I met this problem in codewars and I do not understand the solution from other users.

This is the question

Write a function which makes a list of strings representing all of the ways you can balance n pairs of parentheses

Examples
balanced_parens(0) => [""]
balanced_parens(1) => ["()"]
balanced_parens(2) => ["()()","(())"]
balanced_parens(3) => ["()()()","(())()","()(())","(()())","((()))"]

My solution involves using itertools permutations to get all permutations from input and adding them to a list. However, this will use up too much memory once n gets to 10.

this is the solution from another user.

def balanced_parens(n):
    '''
    To construct all the possible strings with n pairs of balanced parentheses
    this function makes use of a stack of items with the following structure:
        (current, left, right)
    Where:
        current is the string being constructed
        left is the count of '(' remaining
        right is the count of  ')' remaining
    '''
    stack = [('', n, 0)]
    result = []

    # Loop until we run out of items in the stack
    while stack:
        current, left, right = stack.pop()

        # if no '(' or ')' left to add, add current to the result
        if left == 0 and right == 0:
            result.append(current)

        # if we can, add a '(' and return to the stack
        if left > 0:
            stack.append((current + '(', left - 1, right + 1))

        # if we can, add a ')' and return to the stack
        if right > 0:
            stack.append((current + ')', left, right - 1))

    return result

I do not understand how this code will cycle through all permutations.

From my understanding, I know that this code will add a ‘(‘ while in the loop, and a ‘)’ when there is an open ‘(‘. So n=3 will return ‘()()()’

But how does it cycle through the rest, eg ‘((()))’?

i tried looking through the comments for this answer. Other than saying that this is a very elegant solution, not much else was said. I was not able to understand much from chatgpt either.