Generate Parentheses

题目：Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses.For example, given n = 3, a solution set is:

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

思路：递归求解，对于输入数据n，有n个左括号，n个右括号，共2n个括号，设left为剩余的左括号个数，right为剩余的右括号个数。根据括号匹配的规则可知当left=0且right=0时，完成一个合法的排列，输出。当left>0时，打印'（'。当right>0且right>left，打印‘）’。代码：#include <iostream>#include <stack>#include <vector>#include <string>using namespace std;class Solution {public:vector<string> generateParenthesis(int n) {vector<string> svec;if(n==0) return svec;string str="";generate(svec,n,n,str);return svec;}void generate(vector<string >& ret,int left,int right,string str){if(left==0&&right==0)ret.push_back(str);if(left>0)//可直接打印左括号，不影响规则{generate(ret,left-1,right,str+'(');}if(right>0&&left<right)//{generate(ret,left,right-1,str+')');}}};int main(){int num;;cin>>num;Solution s;vector<string> ret;ret=s.generateParenthesis(num);for(auto iter=ret.begin();iter!=ret.end();++iter){cout<<"\""<<*iter<<"\""<<" ";}cout<<endl;system("pause");return 0;}