C++ Programming Code Examples
C++ > Data Structures and Algorithm Analysis in C++ Code Examples
Implementation for AVL tree
/* Implementation for AVL tree */
#include "AvlTree.h"
#include <iostream.h>
/**
* Implements an unbalanced Avl search tree.
* Note that all "matching" is based on the compares method.
*/
/**
* Construct the tree.
*/
template <class Comparable>
AvlTree<Comparable>::AvlTree( const Comparable & notFound ) :
ITEM_NOT_FOUND( notFound ), root( NULL )
{
}
/**
* Copy constructor.
*/
template <class Comparable>
AvlTree<Comparable>::AvlTree( const AvlTree<Comparable> & rhs ) :
ITEM_NOT_FOUND( rhs.ITEM_NOT_FOUND ), root( NULL )
{
*this = rhs;
}
/**
* Destructor for the tree.
*/
template <class Comparable>
AvlTree<Comparable>::~AvlTree( )
{
makeEmpty( );
}
/**
* Insert x into the tree; duplicates are ignored.
*/
template <class Comparable>
void AvlTree<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 AvlTree<Comparable>::remove( const Comparable & x )
{
cout << "Sorry, remove unimplemented; " << x <<
" still present" << endl;
}
/**
* Find the smallest item in the tree.
* Return smallest item or ITEM_NOT_FOUND if empty.
*/
template <class Comparable>
const Comparable & AvlTree<Comparable>::findMin( ) const
{
return elementAt( findMin( root ) );
}
/**
* Find the largest item in the tree.
* Return the largest item of ITEM_NOT_FOUND if empty.
*/
template <class Comparable>
const Comparable & AvlTree<Comparable>::findMax( ) const
{
return elementAt( findMax( root ) );
}
/**
* Find item x in the tree.
* Return the matching item or ITEM_NOT_FOUND if not found.
*/
template <class Comparable>
const Comparable & AvlTree<Comparable>::
find( const Comparable & x ) const
{
return elementAt( find( x, root ) );
}
/**
* Make the tree logically empty.
*/
template <class Comparable>
void AvlTree<Comparable>::makeEmpty( )
{
makeEmpty( root );
}
/**
* Test if the tree is logically empty.
* Return true if empty, false otherwise.
*/
template <class Comparable>
bool AvlTree<Comparable>::isEmpty( ) const
{
return root == NULL;
}
/**
* Print the tree contents in sorted order.
*/
template <class Comparable>
void AvlTree<Comparable>::printTree( ) const
{
if( isEmpty( ) )
cout << "Empty tree" << endl;
else
printTree( root );
}
/**
* Deep copy.
*/
template <class Comparable>
const AvlTree<Comparable> &
AvlTree<Comparable>::
operator=( const AvlTree<Comparable> & rhs )
{
if( this != &rhs )
{
makeEmpty( );
root = clone( rhs.root );
}
return *this;
}
/**
* Internal method to get element field in node t.
* Return the element field or ITEM_NOT_FOUND if t is NULL.
*/
template <class Comparable>
const Comparable & AvlTree<Comparable>::elementAt( AvlNode<Comparable> *t ) const
{
if( t == NULL )
return ITEM_NOT_FOUND;
else
return t->element;
}
/**
* Internal method to insert into a subtree.
* x is the item to insert.
* t is the node that roots the tree.
*/
template <class Comparable>
void AvlTree<Comparable>::insert( const Comparable & x, AvlNode<Comparable> * & t ) const
{
if( t == NULL )
t = new AvlNode<Comparable>( x, NULL, NULL );
else if( x < t->element )
{
insert( x, t->left );
if( height( t->left ) - height( t->right ) == 2 )
if( x < t->left->element )
rotateWithLeftChild( t );
else
doubleWithLeftChild( t );
}
else if( t->element < x )
{
insert( x, t->right );
if( height( t->right ) - height( t->left ) == 2 )
if( t->right->element < x )
rotateWithRightChild( t );
else
doubleWithRightChild( t );
}
else
; // Duplicate; do nothing
t->height = max( height( t->left ), height( t->right ) ) + 1;
}
/**
* Internal method to find the smallest item in a subtree t.
* Return node containing the smallest item.
*/
template <class Comparable>
AvlNode<Comparable> *
AvlTree<Comparable>::findMin( AvlNode<Comparable> *t ) const
{
if( t == NULL)
return t;
while( t->left != NULL )
t = t->left;
return t;
}
/**
* Internal method to find the largest item in a subtree t.
* Return node containing the largest item.
*/
template <class Comparable>
AvlNode<Comparable> *
AvlTree<Comparable>::findMax( AvlNode<Comparable> *t ) const
{
if( t == NULL )
return t;
while( t->right != NULL )
t = t->right;
return t;
}
/**
* Internal method to find an item in a subtree.
* x is item to search for.
* t is the node that roots the tree.
* Return node containing the matched item.
*/
template <class Comparable>
AvlNode<Comparable> *
AvlTree<Comparable>::find( const Comparable & x, AvlNode<Comparable> *t ) const
{
while( t != NULL )
if( x < t->element )
t = t->left;
else if( t->element < x )
t = t->right;
else
return t; // Match
return NULL; // No match
}
/**
* Internal method to make subtree empty.
*/
template <class Comparable>
void AvlTree<Comparable>::makeEmpty( AvlNode<Comparable> * & t ) const
{
if( t != NULL )
{
makeEmpty( t->left );
makeEmpty( t->right );
delete t;
}
t = NULL;
}
/**
* Internal method to clone subtree.
*/
template <class Comparable>
AvlNode<Comparable> *
AvlTree<Comparable>::clone( AvlNode<Comparable> * t ) const
{
if( t == NULL )
return NULL;
else
return new AvlNode<Comparable>( t->element, clone( t->left ),
clone( t->right ), t->height );
}
/**
* Return the height of node t or -1 if NULL.
*/
template <class Comparable>
int AvlTree<Comparable>::height( AvlNode<Comparable> *t ) const
{
return t == NULL ? -1 : t->height;
}
/**
* Return maximum of lhs and rhs.
*/
template <class Comparable>
int AvlTree<Comparable>::max( int lhs, int rhs ) const
{
return lhs > rhs ? lhs : rhs;
}
/**
* Rotate binary tree node with left child.
* For AVL trees, this is a single rotation for case 1.
* Update heights, then set new root.
*/
template <class Comparable>
void AvlTree<Comparable>::rotateWithLeftChild( AvlNode<Comparable> * & k2 ) const
{
AvlNode<Comparable> *k1 = k2->left;
k2->left = k1->right;
k1->right = k2;
k2->height = max( height( k2->left ), height( k2->right ) ) + 1;
k1->height = max( height( k1->left ), k2->height ) + 1;
k2 = k1;
}
/**
* Rotate binary tree node with right child.
* For AVL trees, this is a single rotation for case 4.
* Update heights, then set new root.
*/
template <class Comparable>
void AvlTree<Comparable>::rotateWithRightChild( AvlNode<Comparable> * & k1 ) const
{
AvlNode<Comparable> *k2 = k1->right;
k1->right = k2->left;
k2->left = k1;
k1->height = max( height( k1->left ), height( k1->right ) ) + 1;
k2->height = max( height( k2->right ), k1->height ) + 1;
k1 = k2;
}
/**
* Double rotate binary tree node: first left child.
* with its right child; then node k3 with new left child.
* For AVL trees, this is a double rotation for case 2.
* Update heights, then set new root.
*/
template <class Comparable>
void AvlTree<Comparable>::doubleWithLeftChild( AvlNode<Comparable> * & k3 ) const
{
rotateWithRightChild( k3->left );
rotateWithLeftChild( k3 );
}
/**
* Double rotate binary tree node: first right child.
* with its left child; then node k1 with new right child.
* For AVL trees, this is a double rotation for case 3.
* Update heights, then set new root.
*/
template <class Comparable>
void AvlTree<Comparable>::doubleWithRightChild( AvlNode<Comparable> * & k1 ) const
{
rotateWithLeftChild( k1->right );
rotateWithRightChild( k1 );
}
/**
* Internal method to print a subtree in sorted order.
* t points to the node that roots the tree.
*/
template <class Comparable>
void AvlTree<Comparable>::printTree( AvlNode<Comparable> *t ) const
{
if( t != NULL )
{
printTree( t->left );
cout << t->element << endl;
printTree( t->right );
}
}
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