FZU Problem 2030 括号问题

Problem Description

给出一个字符串，其中包括3种字符: ‘(‘, ‘)’, ‘?’.其中?表示这个字符可以是’(‘也可以是’)’. 现在给出字符串S,你可以在’?’处填写’(‘ 或者 ‘)’，当然随意填写得到的序列可能是括号不匹配的。例如”(?”，如果你填写’(‘那么”((“是括号不匹配的！现在你的任务是确定你有多少种填写方案，使得最终的字符串是括号匹配的！2种方案是不同的，当2种方案中至少存在1个填写字符是不同的。例如，对于”((??))”,我们可以得到2种方案: “((()))”, “(()())”。

Input

数据包含多组测试数据第一行输入一个字符串S(S的长度不超过16)。

Output

输出一个整数,表示合法的填写方案数。

Sample Input

((??))

Sample Output

讲解：刚开始看这个题，你会想到括号配对，但是呢这两个题却又不太一样，所以我们依然也可以采用那种方式来做的，只不过要变换一次递归一次，最后递归出来结果，下面就以例题为例子讲解一下：

注意：遇见0了则不能再进性下去；

如图所示：

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" alt="" />

 #include<iostream>

 #include<cstdio>

 #include<cstring>

 using namespace std;

 char str[];

 int len;

 int ans;

 void fun(int end,int k)

 {

     if(end==len && k==)

     {

         ans++;

     }

     if(k<)

     {

     }

     else if(str[end]=='?')

     {

         fun(end+,k-);

         fun(end+,k+);

     }

     else if(str[end]=='(')

     {

         fun(end+,k+);

     }

     else if(str[end]==')')

     {

         fun(end+,k-);

     }

 }

 int main()

 {

     while(gets(str))

     {

         ans=;

         len=strlen(str);

         fun(,);

         printf("%d\n",ans);

     }

     return ;

 }