Implementation of Top-Down Splay Trees in Java

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The splay tree class interface is shown in Figure 2213 We have the usual methods, except that find is a mutator rather than an accessor The BinaryNode class is our standard node class that contains data and two pointers and declares that SplayTree is a friend, but it is not shown To eliminate annoying special cases, we maintain a nullNode sentinel We allocate and initialize the sentinel in the constructor, as shown in Figure 2214 Implementing the copy assignment operator and destructor turns out to be tricky, so we discuss this problem last Figure 2215 shows the member function for insertion of an item x A new node (new~ode) allocated, and if the tree is empty, a one-node tree is is created Otherwise, we splay around x If the data in the tree's new root equal x, we have a duplicate In this case, we do not want to insert x; we throw an exception instead Before throwing the exception at line 36, we would normally call delete to avoid a memory leak However, rather than calling delete for the newly allocated node, we use a static local variable so that the next call to insert can avoid calling new
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Implementation of Top-Down Splay Trees
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Figure 2212 Steps in a top-down splay (accessing 19 in the top tree)
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/ / SplayTree class // / / CONSTRUCTION: with no parameters or another SplayTree // / / ******************PUBLICp E R A T I O N S X * * * * k * * * * * * * * * * * * * * * O
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void insert ( x ) void remove( x ) Comparable find( x boo1 isEmpty( ) void makeEmpty ( )
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Insert Remove Return Return - - > Remove
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x x item that matches x true if empty; else false all items
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template <class Comparable> class SplayTree
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public: SplayTree ( ) ; SplayTree( const SplayTree -SplayTree ( ) ; boo1 isEmpty ( ) const; void makeEmpty ( ) ;
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Cref<Comparable> find( const Comparable & x ) ; void insert( const Comparable & x ) ; void remove( const Comparable & x ) ; const SplayTree & operator=( const SplayTree & rhs private: BinaryNode<Comparable> *root; BinaryNode<Comparable> *nullNode; typedef BinaryNode<Comparable> Node; Cref<Comparable> elernentAt( Node *t ) const; Node * clone( Node *t ) const;
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/ / Tree manipulations void rotateWithLeftChild( Node * & k2 ) const; void rotateWithRightChild( Node * & kl ) const; void splay( const Comparable & x, Node * & t ) const;
42 1 ;
Figure 2213 The top-down SplayTree class interface
1 template <class Comparable> 2 SplayTree<Comparable>: :SplayTree( ) 3 { 4 nullNode = new BinaryNode<Comparable>; 5 nullNode->left = nullNode->right = nullNode; 6 root = nullNode; 7 } Figure 2214 The SplayTree class constructor 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
/ / Insert x into the tree / / Throws DuplicateItemException if x is already there
template <class Comparable> void SplayTree<Comparable>::insert( const Comparable
static BinaryNode<Comparable> *newNode if ( newNode newNode
== =
NULL;
NULL ) new BinaryNode<Comparable>;
newNode->element = x ; if( root = = nullNode ) i newNode->left = newNode->right = nullNode; root = newNode;
else
splay ( x , root ) ; if( x < root->element
newNode->left = root->left; newNode->right = root; root->left = nullNode; root = newNode;
else if( root->element < x
newNode->right = root->right; newNode->left = root; root->right = nullNode; root = newNode;
else throw D u p l i c a t e I t e r n E x c e p t i o n (
newNode
NULL;
i / So next insert will call new
Figure 2215 The top-down SplayTree class insertion routine
- - -
Trees
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