Question

I’m stumped by this seemingly trivial problem…

I would like to use python to take a string of numbers ("123" for example) and create a list that has all possible expressions where a "+" or "-" (or nothing at all) can be inserted between any numbers.

For the example "123" the list would be:

["123","12+3","12-3","1+23","1+2+3","1+2-3","1-23","1-2+3","1-2-3"]

If the length of the string of numbers is N, then the list should contain 3^(N-1) strings.

I feel like this should be done recursively, but I’m stuck trying to figure out how to return the 3 different options (+,-,None).

I believe that the base case of the function should be:

def options(string):
  if len(string) == 1:
    return string
  else:
    #This is where I am stuck

Answer 1

Here’s a slightly hacky, but short solution using itertools.product():

def plus_minus(s):
    for t in itertools.product(["", "+", "-"], repeat=len(s) - 1):
        yield "".join(itertools.chain.from_iterable(zip(s, t))) + s[-1]

Example:

>>> list(plus_minus("123"))
['123', '12+3', '12-3', '1+23', '1+2+3', '1+2-3', '1-23', '1-2+3', '1-2-3']

And here’s a recursive solution:

def plus_minus(s):
    if len(s) <= 1:
        yield s
        return
    for x in ["", "+", "-"]:
        for y in plus_minus(s[1:]):
            yield s[0] + x + y

I think the recursive solution is indeed cleaner here.