【算法】括号生成

Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses.

数字 n 代表生成括号的对数，请你设计一个函数，用于能够生成所有可能的并且 有效的 括号组合。

示例 1：

输入：n = 3
输出：["((()))","(()())","(())()","()(())","()()()"]

示例 2：

输入：n = 1
输出：["()"]

分享两种解题方式：

  /**
   * Brute Force
   */
  public List<String> generateParenthesis(int n) {
    List<String> returnList = new ArrayList<>();
    if (n < 1) {
      return returnList;
    }
    generateResult(n, n, "", returnList);
    return returnList;
  }

  private void generateResult(int left, int right, String result, List<String> returnList) {
    if (left == 0 && right == 0) {
      returnList.add(result);
      return;
    }
    if (left > 0) {
      generateResult(left - 1, right, result + "(", returnList);
    }
    if (right >  left) {
      generateResult(left, right - 1, result + ")", returnList);
    }
  }

  public static void main(String[] args) {
    GenerateParentheses generateParentheses = new GenerateParentheses();
    System.out.println(generateParentheses.generateParenthesis(2));
  }

public static List<String> generateParenthesis(int n) {
    List<String> ans = new ArrayList();
    if (n == 0) {
      ans.add("");
    } else {
      for (int c = 0; c < n; ++c)
        for (String left: generateParenthesis(c))
          for (String right: generateParenthesis(n-1-c))
            ans.add("(" + left + ")" + right);
    }
    return ans;
  }

  public static void main(String[] args) {
    System.out.println(generateParenthesis(2));
  }