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:

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

https://oj.leetcode.com/problems/generate-parentheses/

思路1：自己模仿permutation之类的题目，一个一个往数据里面填，填的时候判断是否是valid的，每次都要统计括号数，麻烦。

思路2：改进思路1，也是递归实现，将已有的左右括号数作为参数递归下去，写起来很简洁。

思路1：

public class Solution {	public ArrayList<String> generateParenthesis(int n) {		ArrayList<String> result = new ArrayList<String>();		if (n <= 0)			return result;		n = n * 2;		char str[] = new char[n];		generate(0, n, str, result);		return result;	}	private void generate(int cur, int n, char[] s, ArrayList<String> result) {		if (cur == n) {			result.add(new String(s));		} else {			int j;			int cntL = 0, cntR = 0;			for (j = 0; j < cur; j++) {				if (s[j] == ‘(‘)					cntL++;				else					cntR++;			}			if (cntL > cntR) {				s[cur] = ‘)‘;				generate(cur + 1, n, s, result);				if (cntL < n / 2) {					s[cur] = ‘(‘;					generate(cur + 1, n, s, result);				}			} else if (cntL == cntR) {				s[cur] = ‘(‘;				generate(cur + 1, n, s, result);			} else {				return;			}		}	}	public static void main(String[] args) {		System.out.println(new Solution().generateParenthesis(3));	}}

思路2：

import java.util.ArrayList;public class Solution {    public ArrayList<String> generateParenthesis(int n) {        ArrayList<String> res = new ArrayList<String>();        if (n <= 0)            return res;        StringBuilder sb = new StringBuilder();        generate(n, n, sb, res);        return res;    }    private void generate(int l, int r, StringBuilder sb, ArrayList<String> res) {        if (r < l)            return;        if (l == 0 && r == 0) {            res.add(sb.toString());        }        if (l > 0) {            sb.append("(");            generate(l - 1, r, sb, res);            sb.deleteCharAt(sb.length() - 1);        }        if (r > 0) {            sb.append(")");            generate(l, r - 1, sb, res);            sb.deleteCharAt(sb.length() - 1);        }    }    public static void main(String[] args) {        System.out.println(new Solution().generateParenthesis(3));    }}

参考：

http://blog.csdn.net/linhuanmars/article/details/19873463

http://blog.csdn.net/fightforyourdream/article/details/14159435