package weiss.nonstandard;
// AATree class
//
// CONSTRUCTION: with no initializer
//
// ******************PUBLIC OPERATIONS*********************
// void insert( x ) --> Insert x
// void remove( x ) --> Remove x
// 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 and remove if warranted
/**
* Implements an AA-tree.
* Note that all "matching" is based on the compareTo method.
* @author Mark Allen Weiss
*/
public class AATree<AnyType extends Comparable<? super AnyType>>
{
/**
* Construct the tree.
*/
public AATree( )
{
nullNode = new AANode<AnyType>( null, null, null );
nullNode.left = nullNode.right = nullNode;
nullNode.level = 0;
root = nullNode;
}
/**
* Insert into the tree.
* @param x the item to insert.
* @throws DuplicateItemException if x is already present.
*/
public void insert( AnyType 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( AnyType x )
{
deletedNode = nullNode;
root = remove( x, root );
}
/**
* Find the smallest item in the tree.
* @return the smallest item or null if empty.
*/
public AnyType findMin( )
{
if( isEmpty( ) )
return null;
AANode<AnyType> ptr = root;
while( ptr.left != nullNode )
ptr = ptr.left;
return ptr.element;
}
/**
* Find the largest item in the tree.
* @return the largest item or null if empty.
*/
public AnyType findMax( )
{
if( isEmpty( ) )
return null;
AANode<AnyType> ptr = root;
while( ptr.right != nullNode )
ptr = ptr.right;
return ptr.element;
}
/**
* Find an item in the tree.
* @param x the item to search for.
* @return the matching item of null if not found.
*/
public AnyType find( AnyType x )
{
AANode<AnyType> current = root;
nullNode.element = x;
for( ; ; )
{
if( x.compareTo( current.element ) < 0 )
current = current.left;
else if( x.compareTo( current.element ) > 0 )
current = current.right;
else if( current != nullNode )
return current.element;
else
return null;
}
}
/**
* Make the tree logically empty.
*/
public void makeEmpty( )
{
root = nullNode;
}
/**
* Test if the tree is logically empty.
* @return true if empty, false otherwise.
*/
public boolean isEmpty( )
{
return root == nullNode;
}
/**
* 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.
*/
private AANode<AnyType> insert( AnyType x, AANode<AnyType> t )
{
if( t == nullNode )
t = new AANode<AnyType>( x, nullNode, nullNode );
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( ) );
t = skew( t );
t = split( t );
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.
*/
private AANode<AnyType> remove( AnyType x, AANode<AnyType> t )
{
if( t != nullNode )
{
// Step 1: Search down the tree and set lastNode and deletedNode
lastNode = t;
if( x.compareTo( t.element ) < 0 )
t.left = remove( x, t.left );
else
{
deletedNode = t;
t.right = remove( x, t.right );
}
// Step 2: If at the bottom of the tree and
// x is present, we remove it
if( t == lastNode )
{
if( deletedNode == nullNode || x.compareTo( deletedNode.element ) != 0 )
throw new ItemNotFoundException( x.toString( ) );
deletedNode.element = t.element;
t = t.right;
}
// Step 3: Otherwise, we are not at the bottom; rebalance
else
if( t.left.level < t.level - 1 || t.right.level < t.level - 1 )
{
if( t.right.level > --t.level )
t.right.level = t.level;
t = skew( t );
t.right = skew( t.right );
t.right.right = skew( t.right.right );
t = split( t );
t.right = split( t.right );
}
}
return t;
}
/**
* Skew primitive for AA-trees.
* @param t the node that roots the tree.
* @return the new root after the rotation.
*/
private static <AnyType> AANode<AnyType> skew( AANode<AnyType> t )
{
if( t.left.level == t.level )
t = rotateWithLeftChild( t );
return t;
}
/**
* Split primitive for AA-trees.
* @param t the node that roots the tree.
* @return the new root after the rotation.
*/
private static <AnyType> AANode<AnyType> split( AANode<AnyType> t )
{
if( t.right.right.level == t.level )
{
t = rotateWithRightChild( t );
t.level++;
}
return t;
}
/**
* Rotate binary tree node with left child.
*/
private static <AnyType> AANode<AnyType> rotateWithLeftChild( AANode<AnyType> k2 )
{
AANode<AnyType> k1 = k2.left;
k2.left = k1.right;
k1.right = k2;
return k1;
}
/**
* Rotate binary tree node with right child.
*/
private static <AnyType> AANode<AnyType> rotateWithRightChild( AANode<AnyType> k1 )
{
AANode<AnyType> k2 = k1.right;
k1.right = k2.left;
k2.left = k1;
return k2;
}
private static class AANode<AnyType>
{
// Constructors
AANode( AnyType theElement, AANode<AnyType> lt, AANode<AnyType> rt )
{
element = theElement;
left = lt;
right = rt;
level = 1;
}
AnyType element; // The data in the node
AANode<AnyType> left; // Left child
AANode<AnyType> right; // Right child
int level; // Level
}
private AANode<AnyType> root;
private AANode<AnyType> nullNode;
private AANode<AnyType> deletedNode;
private AANode<AnyType> lastNode;
// Test program; should print min and max and nothing else
public static void main( String [ ] args )
{
AATree<Integer> t = new AATree<Integer>( );
final int NUMS = 40000;
final int GAP = 307;
System.out.println( "Checking... (no bad output means success)" );
t.insert( NUMS * 2 );
t.insert( NUMS * 3 );
for( int i = GAP; i != 0; i = ( i + GAP ) % NUMS )
t.insert( i );
System.out.println( "Inserts complete" );
t.remove( t.findMax( ) );
for( int i = 1; i < NUMS; i+= 2 )
t.remove( i );
t.remove( t.findMax( ) );
System.out.println( "Removes complete" );
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.find( i ) != i )
System.out.println( "Error: find fails for " + i );
for( int i = 1; i < NUMS; i+=2 )
if( t.find( i ) != null )
System.out.println( "Error: Found deleted item " + i );
}
}