How to configure in IdeaVIM Ctrl + N and Ctrl + P completion from Vim?

This is the way I found to make the word completion work with CTRL-N and CTRL-P, while still having the shortcuts work for DOWN and UP in lists.

In Settings -> Keymap, map CTRL-N and CTRL-P to Down and Up respectively. Then, in the Other Settings -> Vim Emulation, set CTRL-N and CTRL-P handlers to Vim.

Finally, add the following to your .ideavimrc

imap <C-n> <ESC>:action HippieCompletion<CR>a
imap <C-p> <ESC>:action HippieBackwardCompletion<CR>a

Alt + / and Alt + Shift + / work both in plain IntelliJ and with IdeaVim installed.

Please see documentation on JetBrains page - it's called Hippie Completion (newer versions call this completion Cyclic Expand Word).

And of course you can always use Ctrl + Space, Ctrl + Shift + Space, Ctrl + Alt + Space.

I could not get CTRL-N and CTRL-P to work after mapping them to "Cyclic Expand Word" and "Cyclic Expand Word (Backward)" in IDEA 2016.2.5 (while running IdeaVIM). Both keystrokes just did nothing.

The solution was to additionally select "Settings" from the File Menu, then "Other Settings" -> "Vim Emulation", and set the "Handler" for Ctrl+N and Ctrl+P to "IDE" instead of "Vim".