#include <iostream>
    #include <vector>

    using namespace std;

    /**
     * Quick illustration of a two-dimensional tree.
     * No abstraction here.
     */
    template <class Comparable>
    class KdTree
    {
      public:
        KdTree( ) : root( NULL ) { }

        void insert( const vector<Comparable> & x )
        {
            insert( x, root, 0 );
        }

        /**
         * Print items satisfying
         * low[ 0 ] <= x[ 0 ] <= high[ 0 ] and
         * low[ 1 ] <= x[ 1 ] <= high[ 1 ]
         */
        void printRange( const vector<Comparable> & low, 
                         const vector<Comparable> & high ) const
        {
            printRange( low, high, root, 0 );
        }

      private:
        struct KdNode
        {
            vector<Comparable> data;
            KdNode            *left;
            KdNode            *right;

            KdNode( const vector<Comparable> & item )
              : data( item ), left( NULL ), right( NULL ) { }
        };

        KdNode *root;

        void insert( const vector<Comparable> & x, KdNode * & t, int level )
        {
            if( t == NULL )
                t = new KdNode( x );
            else if( x[ level ] < t->data[ level ] )
                insert( x, t->left, 1 - level );
            else
                insert( x, t->right, 1 - level );
        }


        void printRange( const vector<Comparable> & low,
                         const vector<Comparable> & high,
                         KdNode *t, int level ) const
        {
            if( t != NULL )
            {
                if( low[ 0 ] <= t->data[ 0 ] && high[ 0 ] >= t->data[ 0 ] && 
                    low[ 1 ] <= t->data[ 1 ] && high[ 1 ] >= t->data[ 1 ] )
                    cout << "(" << t->data[ 0 ] << "," 
                                << t->data[ 1 ] << ")" << endl;

                if( low[ level ] <= t->data[ level ] )
                    printRange( low, high, t->left, 1 - level );
                if( high[ level ] >= t->data[ level ] )
                    printRange( low, high, t->right, 1 - level );
            }
        }
    };

        // Test program
        int main( )
        {
            KdTree<int> t;
            
            cout << "Starting program" << endl;
            for( int i = 300; i < 370; i++ )
            {
                vector<int> it( 2 );
                it[ 0 ] =  i;
                it[ 1 ] =  2500 - i;
                t.insert( it );
            }

            vector<int> low( 2 ), high( 2 );
            low[ 0 ] = 70;
            low[ 1 ] = 2186;
            high[ 0 ] = 1200;
            high[ 1 ] = 2200;

            t.printRange( low, high );

            return 0;
        }