数据结构-二叉搜索树

实现：

#ifndef BINARY_SEARCH_TREE_H
#define BINARY_SEARCH_TREE_H

#include "dsexceptions.h"
#include <iostream>    // For NULL
using namespace std;       

// BinarySearchTree class
//
// CONSTRUCTION: with ITEM_NOT_FOUND object used to signal failed finds
//
// ******************PUBLIC OPERATIONS*********************
// void insert( x )       --> Insert x
// void remove( x )       --> Remove x
// bool contains( x )     --> Return true if x is present
// Comparable findMin( )  --> Return smallest item
// Comparable findMax( )  --> Return largest item
// boolean isEmpty( )     --> Return true if empty; else false
// void makeEmpty( )      --> Remove all items
// void printTree( )      --> Print tree in sorted order
// ******************ERRORS********************************
// Throws UnderflowException as warranted

template <typename Comparable>
class BinarySearchTree
{
  public:
    BinarySearchTree( ) :root( NULL )
    {
    }

    BinarySearchTree( const BinarySearchTree & rhs ) : root( NULL )
    {
        *this = rhs;
    }

    /**
     * Destructor for the tree
     */
    ~BinarySearchTree( )
    {
        makeEmpty( );
    }

    /**
     * Find the smallest item in the tree.
     * Throw UnderflowException if empty.
     */
    const Comparable & findMin( ) const
    {
        if( isEmpty( ) )
            throw UnderflowException( );
        return findMin( root )->element;
    }

    /**
     * Find the largest item in the tree.
     * Throw UnderflowException if empty.
     */
    const Comparable & findMax( ) const
    {
        if( isEmpty( ) )
            throw UnderflowException( );
        return findMax( root )->element;
    }

    /**
     * Returns true if x is found in the tree.
     */
    bool contains( const Comparable & x ) const
    {
        return contains( x, root );
    }

    /**
     * Test if the tree is logically empty.
     * Return true if empty, false otherwise.
     */
    bool isEmpty( ) const
    {
        return root == NULL;
    }

    /**
     * Print the tree contents in sorted order.
     */
    void printTree( ostream & out = cout ) const
    {
        if( isEmpty( ) )
            out << "Empty tree" << endl;
        else
            printTree( root, out );
    }

    /**
     * Make the tree logically empty.
     */
    void makeEmpty( )
    {
        makeEmpty( root );
    }

    /**
     * Insert x into the tree; duplicates are ignored.
     */
    void insert( const Comparable & x )
    {
        insert( x, root );
    }
     
    /**
     * Remove x from the tree. Nothing is done if x is not found.
     */
    void remove( const Comparable & x )
    {
        remove( x, root );
    }

    /**
     * Deep copy.
     */
    const BinarySearchTree & operator=( const BinarySearchTree & rhs )
    {
        if( this != &rhs )
        {
            makeEmpty( );
            root = clone( rhs.root );
        }
        return *this;
    }

  private:
    struct BinaryNode
    {
        Comparable element;
        BinaryNode *left;
        BinaryNode *right;

        BinaryNode( const Comparable & theElement, BinaryNode *lt, BinaryNode *rt )
            : element( theElement ), left( lt ), right( rt ) { }
    };

    BinaryNode *root;


    /**
     * Internal method to insert into a subtree.
     * x is the item to insert.
     * t is the node that roots the subtree.
     * Set the new root of the subtree.
     */
    void insert( const Comparable & x, BinaryNode * & t )
    {
        if( t == NULL )
            t = new BinaryNode( x, NULL, NULL );
        else if( x < t->element )
            insert( x, t->left );
        else if( t->element < x )
            insert( x, t->right );
        else
            ;  // Duplicate; do nothing
    }

    /**
     * Internal method to remove from a subtree.
     * x is the item to remove.
     * t is the node that roots the subtree.
     * Set the new root of the subtree.
     */
    void remove( const Comparable & x, BinaryNode * & t )
    {
        if( t == NULL )
            return;   // Item not found; do nothing
        if( x < t->element )
            remove( x, t->left );
        else if( t->element < x )
            remove( x, t->right );
        else if( t->left != NULL && t->right != NULL ) // Two children
        {
            t->element = findMin( t->right )->element;
            remove( t->element, t->right );
        }
        else
        {
            BinaryNode *oldNode = t;
            t = ( t->left != NULL ) ? t->left : t->right;
            delete oldNode;
        }
    }

    /**
     * Internal method to find the smallest item in a subtree t.
     * Return node containing the smallest item.
     */
    BinaryNode * findMin( BinaryNode *t ) const
    {
        if( t == NULL )
            return NULL;
        if( t->left == NULL )
            return t;
        return findMin( t->left );
    }

    /**
     * Internal method to find the largest item in a subtree t.
     * Return node containing the largest item.
     */
    BinaryNode * findMax( BinaryNode *t ) const
    {
        if( t != NULL )
            while( t->right != NULL )
                t = t->right;
        return t;
    }


    /**
     * Internal method to test if an item is in a subtree.
     * x is item to search for.
     * t is the node that roots the subtree.
     */
    bool contains( const Comparable & x, BinaryNode *t ) const
    {
        if( t == NULL )
            return false;
        else if( x < t->element )
            return contains( x, t->left );
        else if( t->element < x )
            return contains( x, t->right );
        else
            return true;    // Match
    }
/****** NONRECURSIVE VERSION*************************
    bool contains( const Comparable & x, BinaryNode *t ) const
    {
        while( t != NULL )
            if( x < t->element )
                t = t->left;
            else if( t->element < x )
                t = t->right;
            else
                return true;    // Match

        return false;   // No match
    }
*****************************************************/

    /**
     * Internal method to make subtree empty.
     */
    void makeEmpty( BinaryNode * & t )
    {
        if( t != NULL )
        {
            makeEmpty( t->left );
            makeEmpty( t->right );
            delete t;
        }
        t = NULL;
    }

    /**
     * Internal method to print a subtree rooted at t in sorted order.
     */
    void printTree( BinaryNode *t, ostream & out ) const
    {
        if( t != NULL )
        {
            printTree( t->left, out );
            out << t->element << endl;
            printTree( t->right, out );
        }
    }

    /**
     * Internal method to clone subtree.
     */
    BinaryNode * clone( BinaryNode *t ) const
    {
        if( t == NULL )
            return NULL;
        else
            return new BinaryNode( t->element, clone( t->left ), clone( t->right ) );
    }
};

#endif

测试：

#include <iostream>
#include "BinarySearchTree.h"
using namespace std;

    // Test program
int main( )
{
    BinarySearchTree<int> t;
    int NUMS = 400000;
    const int GAP  =   3711;
    int i;

    cout << "Checking... (no more output means success)" << endl;

    for( i = GAP; i != 0; i = ( i + GAP ) % NUMS )
        t.insert( i );

    for( i = 1; i < NUMS; i+= 2 )
        t.remove( i );

    if( NUMS < 40 )
        t.printTree( );
    if( t.findMin( ) != 2 || t.findMax( ) != NUMS - 2 )
        cout << "FindMin or FindMax error!" << endl;

    for( i = 2; i < NUMS; i+=2 )
        if( !t.contains( i ) )
            cout << "Find error1!" << endl;

    for( i = 1; i < NUMS; i+=2 )
    {
        if( t.contains( i ) )
            cout << "Find error2!" << endl;
    }

    BinarySearchTree<int> t2;
    t2 = t;

    for( i = 2; i < NUMS; i+=2 )
        if( !t2.contains( i ) )
            cout << "Find error1!" << endl;

    for( i = 1; i < NUMS; i+=2 )
    {
        if( t2.contains( i ) )
            cout << "Find error2!" << endl;
    }

    cout << "Finished testing" << endl;

    return 0;
}