How to root android one without pc?
You will need to use a PC 
Please have a look at this question recently asked, it brings clarity to the causes of a failure.
Why don't root apps work anymore ?

So after you understand that, you can unlock your bootloader and install a custom recovery, then flash a Systemless root like SuperSU or Magisk 

Please follow the complete guide for your device ..
Unlock Bootloader - Install CWM - Root with SuperSU guides