Leetcode: Generate parentheses

Given a strictly positive integer n, write a function that returns all possible combinations of well-formed parentheses. Parentheses can be nested and added one after the other. It is important that we don’t create invalid combinations, such as )(. The idea then becomes to start with a single set of parentheses (). We can add another set of parentheses at three possible places: 1(2)3. When looking closely, we see that 1 and 3 are the same position. We can then utilize Pythons string splitting capabilities which allow us to insert one or more characters at any place in the string. We do this by iterating over the string and inserting () at every possible position. This creates all valid pairs like (()) and ()() etc. To avoid the aforementioned duplicates we can add a memory to the function and store all the visited possible combinations. This allows us to speed the process up significantly. For example when we visit ()(), we don’t need to visit it again to form ()()() or ()(()) (for n=3) because they would already been visited.

from typing import List


class Solution:
  def generateParenthesis(self, n: int) -> List[str]:
    if n == 0:
      return []
    memo = set()
    
    def inner(n, s):
      if n == 0:
        return [s]
      res = []

      for p in range(len(s)):
        cand = s[:p] + '()' + s[p:]
        if cand in memo:
          continue
        memo.add(cand)
        res += inner(n-1, cand)
        
      return res

    res = inner(n-1, '()')
    return res
    

if __name__ == '__main__':
  s = Solution().generateParenthesis
  print(s(0), [])
  print(s(1), ['()'])
  print(s(2), ['()()', '(())'])
  print(s(3), ['((()))', '(()())', '(())()', '()(())', '()()()'])