Walker::paged_walk()

	public function paged_walk( $elements, $max_depth, $page_num, $per_page, ...$args ) {
		if ( empty( $elements ) || $max_depth < -1 ) {
			return '';
		}

		$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 ( empty( $e->$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;
	}