[leetcode]Generate Parentheses

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:

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

题目是要生成所有的匹配的括号序列： 左括号和右括号的数目都为n， 序列的任意位置index之前(左边的)的左括号总数都是要大于或者等于右括号总数。

总的序列的数目应该是卡特兰数：h(n)=C(2n,n)/(n+1) (n=0,1,2,...)或者h(n)=c(2n,n)-c(2n,n+1)(n=0,1,2,...)

 

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



void help(int total, int left, int right, string str, vector<string>& svec)
{
    if(left>total || right>total || right>left)
        return;
    if(total==right&&left==total)
    {
        svec.push_back(str);
        return;
    }
    else
    {
        if(left<total)
            help(total, left+1, right, str+"(", svec);
        if(right<left&&left<=total)
            help(total, left, right+1, str+")", svec);
    }
}


vector<string> generateParenthesis(int n) {
    vector<string> svec;
    help(n, 0, 0, "", svec);
    
    return svec;
}



int main()
{
    vector<string> svec;
    svec=generateParenthesis(3);
}