[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:

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

思路：这道题要是不分析规律的话，很难想出答案本题的规律是假如left的个数大于right的个数，就可以添加')'；假如left的个数小于n，就可以添加'('。利用递归，先给出递归结束条件，然后不断深入。

代码：

public class Solution {
public List<String> generateParenthesis(int n) {
List<String> list=new ArrayList<String>();
if(n<=0)return list;
generate(0, list, 2*n, "", 0, 0);
System.out.println(list);
return list;
}
public void generate(int index,List<String> list,int size,String str,int left,int right)
{
if(index==size)
{
list.add(str);
return;
}
index++;
if(left>right)
generate(index, list, size, str+')', left, right+1);
if(left<size/2)
generate(index, list, size, str+'(', left+1, right);
}
}