[LintCode] Generate Parentheses 生成括号

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

Have you met this question in a real interview?

Example

Given

n = 3

, a solution set is:

"((()))", "(()())", "(())()", "()(())", "()()()"

LeetCode上的原题，请参见我之前的博客Generate Parentheses。

解法一：

class Solution {
public:
/**
* @param n n pairs
* @return All combinations of well-formed parentheses
*/
vector<string> generateParenthesis(int n) {
if (n == 0) return {};
vector<string> res;
helper(n, n, "", res);
return res;
}
void helper(int left, int right, string out, vector<string>& res) {
if (left < 0 || right < 0 || left > right) return;
if (left == 0 && right == 0) {
res.push_back(out);
return;
}
helper(left - 1, right, out + "(", res);
helper(left, right - 1, out + ")", res);
}
};

解法二：

class Solution {
public:
/**
* @param n n pairs
* @return All combinations of well-formed parentheses
*/
vector<string> generateParenthesis(int n) {
set<string> res;
if (n == 0) {
res.insert("");
} else {
vector<string> pre = generateParenthesis(n - 1);
for (auto a : pre) {
for (int i = 0; i < a.size(); ++i) {
if (a[i] == '(') {
a.insert(a.begin() + i + 1, '(');
a.insert(a.begin() + i + 2, ')');
res.insert(a);
a.erase(a.begin() + i + 1, a.begin() + i + 3);
}
}
res.insert("()" + a);
}
}
return vector<string>(res.begin(), res.end());
}
};