ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: NO)

2016-10-26T10:23:01.845088Z 0 [Warning] User entry 'root'@'localhost' has an empty plugin value. The user will be ignored and no one can login with this user anymore.
2016-10-26T10:23:01.845112Z 0 [Warning] User entry 'mysql.sys'@'localhost' has an empty plugin value. The user will be ignored and no one can login with this user anymore.
2016-10-26T10:23:01.845127Z 0 [Warning] User entry 'debian-sys-maint'@'localhost' has an empty plugin value. The user will be ignored and no one can login with this user anymore.
2016-10-26T10:23:01.845142Z 0 [Warning] User entry 'phpmyadmin'@'localhost' has an empty plugin value. The user will be ignored and no one can login with this user anymore.
2016-10-26T10:23:01.845155Z 0 [Warning] Some of the user accounts with SUPER privileges were disabled because of empty mysql.user.plugin value. If you are upgrading from MySQL 5.6 to MySQL 5.7 it means we were not able to substitute for empty plugin column. Probably because of pre 4.1 password hash. If your account is disabled you will need to:
2016-10-26T10:23:01.845183Z 0 [Warning] 1. Stop the server and restart it with --skip-grant-tables.
2016-10-26T10:23:01.845192Z 0 [Warning] 2. Run mysql_upgrade.
2016-10-26T10:23:01.845200Z 0 [Warning] 3. Restart the server with the parameters you normally use.
2016-10-26T10:23:01.845207Z 0 [Warning] For complete instructions on how to upgrade MySQL to a new version please see the 'Upgrading MySQL' section from the MySQL manual
2016-10-26T10:23:01.853461Z 0 [Note] Event Scheduler: Loaded 0 events
2016-10-26T10:23:01.853962Z 0 [Note] /usr/sbin/mysqld: ready for connections.
Version: '5.7.16-0ubuntu0.16.04.1'  socket: '/var/run/mysqld/mysqld.sock'  port: 3306  (Ubuntu)
2016-10-26T10:23:02.138961Z 2 [Note] Access denied for user 'root'@'localhost' (using password: NO)

> service mysql stop

> sudo mysqld_safe --skip-grant-tables

> sudo mysql_upgrade

2016-10-26T10:40:54.073975Z 0 [ERROR] InnoDB: Unable to lock ./ibdata1 error: 11
2016-10-26T10:40:54.074060Z 0 [Note] InnoDB: Check that you do not already have another mysqld process using the same InnoDB data or log files.

> service mysql start

> mysqldump -u root -p --databases db1 db2 > alldb.sql

> sudo apt-get purge mysql-server mysql-client mysql-common mysql-server-core-5.7 mysql-client-core-5.7
> sudo rm -rf /etc/mysql /var/lib/mysql
> sudo apt-get autoremove
> sudo apt-get autoclean

> sudo apt-get install mysql-server

> mysql -u root -p < alldb.sql

> sudo service stop mysql
> sudo mkdir /var/run/mysqld # needed to launch mysql in ubuntu from command line...may not apply to other distros
> sudo chown mysql:mysql /var/run/mysqld # same reason as above
> sudo mysqld_safe --skip-grant-tables

> mysql -uroot
> select User, host, authentication_string,plugin from mysql.user; #see what users don't have a password (authentication_string and plugin are empty)
> update mysql.user set authentication_string=PASSWORD('woot') where user='user';
> update mysql.user set plugin='mysql_native_password' where user='user';
> FLUSH PRIVILEGES;
> exit;

> ^ #to tell the mysqld_safe process to quit itself
> sudo service mysqld start