9.6 Implement an algorithm to print all valid (e.g., properly opened and closed) combinations of n-pairs of parentheses.
EXAMPLE
Input: 3
Output: ((())), (()()), (())(), ()(()), ()()()
LeetCode上的原题，请参见我之前的博客Generate Parentheses 生成括号。
解法一：
class Solution { public:vector<string> generateParens(int n) {set<string> t;if (n == 0) t.insert("");else {vector<string> pre = generateParens(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, ')');t.insert(a);a.erase(a.begin() + i + 1, a.begin() + i + 3);}}t.insert("()" + a);}}return vector<string>(t.begin(), t.end());} };
解法二:
class Solution { public:vector<string> generateParens(int n) {vector<string> res;generateParensDFS(n, n, "", res);return res;}void generateParensDFS(int left, int right, string out, vector<string> &res) {if (left > right) return;if (left == 0 && right == 0) res.push_back(out);else {if (left > 0) generateParensDFS(left - 1, right, out + '(', res);if (right > 0) generateParensDFS(left, right - 1, out + ')', res);}} };
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