Automatically Assign Parent Terms When A Child Term is Selected

I have deep hierarchical taxonomy and I want to have all parent term assigned when I select a child term. I need it for category structure on a online listing/classified site.

CPT name: product

Taxonomy Name: product_cat

Hooking into save_post action.

add_action('save_post', 'assign_parent_terms', 10, 2);

function assign_parent_terms($post_id, $post){

    if($post->post_type != 'product')
        return $post_id;

    // get all assigned terms   
    $terms = wp_get_post_terms($post_id, 'product_cat' );
    foreach($terms as $term){
        while($term->parent != 0 && !has_term( $term->parent, 'product_cat', $post )){
            // move upward until we get to 0 level terms
            wp_set_post_terms($post_id, array($term->parent), 'product_cat', true);
            $term = get_term($term->parent, 'product_cat');
        }
    }
}

While loop ensures we go upward until we hit top level terms.