For my old job I used to have to manage about 60 passwords that all had different time limits on when they needed to be changed (one was every 3 weeks and some lasted a year for example). I never used a manager because of 2 reasons; insuring my passwords on someone else’s computer (aka the “cloud”) is fundamentally insane and maybe more importantly the passwords are not used all on the same machine (end users server, phone, laptop, on the phone etc.).
If I did not use a similar system of “algorithms” I would go insane. Although this was on paper or in my head. I would normally use the month changed, and a cycling root password with the needed special characters in between. For example for a password changed today that required a min of 8 characters and at least one cap and special it would be “Jun” + “!&@” + “1Firstoflistpassword” if there was a limit of say max of 8 then it would not use more then the first 2 letters of the password and if no special characters permitted then the center was dropped.