Write a program to do the following.

• Input an integer n.

• Create a BST S inserting the keys 1, 2, . . . , n in thatorder, which will result in a completely-skewed tree.

• Measure the time to search for n + 1 in S.

• Display the time taken for search.

/**
* Exception class for access in empty containers
* such as stacks, queues, and priority queues.
* @author Mark Allen Weiss
*/
public class UnderflowException extends RuntimeException
{
}

// 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.
* @author Mark Allen Weiss
*/
public class BinarySearchTree>
{
/**
* Construct the tree.
*/
public BinarySearchTree( )
{
root = null;
}

/**
* Insert into the tree; duplicates are ignored.
* @param x the item to insert.
*/
public void insert( AnyType x )
{
root = insert( x, root );
}

/**
* Remove from the tree. Nothing is done if x is not found.
* @param x the item to remove.
*/
public void remove( AnyType x )
{
root = remove( x, root );
}

/**
* Find the smallest item in the tree.
* @return smallest item or null if empty.
*/
public AnyType findMin( )
{
if( isEmpty( ) )
throw new UnderflowException( );
return findMin( root ).element;
}

/**
* Find the largest item in the tree.
* @return the largest item of null if empty.
*/
public AnyType findMax( )
{
if( isEmpty( ) )
throw new UnderflowException( );
return findMax( root ).element;
}

/**
* Find an item in the tree.
* @param x the item to search for.
* @return true if not found.
*/
public boolean contains( AnyType x )
{
return contains( 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;
}

/**
* Print the tree contents in sorted order.
*/
public void printTree( )
{
if( isEmpty( ) )
System.out.println( \"Empty tree\" );
else
printTree( root );
}

/**
* Internal method to insert into a subtree.
* @param x the item to insert.
* @param t the node that roots the subtree.
* @return the new root of the subtree.
*/
private BinaryNode insert( AnyType x,BinaryNode 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
; // Duplicate; do nothing
return t;
}

/**
* Internal method to remove from a subtree.
* @param x the item to remove.
* @param t the node that roots the subtree.
* @return the new root of the subtree.
*/
private BinaryNode remove( AnyType x,BinaryNode t )
{
if( t == null )
return t; // Item not found; do nothing
  
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 ) // Twochildren
{
t.element = findMin( t.right ).element;
t.right = remove( t.element, t.right );
}
else
t = ( t.left != null ) ? t.left : t.right;
return t;
}

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

/**
* Internal method to find the largest item in a subtree.
* @param t the node that roots the subtree.
* @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 subtree.
* @return node containing the matched item.
*/
private boolean contains( AnyType x, BinaryNode 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; // Match
}

/**
* Internal method to print a subtree in sorted order.
* @param t the node that roots the subtree.
*/
private void printTree( BinaryNode t )
{
if( t != null )
{
printTree( t.left );
System.out.println( t.element );
printTree( t.right );
}
}

/**
* Internal method to compute height of a subtree.
* @param t the node that roots the subtree.
*/
private int height( BinaryNode t )
{
if( t == null )
return -1;
else
return 1 + Math.max( height( t.left ), height( t.right ) );
}
  
// Basic node stored in unbalanced binary search trees
private static class BinaryNode
{
// Constructors
BinaryNode( AnyType theElement )
{
this( theElement, null, null );
}

BinaryNode( AnyType theElement, BinaryNode lt,BinaryNode rt )
{
element = theElement;
left = lt;
right = rt;
}

AnyType element; // The data in the node
BinaryNode left; // Left child
BinaryNode right; // Right child
}

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

// Test program
public static void main( String [ ] args )
{
BinarySearchTree t = newBinarySearchTree( );
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!\" );
}
}
}