generate parenthesis

class Solution:
    def helper(self, numOpen, numClosed, n, solutionSoFar, result):
        # Goal
        if numOpen == n and numClosed == n:
            result.append(solutionSoFar)
            return
        
        # Choice
        
        # Choice 1: Place an open parenthesis
        # Constraint on choice 1: When I have open parenthesis available to me.
        if numOpen < n:
            self.helper(numOpen + 1, numClosed, n, solutionSoFar + '(', result)
        
        # Choice 2: Place a closed parenthesis
        # Constraint on choice 2: I can only close an open parenthesis. (# open > # Closed)
        if numOpen > numClosed:
            self.helper(numOpen, numClosed + 1, n, solutionSoFar + ')', result)
        
    def generateParenthesis(self, n: int) -> List[str]:
        '''
        n = 3
        Well Formed
        ()()()
        (())()
        
        Not Well Formed
        ())()(
        )()()()
        
        Optimization
            Greedy approach (only if you can prove that the greedy choice leads to the optimal answer)
            Do an "informed" exhaustive search.
        Exhaustive Search
            Generate All
            Find All
        Application
            Permutations
            Subsets
            Combinations
        
        
        numOpenToPlace: 2
        numClosedToPlace: 3

        1. Choices (2 choices)
            I can Open a Parenthesis
            I can Close a parenthesis
        2. Constraint
            I can open a parenthesis when:
                When I have open parenthesis available to me.
            I can close a parenthesis when:
                I can only close an open parenthesis.
                # open > # Closed
        3. Goal
            Place 'n' open parenthesis and 'n' closed parenthesis.
        '''
        result = []
        
        self.helper(0, 0, n, '', result)
        return result