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Logically, the only changes required are the adding of f indKth and the maintenance of the size data members in insert, remove, and removeMinWe derive a new class from BinarySearchTree,the interface for which is shown in Figure 1914 We need to make the new class a friend of BinaryNode Let us first examine the new public member functions Because constructors and a destructor are not explicitly provided, the defaults are used For the constructor, the inherited data member is initialized by the BinarySearchTree constructor For the destructor, the base class destructor is eventually called to clean up the memory The publicly visible member functions find~thinsert,remove,and , removeMin, declared at lines 15, 17, 19, and 21, respectively, logically call a corresponding hidden member function We might expect that a routine such as insert at line 17 does not need to be redefined, as its body is simply a call to the BinarySearchTree insertHowever, because we are rewriting the hidden recursive versions of insert,remove,and removeMin,
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We must redefine both the hidden and public update functions
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/ / BinarySearchTreeWithRank class // / / CONSTRUCTION: with no parameters or // another BinarySearchTreeWithRank
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6 / / ******************~~BLIc E R F ; T I o N s * * * * * * * * * * * * * * * * * * * * * o~ 7 / / Comparable findKth( k )--> Return kth smallest item 8 / / All other operations are in effect inherited 9 10 template <class Comparable> 11 class BinarySearchTreeWithRank : 12 public ~inarySearchTree<Comparable> 13 { 14 public: 15 Cref<Comparable> findKth( int k ) const 16 { return elementAt( findKth( k, root ) ; } 17 void insert( const Comparable & x ) 18 ( BinarySearchTree<Comparable>::insert(x ) ; 1 19 void remove( const Comparable & x i 20 { BinarySearchTree<Comparable>::remove(x 1 ; I 21 void removeMin( ) 22 { BinarySearchTree<Comparable>::removeMin( 1 ; 1 23 typedef BinaryNode<Comparable> Node; 24 25 26 private: 27 void insert( const Comparable & x, Node * & t ) const; 28 void remove( const Comparable & x , Node * & t ) const; 29 void removeMin( Node * & t ) const; 30 Node *findKth( int k , Node *t ) const; 31 int treesize( Node *t ) const 32 33 ( return t == NULL 0 : t->size; 1 34 1 ;
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Figure 1914 The BinarySearchTree class interface
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these versions hide the public members with the same name (see Section 443) Thus for this technical reason, we rewrite the public member functions and have them simply call the corresponding base class member functions This is C++ ugliness because, if the private member functions in the BinarySearchTree base class simply would have had different names than their public counterparts, we would have been able to completely remove lines 1 7-22 in Figure 1914 and only had to override the private member functions (In Exercise 1919 you are asked to rewrite both classes to verify that this assertion is true)
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template <class Comparabie> BinaryNode<Comparable> * BinarySearchTreeWithRank<Comparable>:: 6 findKth( int k , Node * t ) const 7 { 8 if( t = = N U L L ) 9 return NULL; 10 11 int leftsize = treesize( t->left ) ; 12 13 if( k < = leftsize ) 14 return findKtn( k , t->left ) ; 15 else if( k == leftsize + 1 ) 16 return t ; 17 else 18 return findKtn( k - leftsize - 1, t->right ) ; 19 Figure 1915 The f i n d K t h operation for a search tree with order statistics
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/ / Internal method to find kth item in a subtree / / k is the desired rank / / t is the node that roots the tree
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The f i n d K t h operation shown in Figure 1915 is written recursively, although clearly it need not be It follows the algorithmic description line for line The test against NULL at line 8 is necessary because k could be invalid At line I 1 we compute the size of the left subtree If the left subtree exists, accessing its s i z e member gives the required answer If the left subtree does not exist, its size can be taken to be 0 (see the definition of t r e e s i z e at lines 32 and 33 in the class interface) Note that this test is performed after we are sure that t is not NULL The i n s e r t operation is shown in Figure 1916 The potentially tricky part is that, if the insertion call succeeds, we want to increment t ' s s i z e member If the recursive call fails, t ' s s i z e member is unchanged and an exception should be thrown In an unsuccessful insertion can some sizes change The answer is no; s i z e is updated only if the recursive call succeeds without an exception Note that when a new node is allocated by a call to new, the s i z e member is set to 0 by the B i n a r y N o d e constructor, and then incremented at line I 8 Figure 1917 shows that the same trick can be used for removeMin If the recursive call succeeds, the s i z e member is decremented; if the recursive call fails, s i z e is unchanged The remove operation is similar and is shown in Figure 1918
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