C++ Programming Code Examples
C++ > Data Structures and Algorithm Analysis in C++ Code Examples
Implementation for AA-tree
/* Implementation for AA-tree */
#include "AATree.h"
#include <iostream.h>
/**
* Construct the tree.
*/
template <class Comparable>
AATree<Comparable>::AATree( const Comparable & notFound ) :
ITEM_NOT_FOUND( notFound )
{
nullNode = new AANode<Comparable>;
nullNode->left = nullNode->right = nullNode;
nullNode->level = 0;
root = nullNode;
}
/**
* Copy constructor.
*/
template <class Comparable>
AATree<Comparable>::AATree( const AATree<Comparable> & rhs ) :
ITEM_NOT_FOUND( rhs.ITEM_NOT_FOUND )
{
nullNode = new AANode<Comparable>;
nullNode->left = nullNode->right = nullNode;
nullNode->level = 0;
root = clone( rhs.root );
}
/**
* Destructor for the tree.
*/
template <class Comparable>
AATree<Comparable>::~AATree( )
{
makeEmpty( );
delete nullNode;
}
/**
* Insert x into the tree; duplicates are ignored.
*/
template <class Comparable>
void AATree<Comparable>::insert( const Comparable & x )
{
insert( x, root );
}
/**
* Remove x from the tree. Nothing is done if x is not found.
*/
template <class Comparable>
void AATree<Comparable>::remove( const Comparable & x )
{
remove( x, root );
}
/**
* Find the smallest item in the tree.
* Return smallest item or ITEM_NOT_FOUND if empty.
*/
template <class Comparable>
const Comparable & AATree<Comparable>::findMin( ) const
{
if( isEmpty( ) )
return ITEM_NOT_FOUND;
AANode<Comparable> *ptr = root;
while( ptr->left != nullNode )
ptr = ptr->left;
return ptr->element;
}
/**
* Find the largest item in the tree.
* Return the largest item of ITEM_NOT_FOUND if empty.
*/
template <class Comparable>
const Comparable & AATree<Comparable>::findMax( ) const
{
if( isEmpty( ) )
return ITEM_NOT_FOUND;
AANode<Comparable> *ptr = root;
while( ptr->right != nullNode )
ptr = ptr->right;
return ptr->element;
}
/**
* Find item x in the tree.
* Return the matching item or ITEM_NOT_FOUND if not found.
*/
template <class Comparable>
const Comparable & AATree<Comparable>::
find( const Comparable & x ) const
{
AANode<Comparable> *current = root;
nullNode->element = x;
for( ; ; )
{
if( x < current->element )
current = current->left;
else if( current->element < x )
current = current->right;
else if( current != nullNode )
return current->element;
else
return ITEM_NOT_FOUND;
}
}
/**
* Make the tree logically empty.
*/
template <class Comparable>
void AATree<Comparable>::makeEmpty( )
{
makeEmpty( root );
}
/**
* Test if the tree is logically empty.
* Return true if empty, false otherwise.
*/
template <class Comparable>
bool AATree<Comparable>::isEmpty( ) const
{
return root == nullNode;
}
/**
* Print the tree contents in sorted order.
*/
template <class Comparable>
void AATree<Comparable>::printTree( ) const
{
if( root == nullNode )
cout << "Empty tree" << endl;
else
printTree( root );
}
/**
* Deep copy.
*/
template <class Comparable>
const AATree<Comparable> &
AATree<Comparable>::operator=( const AATree<Comparable> & rhs )
{
if( this != &rhs )
{
makeEmpty( );
root = clone( rhs.root );
}
return *this;
}
/**
* 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.
*/
template <class Comparable>
void AATree<Comparable>::
insert( const Comparable & x, AANode<Comparable> * & t )
{
if( t == nullNode )
t = new AANode<Comparable>( x, nullNode, nullNode );
else if( x < t->element )
insert( x, t->left );
else if( t->element < x )
insert( x, t->right );
else
return; // Duplicate; do nothing
skew( t );
split( t );
}
/**
* Internal method to remove from a subtree.
* x is the item to remove.
* t is the node that roots the tree.
* Set the new root.
*/
template <class Comparable>
void AATree<Comparable>::
remove( const Comparable & x, AANode<Comparable> * & t )
{
static AANode<Comparable> *lastNode, *deletedNode = nullNode;
if( t != nullNode )
{
// Step 1: Search down the tree and set lastNode and deletedNode
lastNode = t;
if( x < t->element )
remove( x, t->left );
else
{
deletedNode = t;
remove( x, t->right );
}
// Step 2: If at the bottom of the tree and
// x is present, we remove it
if( t == lastNode )
{
if( deletedNode == nullNode || x != deletedNode->element )
return; // Item not found; do nothing
deletedNode->element = t->element;
deletedNode = nullNode;
t = t->right;
delete lastNode;
}
// Step 3: Otherwise, we are not at the bottom; rebalance
else
if( t->left->level < t->level - 1 ||
t->right->level < t->level - 1 )
{
if( t->right->level > --t->level )
t->right->level = t->level;
skew( t );
skew( t->right );
skew( t->right->right );
split( t );
split( t->right );
}
}
}
/**
* Internal method to make subtree empty.
*/
template <class Comparable>
void AATree<Comparable>::makeEmpty( AANode<Comparable> * & t )
{
if( t != nullNode )
{
makeEmpty( t->left );
makeEmpty( t->right );
delete t;
}
t = nullNode;
}
/**
* Internal method to print a subtree in sorted order.
* @param t the node that roots the tree.
*/
template <class Comparable>
void AATree<Comparable>::printTree( AANode<Comparable> *t ) const
{
if( t != nullNode )
{
printTree( t->left );
cout << t->element << endl;
printTree( t->right );
}
}
/**
* Rotate binary tree node with left child.
*/
template <class Comparable>
void AATree<Comparable>::rotateWithLeftChild( AANode<Comparable> * & k2 ) const
{
AANode<Comparable> *k1 = k2->left;
k2->left = k1->right;
k1->right = k2;
k2 = k1;
}
/**
* Rotate binary tree node with right child.
*/
template <class Comparable>
void AATree<Comparable>::rotateWithRightChild( AANode<Comparable> * & k1 ) const
{
AANode<Comparable> *k2 = k1->right;
k1->right = k2->left;
k2->left = k1;
k1 = k2;
}
/**
* Skew primitive for AA-trees.
* t is the node that roots the tree.
*/
template <class Comparable>
void AATree<Comparable>::skew( AANode<Comparable> * & t ) const
{
if( t->left->level == t->level )
rotateWithLeftChild( t );
}
/**
* Split primitive for AA-trees.
* t is the node that roots the tree.
*/
template <class Comparable>
void AATree<Comparable>::split( AANode<Comparable> * & t ) const
{
if( t->right->right->level == t->level )
{
rotateWithRightChild( t );
t->level++;
}
}
/**
* Internal method to clone subtree.
*/
template <class Comparable>
AANode<Comparable> *
AATree<Comparable>::clone( AANode<Comparable> * t ) const
{
if( t == t->left ) // Cannot test against nullNode!!!
return nullNode;
else
return new AANode<Comparable>( t->element, clone( t->left ),
clone( t->right ), t->level );
}
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