a regular expression generator for number ranges

Question

I checked on the stackExchange description, and algorithm questions are one of the allowed topics. So here goes.

Given an input of a range, where begin and ending number

Answer 1

One option would be to (for a range [n, m]) generate the regexp n|n+1|...|m-1|m. However, I think you're after getting something more optimised. You can still do essentially the same, generate a FSM that matches each number using a distinct path through a state machine, then use any of the well-known FSM minimisation algorithms to generate a smaller machine, then turn that into a more condensed regular expression (since "regular expressions" without the Perl extensions are isomorphic to finite state machines).

Let's say we are looking at the range [107, 112]:

state1:
  1 -> state2
  * -> NotOK
state2:
  0 -> state2.0
  1 -> state2.1
  * -> NotOK
state2.0:
  7 -> OK
  8 -> OK
  9 -> OK
  * -> NotOK
state2.1:
  0 -> OK
  1 -> OK
  2 -> OK
  * -> NotOK

We can't really reduce this machine any further. We can see that state2.0 correspond to the RE [789] and 2.1 corresponds to [012]. We can then see that state2.0 is (0[789])|(1[012]) and the whole is 1(0[789])|(1[012]).

Further reading on DFA minimization can be found on Wikipedia (and pages linked from there).