$ sudo /etc/init.d/mysql stop

$ sudo mysqld_safe --skip-grant-tables &
   

[1] 24361 
$180426 10:20:56 mysqld_safe Logging to syslog.
180426 10:20:57 mysqld_safe Starting mysqld daemon with databases from /var/lib/mysql 

$ mysql -u root
Welcome to the MariaDB monitor.  Commands end with ; or \g.
Your MariaDB connection id is 1
Server version: 5.5.33a-MariaDB MariaDB Server
   
Copyright (c) 2000, 2013, Oracle, Monty Program Ab and others.
   
Type 'help;' or '\h' for help. Type '\c' to clear the current input statement.
MariaDB >

MariaDB [(none)]> use mysql;
Reading table information for completion of table and column names
You can turn off this feature to get a quicker startup with -A
Database changed
   
MariaDB [mysql]> update user set password=PASSWORD("new_password;") where User='root';
Query OK, 1 row affected (0.01 sec)
Rows matched: 1  Changed: 1  Warnings: 0
   
MariaDB [mysql]> flush privileges;
Query OK, 0 rows affected (0.00 sec)
   
MariaDB [mysql]> quit
Bye

$ sudo /etc/init.d/mysql restart

# mysql -u root -p
Enter password: 
Welcome to the MariaDB monitor.  Commands end with ; or \g.
Your MariaDB connection id is 4
Server version: 10.1.29-MariaDB-6 Debian buildd-unstable
   
Copyright (c) 2000, 2017, Oracle, MariaDB Corporation Ab and others.
   
Type 'help;' or '\h' for help. Type '\c' to clear the current input statement.
   
MariaDB [(none)]>

ERROR 1698 (28000): Access denied for user 'root'@'localhost'

MariaDB [(none)]> use mysql;
Reading table information for completion of table and column names
You can turn off this feature to get a quicker startup with -A
Database changed
   
Database changed
MariaDB [mysql]> UPDATE user SET plugin="";
Query OK, 1 row affected (0.00 sec)
Rows matched: 1  Changed: 1  Warnings: 0
   
MariaDB [mysql]> flush privileges;
Query OK, 0 rows affected (0.00 sec)
   
MariaDB [mysql]> quit
Bye