[Usaco2012 Nov]Clumsy Cows

时间限制：1s 空间限制：128MB

题目描述

Bessie the cow is trying to type a balanced string of parentheses into her new laptop, but she is sufficiently clumsy (due to her large hooves) that she keeps mis-typing characters. Please help her by computing the minimum number of characters in the string that one must reverse (e.g., changing a left parenthesis to a right parenthesis, or vice versa) so that the string would become balanced. There are several ways to define what it means for a string of parentheses to be "balanced". Perhaps the simplest definition is that there must be the same total number of ('s and )'s, and for any prefix of the string, there must be at least as many ('s as )'s. For example, the following strings are all balanced:

()

(())

()(()())

while these are not:

)(

())(

((())))

问题描述

给定长度为n的一个括号序列，每次修改可以修改一个位置的括号，若这个括号为’(‘，则修改为’)’，若这个括号为’)’，则修改为’(‘，问最少修改多少个使得原括号序列合法。

其中：

① ()是合法的；

② 若A是合法的，则(A)是合法的；

③ 若A，B都是合法的，则AB是合法的。

输入格式

一个长度为n个括号序列。

输出格式

最少的修改次数。

样例输入

  ())(

样例输出

 2
 样例说明
       修改为()()，其中红色部分表示修改的括号。
 
数据范围
       100%的数据满足：1 <= n <= 100,000。

提示

没有写明提示

题目来源

Silver