c_cpp 给定n对括号，编写一个函数来生成格式正确的括号的所有组合。例如，给定n = 3，解决方案

Posted 2021-05-14

#include <iostream>
#include <vector>
#include <string>
using namespace std;

void helper(vector<string> &res, string s, int left, int right, int n) {
	if(left == n && right == n) {
		res.push_back(s);
		return;
	}    
	if(left < n) 
		helper(res, s + "(", left + 1, right, n);
	if(left > right) {
		helper(res, s + ")", left, right + 1, n);
	}
}

h(res, "", 0, 0, 3)
{
h(res, "(", 1, 0, 3){
	h(res, "((", 2, 0, 3){
		h(res, "(((", 3, 0, 3){
			h(res, "((()", 3, 1, 3){
				h(res, "((())", 3, 2, 3){
					h(res, "((()))", 3, 3, 3); // done
				}
			}
		}
		h(res, "(()", 2, 1, 3){
			h(res, "(()(", 3, 1, 3){
				h(res, "(()()", 3, 2, 3){
					h(res, "(()())", 3, 3, 3); // done
				}
			}
			h(res, "(())", 2, 2, 3){
				h(res, "(())(", 3, 2, 3){
					h(res, "(())()", 3, 3, 3); // done
				}
			}
		}
	}
	h(res, "()", 1, 1, 3){
		h(res, "()(", 2, 1, 3){
			h(res, "()((", 3, 1, 3){
				h(res, "()(()", 3, 2, 3){
					h(res, "()(())", 3, 3, 3); // done
				}
			}
			h(res, "()()", 2, 2, 3){
				h(res, "()()(", 3, 2, 3){
					h(res, "()()()", 3, 3, 3); // done
				}
			}
		}
	}
}
}

vector<string> generate_parenthesis(int n) {
	vector<string> res;
	string s;
	helper(res, s, 0, 0, n);
	return res;
}

int main()
{
vector<string> res = generate_parenthesis(3);
for(string t : res)
	cout << t << endl;
return 0;
}