LeeCode - brackets generation

给出 n 代表生成括号的对数，请你写出一个函数，使其能够生成所有可能的并且有效的括号组合。

例如，给出 n = 3，生成结果为：

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

• Solution a:
  mathematical induction from n = 1 -> n = 2 -> n = x, from small to large, we found rule.

• Solution two:

  DFS + recursive word symbol length 2 * n
  violent solution, binding the stack

  O (2 ** 2n)

• Solution three:
  improvement Solution two pruning +
  O (2 ** n)