/ / Throws exceptions as warranted in Java

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template <class Comparable> class AATree
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public: AATree( ) ; AATree( const AATree -AATree( ) ;
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CrefiComparable> find( const Comparable boo1 isEmpty( ) const; void makeEmpty ( ) ; void insert( const Comparable void remove( const Comparable const AATree
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operator=( const AATree
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typedef AANode<Comparable> Node; private: Node *root; Node *nullNode; CrefcComparable> elementAt( Node *t
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/ / Recursive routines void insert( const Comparable void remove( const Comparable void makeEmpty( Node * & t 1 ;
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const;
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x, Node * x, Node *
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/ / Rotations
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void void void void
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skew( Node * & t ) const; split( Node * & t ) const; rotateWithLeftChild( Node * & t ) const; rotateWithRightChild( Node * & t ) const;
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AANodeiComparable> * clone( Node * t 1;
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Figure 1965 The class interface for AA-trees
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Internal method to insert into a subtree x is the item to insert t is the node that roots the tree Set the new root Throw DuplicateItemException if x is already in t template <class Comparable> void AATree<Comparable>:: insert( const Comparable & x , Node * & t )
/ / / / /
/ / / / /
if( t = = nullNode ) t = new Node( x, nullNode, nullNode else if( x < t->element ) insert ( x , t->left ) ; else if( t->element < x ) insert ( x, t->right ) ; else throw DuplicateItemException( ) ; skew( t ) ; split( t 1 ; 1
Figure 1966 The insert routine for the AATree class
The deleteaode variable points at the node containing x (if x is found) or nullNode if x is not found The lastNode variable points at the replacementnode\rlle use two-way comparisons instead of three-way comparisons
Figure 1967 skew and split are easily implemented, using the already existing tree rotations Finally, remove is shown in Figure 1968 To help us out, we keep two variables, deletedNode and lastNode, that have lifetime scope by virtue of their stat i c declaration When we traverse a right child, we adjust deletedNodeBecause we call remove recursively until we reach the bottom (we do not test for equality on the way down), we are guaranteed that, if the item to be removed is in the tree, deletedNode will point at the node that contains it Note that this technique can be used in the find procedure to replace the three-way comparisons done at each node with two-way comparisons at each node plus one extra equality test at the bottom lastNode points at the level-] node at which this search terminates Because we do not stop until we reach the bottom, if the item is in the tree, lastNode will point at the level-1 node that contains the replacement value and must be removed from the tree After a given recursive call terminates, we are either at level 1 or we are not If we are at level 1 , we can copy the node's value into the internal node that is to be replaced; we can then call delete Otherwise, we are at a higher level, and we need to determine whether the balance condition has been violated If so, we restore the balance and then make three calls to skew and two calls to splitAs discussed previously, these actions guarantee that the AA-tree properties will be restored
Implementing the STL set and map Classes
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/ / Skew primitive for AA-trees / / t is the node that roots the tree
template <class Comparable> void AATree<Comparable>::skew( Node * i if( t->left->level = = t->level ) rotateiqithleftChild( t ) ; 1
/ / Split primitive for M - t r e e s / / t is the node that roots the tree
const
template <class Comparable> void AATree<Comparable>::spliti Node *
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if( t->right->right->level == t->level i
rotate$:ithRightChild( t t->level++;
Figure 1967 The skew and split procedures for the AATree class
197 Implementing the STL set and m a g Classes
In this section we provide a reasonably efficient implementation of the STL set and nap classes, with additional error checking that is not provided in the STL The code is a blend of the STL list implementation presented in Section 175 and the AA-tree implementation in Section 196 The AA-tree details are, for the most part, not reproduced here because the core private routines such as the tree rotations, recursive insertion and removal, and makeEmpty and clone are essentially unchanged Those routines are contained in the online code Additionally, owing to space constraints, this code is poorly commented and relies on the accompanying text for explanation of any tricky details The online code has the appropriate comments The basic implementation resembles that of the list class with its node, set, and iterator classes However there are three main differences between the classes
1 The set class has two template parameters The second template parameter is a comparison function that assigns a meaning to