WP: remove custom post type slug from post url and make unique post slugs among post types

gistfile1.php

/**
 * Register your custom post type: write all the settings you like in $args.
 *
 * Note the 'slug' set to '/' to remove custom post type slug from url e.g.
 * "/post-slug" instead of default "/custom-type-slug/post-slug"
 */
public function register_my_custom_type() {

	$args = array( 
		/* ... */
		'rewrite' => array('slug' => '/'),
		/* ... */
	); 

	register_post_type( 'custom_type', $args );	
}
add_action( 'init', 'register_my_custom_type' );



/**
 * Check a post slug against among all post types, instead of default WP that allow same slugs for different post types.
 *
 * Include this function as it is. The code is based on wp_unique_post_slug() core function, where the filter is applied.
 *
 * @see wp_unique_post_slug()
 * 
 * @param $slug
 * @param $post_ID
 * @param $post_status
 * @param $post_type
 * @param $post_parent
 * @param $original_slug
 * @return string
 */
function make_unique_post_type_slug ($slug, $post_ID, $post_status, $post_type, $post_parent, $original_slug) {

	global $wpdb, $wp_rewrite;

	$feeds = $wp_rewrite->feeds;
	if ( ! is_array( $feeds ) )
		$feeds = array();

	/*
	 * If a post and one of its attach has the same slug, be sure the rewrite of a post "beats" the attach rewrite.
	 * In this way, the original slug is assigned to the post.
	 * The attach has another slug automatically assigned: you can edit later editing the media screen.
	 */
	$not_attach = '';
	if ( 'attachment' != $post_type ) {
		$not_attach = " AND post_type != 'attachment' ";
	}

        $check_sql = "SELECT post_name FROM $wpdb->posts WHERE post_name = %s AND ID != %d {$not_attach} LIMIT 1";
	$post_name_check = $wpdb->get_var( $wpdb->prepare( $check_sql, $original_slug, $post_ID ) );

	if ( $post_name_check || in_array( $original_slug, $feeds ) ) {
		$suffix = 2;
		do {
			$alt_post_name = _truncate_post_slug( $original_slug, 200 - ( strlen( $suffix ) + 1 ) ) . "-$suffix";
			$post_name_check = $wpdb->get_var( $wpdb->prepare( $check_sql, $alt_post_name, $post_type, $post_ID ) );
			$suffix++;
		} while ( $post_name_check );
		$slug = $alt_post_name;
	} else {
		$slug = $original_slug;
	}

	return $slug;
}
add_filter( 'wp_unique_post_slug', 'make_unique_post_type_slug', 100, 6 );