Intermittent Mathematics (Logarim)

Question

The old keypad of the telephone, it has 10 numbers (10 keys) , this keypad allows the user to enter a text by successively pressing certain key many times in a small period of time. you need to draw a graph of entering a text input using this keypad.  after that you need to have a certain algorithm of finding the length of a path to enter certain text
example 
aaa   --> 6
aba   --> 5

 

the link below shows the phone keypad

https://commons.wikimedia.org/wiki/File:Telephone-keypad.png