leetcode中和括号匹配相关的问题共有三个，分别是：

Valid Parentheses

Given a string containing just the characters ‘(‘, ‘)‘, ‘{‘, ‘}‘, ‘[‘ and ‘]‘, determine if the input string is valid.

The brackets must close in the correct order, "()" and "()[]{}" are all valid but "(]" and "([)]" are not.

Longest Valid Parentheses

Given a string containing just the characters ‘(‘ and ‘)‘, find the length of the longest valid (well-formed) parentheses substring.

For "(()", the longest valid parentheses substring is "()", which has length = 2.

Another example is ")()())", where the longest valid parentheses substring is "()()", which has length = 4.

从转移方程来看，好像是二维DP，但是可以使用堆栈来转化为一维的，简单来说，就是遇到左括号就进栈，遇到右括号就出栈，而出栈的位置就是上

面的j，所以不需要进行二维扫描就可定位到j。

class Solution {
public:
    int longestValidParentheses(string s) {
    	int length = s.size(),i,maxLength = 0;
    	vector<int> dp(length,0);
    	stack<int> stk; // 左括号的下标
    	for(i = 0; i < length;++i)
    	{
    		if(s[i] == '(')stk.push(i);
    		else
    		{
    			if(!stk.empty())
    			{
    				int start = stk.top();
    				stk.pop();
    				dp[i] = i - start + 1;
    				if(start > 0)dp[i] += dp[start-1];
    				if(dp[i] > maxLength)maxLength = dp[i];
    			}
    		}
    	}
    	return maxLength;
    }
};

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:

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