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1 / / Internal method to remove from a subtree 2 / / x is the item to remove 3 / I t is the node that roots the tree 4 / / Set the new root 5 j / Throw ItemNotFoundException is x is not in I 6 template <class Comparable> 7 void AATreeiComparable>:: 8 remove ( const Comparable & x , Node * & t i 9 i 10 static Node "lastNode, *deletedNode = nullNode; 11 12 if( t ! = nullNode ) 13 i 14 / / Step 1: Search down the tree and 15 // set lastNode and deletemode 16 lastNode = t ; 17 if( x i +>element ) 18 remove ( x, I->left ) ; 19 else 20 { 2 1 deletedNode = I; 22 remove ( x, t->right ) ; 23 } 24 ! / Step 2 : If at the bottom of the tree and , 25 / / x is present, we remove it 26 if ( t = = lastNode 27 I 28 if( deletedNode == nullNode ) 1 29 x ! = deletemode->element 30 throw ItemNotFoundException( 1 ; 31 deletemode->element = t->element; 32 deletedNode = nullNode; 33 t = t->right; 34 delete lastNode; 35 i 36 / / Step 3 : Otherwise, not at the bottom; rebalance 37 else 38 if( t->left->level < t->level 1 ) 1 39 t->right->level < t->level - 1 ) 40 i 4 1 if( t->right->level > -t->level ) 42 t->right->level = t->level; 43 skew ( t ) ; 44 skew( t->right 1 ; 45 skew( I->right->right ) ; 46 split( t ) ; 47 split( t->right ) ; 48 I 49 1 50 1
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Figure 1968 The remove method for AA-trees
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2 Generally speaking, the set class has more methods than does the
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3 The set iteration routines are more complex than those of the
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For simplicity, our implementation provides only forward iteration We must decide how to perform the traversal Several alternatives are available:
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1 use parent pointers; 2 have the iterator maintain a stack that represents the nodes on the path to the current position; and 3, have each node maintain a pointer to its inorder successor, a technique known as a threaded tree
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To make the code look as much as possible like the AA-tree code in Section 196, we use the option of having the iterator maintain a stack However, this approach has the significant disadvantage of potentially making iterator objects expensive to copy We leave using parent pointers for you to do as Exercise 193I Figure 1969 shows the basic node class, along with the typical set of incomplete class declarations The set class interface is shown next, in Figure 1970 At line 35 is the data member that stores the comparison function object The routines in lines 41-50 are essentially identical to their AA-tree counterparts For instance, the only difference between the insert method at line 42 and the one in the AATree class is that the AAtree version throws an exception if a duplicate is inserted whereas this insert returns falseThe public methods simply follow the specifications described in Section 77 Figure 1971 contains the interface for the const set I tr class Much 1 of it is similar to that in the list class Line 2 declares path,which is a stack that keeps track of the path to the current node Various assertions are declared at lines 24-27 We also provide some hidden methods that can be used to traverse the tree (goLeft,for example, moves left, and updates path) at lines 31-36 There is no nonconstant iterator class The reason is that if we allow *itr to change a value in the set,it is possible to destroy the order in the setThus iterator and const-iterator represent the same type in our implementation The constructors and Big Three for the s e t class are shown in Figure 1972 The private helpers, init and makeEmpty,are also shown (but the recursive makeEmpty is not) Figure 1973 shows begin,end, size, and emptyThe begin algorithm is to simply go left repeatedly For end, recall that the end iterator represents a position that is one past the last item
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