第12章 高级数据结构及其实现

  1 // SplayTree class
  2 //
  3 // CONSTRUCTION: with no initializer
  4 //
  5 // ******************PUBLIC OPERATIONS*********************
  6 // void insert( x )       --> Insert x
  7 // void remove( x )       --> Remove x
  8 // boolean contains( x )  --> Return true if x is found
  9 // Comparable findMin( )  --> Return smallest item
 10 // Comparable findMax( )  --> Return largest item
 11 // boolean isEmpty( )     --> Return true if empty; else false
 12 // void makeEmpty( )      --> Remove all items
 13 // ******************ERRORS********************************
 14 // Throws UnderflowException as appropriate
 15 
 16 /**
 17  * Implements a top-down splay tree.
 18  * Note that all "matching" is based on the compareTo method.
 19  * @author Mark Allen Weiss
 20  */
 21 public class SplayTree<AnyType extends Comparable<? super AnyType>>
 22 {
 23     /**
 24      * Construct the tree.
 25      */
 26     public SplayTree( )
 27     {
 28         nullNode = new BinaryNode<AnyType>( null );
 29         nullNode.left = nullNode.right = nullNode;
 30         root = nullNode;
 31     }
 32 
 33     private BinaryNode<AnyType> newNode = null;  // Used between different inserts
 34     
 35     /**
 36      * Insert into the tree.
 37      * @param x the item to insert.
 38      */
 39     public void insert( AnyType x )
 40     {
 41         if( newNode == null )
 42             newNode = new BinaryNode<AnyType>( null );
 43         newNode.element = x;
 44 
 45         if( root == nullNode )
 46         {
 47             newNode.left = newNode.right = nullNode;
 48             root = newNode;
 49         }
 50         else
 51         {
 52             root = splay( x, root );
 53             
 54             int compareResult = x.compareTo( root.element );
 55             
 56             if( compareResult < 0 )
 57             {
 58                 newNode.left = root.left;
 59                 newNode.right = root;
 60                 root.left = nullNode;
 61                 root = newNode;
 62             }
 63             else
 64             if( compareResult > 0 )
 65             {
 66                 newNode.right = root.right;
 67                 newNode.left = root;
 68                 root.right = nullNode;
 69                 root = newNode;
 70             }
 71             else
 72                 return;   // No duplicates
 73         }
 74         newNode = null;   // So next insert will call new
 75     }
 76 
 77     /**
 78      * Remove from the tree.
 79      * @param x the item to remove.
 80      */
 81     public void remove( AnyType x )
 82     {
 83         if( !contains( x ) )
 84             return;
 85 
 86         BinaryNode<AnyType> newTree;
 87 
 88             // If x is found, it will be splayed to the root by contains
 89         if( root.left == nullNode )
 90             newTree = root.right;
 91         else
 92         {
 93             // Find the maximum in the left subtree
 94             // Splay it to the root; and then attach right child
 95             newTree = root.left;
 96             newTree = splay( x, newTree );
 97             newTree.right = root.right;
 98         }
 99         root = newTree;
100     }
101 
102     /**
103      * Find the smallest item in the tree.
104      * Not the most efficient implementation (uses two passes), but has correct
105      *     amortized behavior.
106      * A good alternative is to first call find with parameter
107      *     smaller than any item in the tree, then call findMin.
108      * @return the smallest item or throw UnderflowException if empty.
109      */
110     public AnyType findMin( )
111     {
112         if( isEmpty( ) )
113             throw new UnderflowException( );
114 
115         BinaryNode<AnyType> ptr = root;
116 
117         while( ptr.left != nullNode )
118             ptr = ptr.left;
119 
120         root = splay( ptr.element, root );
121         return ptr.element;
122     }
123 
124     /**
125      * Find the largest item in the tree.
126      * Not the most efficient implementation (uses two passes), but has correct
127      *     amortized behavior.
128      * A good alternative is to first call find with parameter
129      *     larger than any item in the tree, then call findMax.
130      * @return the largest item or throw UnderflowException if empty.
131      */
132     public AnyType findMax( )
133     {
134         if( isEmpty( ) )
135             throw new UnderflowException( );
136 
137         BinaryNode<AnyType> ptr = root;
138 
139         while( ptr.right != nullNode )
140             ptr = ptr.right;
141 
142         root = splay( ptr.element, root );
143         return ptr.element;
144     }
145 
146     /**
147      * Find an item in the tree.
148      * @param x the item to search for.
149      * @return true if x is found; otherwise false.
150      */
151     public boolean contains( AnyType x )
152     {
153         if( isEmpty( ) )
154             return false;
155             
156         root = splay( x, root );
157 
158         return root.element.compareTo( x ) == 0;
159     }
160 
161     /**
162      * Make the tree logically empty.
163      */
164     public void makeEmpty( )
165     {
166         root = nullNode;
167     }
168 
169     /**
170      * Test if the tree is logically empty.
171      * @return true if empty, false otherwise.
172      */
173     public boolean isEmpty( )
174     {
175         return root == nullNode;
176     }
177 
178     private BinaryNode<AnyType> header = new BinaryNode<AnyType>( null ); // For splay
179     
180     /**
181      * Internal method to perform a top-down splay.
182      * The last accessed node becomes the new root.
183      * @param x the target item to splay around.
184      * @param t the root of the subtree to splay.
185      * @return the subtree after the splay.
186      */
187     private BinaryNode<AnyType> splay( AnyType x, BinaryNode<AnyType> t )
188     {
189         BinaryNode<AnyType> leftTreeMax, rightTreeMin;
190 
191         header.left = header.right = nullNode;
192         leftTreeMax = rightTreeMin = header;
193 
194         nullNode.element = x;   // Guarantee a match
195 
196         for( ; ; )
197         {
198             int compareResult = x.compareTo( t.element );
199             
200             if( compareResult < 0 )
201             {
202                 if( x.compareTo( t.left.element ) < 0 )
203                     t = rotateWithLeftChild( t );
204                 if( t.left == nullNode )
205                     break;
206                 // Link Right
207                 rightTreeMin.left = t;
208                 rightTreeMin = t;
209                 t = t.left;
210             }
211             else if( compareResult > 0 )
212             {
213                 if( x.compareTo( t.right.element ) > 0 )
214                     t = rotateWithRightChild( t );
215                 if( t.right == nullNode )
216                     break;
217                 // Link Left
218                 leftTreeMax.right = t;
219                 leftTreeMax = t;
220                 t = t.right;
221             }
222             else
223                 break;
224         }    
225 
226         leftTreeMax.right = t.left;
227         rightTreeMin.left = t.right;
228         t.left = header.right;
229         t.right = header.left;
230         return t;
231     }
232 
233     /**
234      * Rotate binary tree node with left child.
235      * For AVL trees, this is a single rotation for case 1.
236      */
237     private static <AnyType> BinaryNode<AnyType> rotateWithLeftChild( BinaryNode<AnyType> k2 )
238     {
239         BinaryNode<AnyType> k1 = k2.left;
240         k2.left = k1.right;
241         k1.right = k2;
242         return k1;
243     }
244 
245     /**
246      * Rotate binary tree node with right child.
247      * For AVL trees, this is a single rotation for case 4.
248      */
249     private static <AnyType> BinaryNode<AnyType> rotateWithRightChild( BinaryNode<AnyType> k1 )
250     {
251         BinaryNode<AnyType> k2 = k1.right;
252         k1.right = k2.left;
253         k2.left = k1;
254         return k2;
255     }
256 
257     // Basic node stored in unbalanced binary search trees
258     private static class BinaryNode<AnyType>
259     {
260             // Constructors
261         BinaryNode( AnyType theElement )
262         {
263             this( theElement, null, null );
264         }
265 
266         BinaryNode( AnyType theElement, BinaryNode<AnyType> lt, BinaryNode<AnyType> rt )
267         {
268             element  = theElement;
269             left     = lt;
270             right    = rt;
271         }
272 
273         AnyType element;            // The data in the node
274         BinaryNode<AnyType> left;   // Left child
275         BinaryNode<AnyType> right;  // Right child
276     }
277 
278     private BinaryNode<AnyType> root;
279     private BinaryNode<AnyType> nullNode;
280     
281 
282         // Test program; should print min and max and nothing else
283     public static void main( String [ ] args )
284     {
285         SplayTree<Integer> t = new SplayTree<Integer>( );
286         final int NUMS = 40000;
287         final int GAP  =   307;
288 
289         System.out.println( "Checking... (no bad output means success)" );
290 
291         for( int i = GAP; i != 0; i = ( i + GAP ) % NUMS )
292             t.insert( i );
293         System.out.println( "Inserts complete" );
294 
295         for( int i = 1; i < NUMS; i += 2 )
296             t.remove( i );
297         System.out.println( "Removes complete" );
298 
299         if( t.findMin( ) != 2 || t.findMax( ) != NUMS - 2 )
300             System.out.println( "FindMin or FindMax error!" );
301 
302         for( int i = 2; i < NUMS; i += 2 )
303             if( !t.contains( i ) )
304                 System.out.println( "Error: find fails for " + i );
305 
306         for( int i = 1; i < NUMS; i += 2 )
307             if( t.contains( i ) )
308                 System.out.println( "Error: Found deleted item " + i );
309     }
310 }