1. Description
Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses.
2. Example
Example 1
Input: n = 3
Output: ["((()))","(()())","(())()","()(())","()()()"]
Example 2
Input: n = 1
Output: ["()"]
3. Constraints
4. Solutions
Backtracking
Time complexity: O($\frac {4^n} {\sqrt{n}}$)
Space complexity: O(n), excluding the output
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| class Solution {
public:
vector<string> generateParenthesis(int n) {
parentheses.clear();
string parenthesis;
generate_parentheses(parenthesis, n, n);
return move(parentheses);
}
private:
vector<string> parentheses;
void generate_parentheses(string &parenthesis, int left_count, int right_count) {
if (left_count == 0 && right_count == 0) {
parentheses.push_back(parenthesis);
return;
}
if (left_count > 0) {
parenthesis.push_back('(');
generate_parentheses(parenthesis, left_count - 1, right_count);
parenthesis.pop_back();
}
if (right_count > left_count) {
parenthesis.push_back(')');
generate_parentheses(parenthesis, left_count, right_count - 1);
parenthesis.pop_back();
}
}
};
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