HDU6400-2018ACM暑假多校联合训练1004-Parentheses Matrix-构造

Parentheses Matrix

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 728    Accepted Submission(s): 294
Special Judge

Problem Description

A parentheses matrix is a matrix where every element is either '(' or ')'. We define the goodness of a parentheses matrix as the number of balanced rows (from left to right) and columns (from up to down). Note that:

- an empty sequence is balanced;
- if A is balanced, then (A) is also balanced;
- if A and B are balanced, then AB is also balanced.

For example, the following parentheses matrix is a 2×4 matrix with goodness 3, because the second row, the second column and the fourth column are balanced:

)()(
()()

Now, give you the width and the height of the matrix, please construct a parentheses matrix with maximum goodness.

 

Input

The first line of input is a single integer T (1≤T≤50), the number of test cases.
Each test case is a single line of two integers h,w (1≤h,w≤200), the height and the width of the matrix, respectively.

 

Output

For each test case, display h lines, denoting the parentheses matrix you construct. Each line should contain exactly w characters, and each character should be either '(' or ')'. If multiple solutions exist, you may print any of them.

 

Sample Input

3

1 1

2 2

2 3

 

Sample Output

(

()

)(

(((

)))

 

这题。。。。WA到死啊 在h=2那里摔倒了好几次都没看出来

题意是构造一个 h×w 的括号矩阵，并且使其匹配的行数、列数之和最大的矩阵之一。

当 h 和 w 中有一个是奇数时，构造的方法是显然的。下面仅讨论 h 和 w 都是偶数的情况。不妨设 h≤w。 首先，第一行、最后一列中最多只有一个能够匹配，第一列、最后一行也只有一个能够匹配（考虑右上角和左下角的括号选取方法），故答案不会超过 w+h−2。

当 h = 2 时，每一列可以构造一对匹配，这样答案已经到达上界。 当 h = 4 时，可以如下构造：

((((((

)))(((

((()))

))))))

这样答案是 w+h−3。若存在更优的答案，则必有一个边界能够匹配，不妨设是第一列。这样，就已 经有除第一行以外的两行（右括号开头的行）不匹配了，而第一行和最后一列中至少有一个不匹配， 因此最优解不会超过 w+h−3。

当 h≥6 时，可以如下构造：

((((((((

()()()()

(()()())

()()()()

(()()())

))))))))
答案是 w+h−4。同理可证明不存在更优的方法。

 #include <iostream>

 using namespace std;

 int main()
 {
     ios::sync_with_stdio(false);
     int t;
     cin >> t;
     while (t--)
     {
         int h, w;
         cin >> h >> w;

         if (h %  && w % )
         {
             for (int i = ; i < h; i++)
             {
                 for (int j = ; j < w; j++)
                     cout << "(";
                 cout << endl;
             }
         }
         else if (!(h % ) && w % )
         {
             for (int i = ; i < h; i++)
             {
                 for (int j = ; j < w; j++)
                 {
                     if (i % )
                         cout << ")";
                     else
                         cout << "(";
                 }
                 cout << endl;
             }
         }
         else if (!(w % ) && h % )
         {
             for (int i = ; i < h; i++)
             {
                 for (int j = ; j < w; j++)
                 {
                     if (j % )
                         cout << ")";
                     else
                         cout << "(";
                 }
                 cout << endl;
             }
         }
         else if (w ==  || h == )
         {
             if (w >= h)
             {
                 for (int j = ; j < w; j++)
                     cout << "(";
                 cout << endl;
                 for (int j = ; j < w; j++)
                     cout << ")";
                 cout << endl;
             }
             else
             {
                 for (int i = ; i < h; i++)
                     cout << "()" << endl;
             }
         }
         else if (w ==  || h == )
         {
             if (w >= h)
             {
                 for (int i = ; i < h; i++)
                 {
                     for (int j = ; j < w; j++)
                     {
                         if (!i)
                             cout << "(";
                         else if (i == )
                         {
                             if (j < w / )
                                 cout << "(";
                             else
                                 cout << ")";
                         }
                         else if (i == )
                         {
                             if (j >= w / )
                                 cout << "(";
                             else
                                 cout << ")";
                         }
                         else
                             cout << ")";
                     }
                     cout << endl;
                 }
             }
             else
             {
                 for (int i = ; i < h; i++)
                 {
                     for (int j = ; j < w; j += )
                     {
                         if (i < h / )
                             cout << "()";
                         else
                         {
                             if (j < w / )
                                 cout << "((";
                             else
                                 cout << "))";
                         }
                     }
                     cout << endl;
                 }
             }
         }
         else
         {
             for (int i = ; i < h; i++)
             {
                 for (int j = ; j < w; j++)
                 {
                     if (!i)
                         cout << "(";
                     else if (i == h - )
                         cout << ")";
                     else if (i %  == )
                     {
                         cout << "()";
                         j++;
                     }
                     else if (i % )
                     {
                         if (!j)
                             cout << "(";
                         else if (j == w - )
                             cout << ")";
                         else
                         {
                             cout << "()";
                             j++;
                         }
                     }
                 }
                 cout << endl;
             }
         }
     }

     return ;
 }