MySQL connection problem (using password: No)

Error 1045 (28000): Access denied for user 'root' @ 'localhost' (using password: No)
My system is Linux. The newly installed MySQL always has an error prompt when it comes to the MySQL tool:
# Mysql-uroot-P
Enter password:
Error 1045 (28000): Access denied for user 'root' @ 'localhost' (using password: No)

Use the methods described on the Internet to change the password of the root user:
# Mysqladmin-uroot-P password 'newpassword'
Enter password:
Mysqladmin: connect to server at 'localhost' failed
Error: 'Access denied for user' root' @ 'localhost' (using password: Yes )'

Now I have found the solution as follows (Please test method 3 first, thank you !) :
Method 1:
#/Etc/init. d/MySQL stop
# Mysqld_safe -- user = MySQL -- skip-grant-tables -- skip-Networking &
# Mysql-u root MySQL
Mysql> Update user SET Password = PASSWORD ('newpassword') where user = 'root ';
Mysql> flush privileges;
Mysql> quit

#/Etc/init. d/MySQL restart
# Mysql-uroot-P
Enter Password: <enter the new password newpassword>

Mysql>

Method 2:
Directly use the username and password provided in the [client] section of the/etc/MySQL/Debian. CNF file:
# Mysql-udebian-sys-Maint-P
Enter Password: <enter the password in the [client] section>
Mysql> Update user SET Password = PASSWORD ('newpassword') where user = 'root ';
Mysql> flush privileges;
Mysql> quit

# Mysql-uroot-P
Enter Password: <enter the new password newpassword>

Mysql>

Method 3:
I have not tested this method, because the default password of my root user has been modified by me. If you have time to test it, let me know the result. Thank you !!
# Mysql-uroot-P
Enter Password: <enter the password provided in [client] in the/etc/MySQL/Debian. CNF File>

At this point, many problems have been solved!