement)
        {
            this(theElement,null,null);
        }
        BinaryNode(AnyType theElement, BinaryNode<AnyType> lt, BinaryNode<AnyType> rt)
        {
            element = theElement;
            left = lt;
            right = rt;
        }
        AnyType element;
        BinaryNode<AnyType> left;
        BinaryNode<AnyType> right;
    }


    //@// Methods
    public void makeEmpty()
    {
        root = null;
    }

    public boolean isEmpty()
    {
        return root==null;
    }

    public void printTree()
    {
        if(isEmpty())
            System.out.println("Empty tree");
        else
            printTree(root);
    }

    private void printTree(BinaryNode<AnyType> t)
    {
        if(t!=null)
        {
            printTree(t.left);
            System.out.println(t.element);
            printTree(t.left);
        }
    }

    private int height(BinaryNode<AnyType> t)
    {
        if(t==null)
            return -1;
        else
            return 1+Math.max(height(t.left),height(t.right));
    }

    public AnyType findMin()
    {
        if(isEmpty())
            throw new UnderflowException();
        return findMin(root).element;
    }   

    private BinaryNode<AnyType> findMin(BinaryNode<AnyType> t)
    {
        if(t==null)
            return null;
        else if(t.left==null)
            return t;
        return findMin(t.left);
    }

    public AnyType findMax()
    {
        if(isEmpty())
            throw new UnderflowException();
        return findMax(root).element;
    }

    private BinaryNode<AnyType> findMax(BinaryNode<AnyType> t)
    {
        if(t!=null)
            while(t.right!=null)
                t = t.right;
        return t;
        // using while to replcae the tail-loop in findMin()
    }

    public boolean contains(AnyType x)
    {
        return contains(x,root);
    }

    private boolean contains(AnyType x, BinaryNode<AnyType> t)
    {
        if(t==null)
            return false;

        int compareResult = x.compareTo(t.element);
        if(compareResult<0)
            return contains(x,t.left);
        else if(compareResult>0)
            return contains(x,t.right);
        else
            return true;
    }

    public void insert(AnyType x)
    {
        root = insert(x,root);
    }

    private BinaryNode<AnyType> insert(AnyType x, BinaryNode<AnyType> t)
    {
        if(t==null)
            return new BinaryNode<>(x,null,null);

        int compareResult = x.compareTo(t.element);
        if(compareResult<0)
            t.left = insert(x,t.left);
        else if(compareResult>0)
            t.right = insert(x,t.right);
        else
            ;
        return t;
    }

    public void remove(AnyType x)
    {
        root = remove(x,root);
    }

    private BinaryNode<AnyType> remove(AnyType x, BinaryNode<AnyType> t)
    {
        if(t==null)
            return t;

        int compareResult = x.compareTo(t.element);
        if(compareResult<0)
            t.left = remove(x,t.left);
        else if(compareResult>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 = remove(t.element, t.right);
        }
        else
            t = (t.left!=null) ? t.left : t.right;  // one child
        return t;
    }

    // Test program
    public static void main(String[] args)
    {
        MyBST<Integer> t = new MyBST<>();
        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(i);
        for(int i=1; i<NUMS; i+=2)
            t.remove(i);

        if(NUMS<40)
            t.printTree();
        if(t.findMin()!=2 || t.findMax()!=NUMS-2)
            System.out.println("FindMin or FindMax error!");

        for(int i=2; i<NUMS; i+=2)
            if(!t.contains(i))
                System.out.println("FInd error1!");

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