方法一：暴力法

class Solution:def generateParenthesis(self, n: int) -> List[str]:def generate(A):if len(A) == 2*n:if valid(A):ans.append("".join(A))else:A.append('(')generate(A)A.pop()A.append(')')generate(A)A.pop()def valid(A):bal = 0for c in A:if c == '(': bal += 1else: bal -= 1if bal < 0: return Falsereturn bal == 0ans = []generate([])return ans

方法二：回溯法

class Solution:def generateParenthesis(self, n: int) -> List[str]:ans = []def backtrack(S, left, right):if len(S) == 2 * n:ans.append(''.join(S))returnif left < n :S.append('(')backtrack(S, left + 1, right)S.pop()if right < left:S.append(')')backtrack(S, left, right+1)S.pop()backtrack([], 0, 0)return ans

方法三：

class Solution:def generateParenthesis(self, n: int) -> List[str]:if n == 0:return ['']ans = []for c in range(n):for left in self.generateParenthesis(c):for right in self.generateParenthesis(n-1-c):ans.append('({}){}'.format(left, right))return ans

方法四：动态规划

class Solution:def generateParenthesis(self, n: int) -> List[str]:dp = [[] for _ in range(n+1)]dp[0] = [""]for i in range(1, n+1):for p in range(i):l1 = dp[p]l2 = dp[i-p-1]for k1 in l1:for k2 in l2:dp[i].append("({0}){1}".format(k1, k2))return dp[n]