Equivalence Partitioning(Software Testing ECP)

Can I have some help doing the Equivalence partitioning for this sub module? So the sub module is called outputShortestRoute. This sub module imports three strings. One string represents a database name, one string represents a origin or start location and the last string represents a destination. The sub module exports nothing. This sub module calculates and outputs a string representing quickets way(shortest sequence of bus routes) from getting from ["Origin"] to ["Destination"]. If there is two or more paths that are equally short then the sub module randomly selects a path.The calculation of which path is shortest is not meant to be displayed as that occurs within the database. Any help will be accepted. My main problem is im not sure how to determine which is shorter and which is longer due to the string having no values. Thanks, Please Help