Generate Parentheses in Python

Suppose we have a value n. We have to generate all possible well-formed parentheses where n number of opening and closing parentheses are present. So if the value of n = 3, then the parentheses set will be ["()()()","()(())","(())()","(()())","((()))"]

To solve this, we will follow these steps −

• Define method called genParenthesisRec(). This takes left, right, temp string and result array. initially result array is empty
• The function genParenthesisRec, will work like below
• if left = 0 and right := 0, then insert temp into result, and return
• if left > 0
  • getParenthesisRec(left – 1, right, temp + “(”, result)
• if right > left
  • getParenthesisRec(left, right – 1, temp + “)”, result)

Example(Python)

Let us see the following implementation to get a better understanding −

 Live Demo

class Solution(object):
   def generateParenthesis(self, n):
      """
      :type n: int
      :rtype: List[str]
      """
      result = []
      self.generateParenthesisUtil(n,n,"",result)
      return result
   def generateParenthesisUtil(self, left,right,temp,result):
      if left == 0 and right == 0:
         result.append(temp)
         return
      if left>0:
         self.generateParenthesisUtil(left-1,right,temp+'(',result)
      if right > left:
         self.generateParenthesisUtil(left, right-1, temp + ')', result)
ob = Solution()
print(ob.generateParenthesis(4))

Input

4

Output

["(((())))",
"((()()))",
"((())())",
"((()))()",
"(()(()))",
"(()()())",
"(()())()",
"(())(())",
"(())()()",
"()((()))",
"()(()())",
"()(())()",
"()()(())",
"()()()()"]