package DataStructures; public class HelloWorld > { public HelloWorld( ) { root = null; } public void insert( AnyType x ) { root = insert( x, root ); } public void remove( AnyType x ) { root = remove( x, root ); } public AnyType findMin( ) { if( isEmpty( ) ) System.out.println(\"tree is empty\"); return findMin( root ).element; } public AnyType findMax( ) { if( isEmpty( ) ) System.out.println(\"tree is empty\"); return findMax( root ).element; } public boolean contains( AnyType x ) { return contains( x, root ); } 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 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; } 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 ) // Two children { t.element = findMin( t.right ).element; t.right = remove( t.element, t.right ); } else t = ( t.left != null ) ? t.left : t.right; return t; } private BinaryNode findMin( BinaryNode t ) { if( t == null ) return null; else if( t.left == null ) return t; return findMin( t.left ); } private BinaryNode findMax( BinaryNode t ) { if( t != null ) while( t.right != null ) t = t.right; return t; } 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 } private void printTree( BinaryNode t ) { if( t != null ) { printTree( t.left ); System.out.println( t.element ); printTree( t.right ); } } 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; public static void main( String [ ] args ) { HelloWorld t = new HelloWorld( ); 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.

1. package DataStructures;
public class HelloWorld >
{
public HelloWorld( )
{
root = null;
}
public void insert( AnyType x )
{
root = insert( x, root );
}
public void remove( AnyType x )
{
root = remove( x, root );
}
public AnyType findMin( )
{
if( isEmpty( ) )
System.out.println("tree is empty");
return findMin( root ).element;
}
public AnyType findMax( )
{
if( isEmpty( ) )
System.out.println("tree is empty");
return findMax( root ).element;
}
public boolean contains( AnyType x )
{
return contains( x, root );
}
public void makeEmpty( )
{
root = null;

2. }
public boolean isEmpty( )
{
return root == null;
}
public void printTree( )
{
if( isEmpty( ) )
System.out.println( "Empty tree" );
else
printTree( root );
}
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;
}
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 );

3. 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;
return t;
}
private BinaryNode findMin( BinaryNode t )
{
if( t == null )
return null;
else if( t.left == null )
return t;
return findMin( t.left );
}
private BinaryNode findMax( BinaryNode t )
{
if( t != null )
while( t.right != null )
t = t.right;
return t;
}
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 )

4. return contains( x, t.right );
else
return true; // Match
}
private void printTree( BinaryNode t )
{
if( t != null )
{
printTree( t.left );
System.out.println( t.element );
printTree( t.right );
}
}
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

5. BinaryNode left; // Left child
BinaryNode right; // Right child
}
/** The tree root. */
private BinaryNode root;
public static void main( String [ ] args )
{
HelloWorld t = new HelloWorld( );
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!" );
}
}
}
Solution
package DataStructures;
public class HelloWorld >

6. {
public HelloWorld( )
{
root = null;
}
public void insert( AnyType x )
{
root = insert( x, root );
}
public void remove( AnyType x )
{
root = remove( x, root );
}
public AnyType findMin( )
{
if( isEmpty( ) )
System.out.println("tree is empty");
return findMin( root ).element;
}
public AnyType findMax( )
{
if( isEmpty( ) )
System.out.println("tree is empty");
return findMax( root ).element;
}
public boolean contains( AnyType x )
{
return contains( x, root );
}
public void makeEmpty( )
{
root = null;
}
public boolean isEmpty( )
{
return root == null;

7. }
public void printTree( )
{
if( isEmpty( ) )
System.out.println( "Empty tree" );
else
printTree( root );
}
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;
}
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 ) // Two children
{

8. t.element = findMin( t.right ).element;
t.right = remove( t.element, t.right );
}
else
t = ( t.left != null ) ? t.left : t.right;
return t;
}
private BinaryNode findMin( BinaryNode t )
{
if( t == null )
return null;
else if( t.left == null )
return t;
return findMin( t.left );
}
private BinaryNode findMax( BinaryNode t )
{
if( t != null )
while( t.right != null )
t = t.right;
return t;
}
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
}

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

10. /** The tree root. */
private BinaryNode root;
public static void main( String [ ] args )
{
HelloWorld t = new HelloWorld( );
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!" );
}
}
}