Add “drop-down arrow” for menu items with sub-menus

I’m using the following code to achieve this. Doesn’t need any walkers or anything else, just insert this into your functions.php and the items with sub-menu will get “menu-parent-item” added as class.

add_filter( 'wp_nav_menu_objects', 'add_menu_parent_class' );
function add_menu_parent_class( $items ) {
    $parents = array();
    foreach ( $items as $item ) {
        //Check if the item is a parent item
        if ( $item->menu_item_parent && $item->menu_item_parent > 0 ) {
            $parents[] = $item->menu_item_parent;
        }
    }

    foreach ( $items as $item ) {
        if ( in_array( $item->ID, $parents ) ) {
            //Add "menu-parent-item" class to parents
            $item->classes[] = 'menu-parent-item'; 
        }
    }

    return $items;    
}

I’ve been using this for a long time. Unfortunately I can’t remember where I found it, so can’t give credits to the one who came up with it.