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