Print all possible combinations of parenthesis in expression

gistfile1.txt

def print_parens(digits, s, n):
    res = []
    def _print_parens(s, pos, n, open, close):
        if(close == n): 
            for i in s: 
                print(i, end = "") 
            print() 
            res.append(''.join(s))
        else: 
            if(open > close):
                s[pos] = ')' 
                _print_parens(s, pos + 1, n, open, close + 1) 
            if(open < n): 
                s[pos] = '(' + digits[open]
                _print_parens(s, pos + 1, n, open + 1, close) 
    
    if(n > 0):
        _print_parens(s, 0, n, 0, 0)
    return res
  
digits = "123456"
n = len(digits)
s = [""] * 2 * n 
res = print_parens(digits, s, n) 
print(len(res))

main.py

def print_parens(digits, s, n):
    res = []
    def _print_parens(s, pos, n, open, close):
        if(close == n): 
            for i in s: 
                print(i, end = "") 
            print() 
            res.append(''.join(s))
        else: 
            if(open > close):
                s[pos] = ')' 
                _print_parens(s, pos + 1, n, open, close + 1) 
            if(open < n): 
                s[pos] = '(' + digits[open]
                _print_parens(s, pos + 1, n, open + 1, close) 
    
    if(n > 0):
        _print_parens(s, 0, n, 0, 0)
    return res
  
digits = "123456"
n = len(digits)
s = [""] * 2 * n 
res = print_parens(digits, s, n) 
print(len(res))