*
	 * $max_depth = 0 means display all levels.
	 * $max_depth > 0 specifies the number of display levels.
	 *
 	 * @since 2.7.0
	 *
	 * @param array $elements
	 * @param int   $max_depth The maximum hierarchical depth.
	 * @param int   $page_num The specific page number, beginning with 1.
	 * @param int   $per_page
	 * @return string XHTML of the specified page of elements
	 */
	public function paged_walk( $elements, $max_depth, $page_num, $per_page ) {
		if ( empty( $elements ) || $max_depth < -1 ) {
			return '';
		}

		$args = array_slice( func_get_args(), 4 );
		$output = '';

		$parent_field = $this->db_fields['parent'];

		$count = -1;
		if ( -1 == $max_depth )
			$total_top = count( $elements );
		if ( $page_num < 1 || $per_page < 0  ) {
			// No paging
			$paging = false;
			$start = 0;
			if ( -1 == $max_depth )
				$end = $total_top;
			$this->max_pages = 1;
		} else {
			$paging = true;
			$start = ( (int)$page_num - 1 ) * (int)$per_page;
			$end   = $start + $per_page;
			if ( -1 == $max_depth )
				$this->max_pages = ceil($total_top / $per_page);
		}

		// flat display
		if ( -1 == $max_depth ) {
			if ( !empty($args[0]['reverse_top_level']) ) {
				$elements = array_reverse( $elements );
				$oldstart = $start;
				$start = $total_top - $end;
				$end = $total_top - $oldstart;
			}

			$empty_array = array();
			foreach ( $elements as $e ) {
				$count++;
				if ( $count < $start )
					continue;
				if ( $count >= $end )
					break;
				$this->display_element( $e, $empty_array, 1, 0, $args, $output );
			}
			return $output;
		}

		/*
		 * Separate elements into two buckets: top level and children elements.
		 * Children_elements is two dimensional array, e.g.
		 * $children_elements[10][] contains all sub-elements whose parent is 10.
		 */
		$top_level_elements = array();
		$children_elements  = array();
		foreach ( $elements as $e) {
			if ( 0 == $e->$parent_field )
				$top_level_elements[] = $e;
			else
				$children_elements[ $e->$parent_field ][] = $e;
		}

		$total_top = count( $top_level_elements );
		if ( $paging )
			$this->max_pages = ceil($total_top / $per_page);
		else
			$end = $total_top;

		if ( !empty($args[0]['reverse_top_level']) ) {
			$top_level_elements = array_reverse( $top_level_elements );
			$oldstart = $start;
			$start = $total_top - $end;
			$end = $total_top - $oldstart;
		}
		if ( !empty($args[0]['reverse_children']) ) {
			foreach ( $children_elements as $parent => $children )
				$children_elements[$parent] = array_reverse( $children );
		}

		foreach ( $top_level_elements as $e ) {
			$count++;

			// For the last page, need to unset earlier children in order to keep track of orphans.
			if ( $end >= $total_top && $count < $start )
					$this->unset_children( $e, $children_elements );

			if ( $count < $start )
				continue;

			if ( $count >= $end )
				break;

			$this->display_element( $e, $children_elements, $max_depth, 0, $args, $output );
		}

		if ( $end >= $total_top && count( $children_elements ) > 0 ) {
			$empty_array = array();
			foreach ( $children_elements as $orphans )
				foreach ( $orphans as $op )
					$this->display_element( $op, $empty_array, 1, 0, $args, $output );
		}

		return $output;
	}

	/**
	 * Calculates the total number of root elements.
	 *
	 * @since 2.7.0
	 *
	 * @param array $elements Elements to list.
	 * @return int Number of root elements.
	 */
	public function get_number_of_root_elements( $elements ){
		$num = 0;
		$parent_field = $this->db_fields['parent'];

		foreach ( $elements as $e) {
			if ( 0 == $e->$parent_field )
				$num++;
		}
		return $num;
	}

	/**
	 * Unset all the children for a given top level element.
	 *
	 * @since 2.7.0
	 *
	 * @param object $e
	 * @param array $children_elements
	 */
	public function unset_children( $e, &$children_elements ){
		if ( ! $e || ! $children_elements ) {
			return;
		}

		$id_field = $this->db_fields['id'];
		$id = $e->$id_field;

		if ( !empty($children_elements[$id]) && is_array($children_elements[$id]) )
			foreach ( (array) $children_elements[$id] as $child )
				$this->unset_children( $child, $children_elements );

		unset( $children_elements[ $id ] );
	}

} // Walker