HDU多校8 Parentheses Matrix（构造）

Posted 2020-12-29 yzm10

Parentheses Matrix

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 0    Accepted Submission(s): 0
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

(

()

)(

(((

)))

 

 

 

构造题。找出每行每列最大匹配数的矩阵。

首先分奇偶性讨论。

1.奇奇情况为0，任意输出。

2.奇偶情况最大匹配为偶数值。

3.偶偶要分两种情况，最大匹配为n+n/2-1或2*n-4，

行和列较小的值若小于等于6，第一行（列）为“（”，最后一行（列）为“）”，大于6则第一行列全为“（”，最后一行列全为“）”。

其他的位置行列下标和若偶为“（”，奇为“）”。

 

 

#include <bits/stdc++.h>
using namespace std;
const int INF = 0x3f3f3f3f;
const int MAX = 205;
typedef long long LL;

int main(void)
{
    int t,n,m,i,j;
    scanf("%d",&t);
    while(t--){
        scanf("%d%d",&n,&m);
        if((n&1)&&(m&1)){
            for(i=1;i<=n;i++){
                for(j=1;j<=m;j++){
                    printf("(");
                }
                printf("
");
            }
        }
        else if(n&1){
            for(i=1;i<=n;i++){
                for(j=1;j<=m;j++){
                    if(j&1) printf("(");
                    else printf(")");
                }
                printf("
");
            }
        }
        else if(m&1){
            for(i=1;i<=n;i++){
                for(j=1;j<=m;j++){
                    if(i&1) printf("(");
                    else printf(")");
                }
                printf("
");
            }
        }
        else{
            if(n>=m){
                for(i=1;i<=n;i++){
                    for(j=1;j<=m;j++){
                        if(i==1&&(m/2-1)>2){
                            printf("(");
                            continue;
                        }
                        if(i==n&&(m/2-1)>2){
                            printf(")");
                            continue;
                        }
                        if(j==1){
                            printf("(");
                            continue;
                        }
                        if(j==m){
                            printf(")");
                            continue;
                        }
                        if((i+j)&1){
                            printf(")");
                        }
                        else{
                            printf("(");
                        }
                    }
                    printf("
");
                }
            }
            else{
                for(i=1;i<=n;i++){
                    for(j=1;j<=m;j++){
                        if(j==1&&(n/2-1)>2){
                            printf("(");
                            continue;
                        }
                        if(j==m&&(n/2-1)>2){
                            printf(")");
                            continue;
                        }
                        if(i==1){
                            printf("(");
                            continue;
                        }
                        if(i==n){
                            printf(")");
                            continue;
                        }
                        if((i+j)&1){
                            printf(")");
                        }
                        else{
                            printf("(");
                        }
                    }
                    printf("
");
                }
            }
        }
    }
    return 0;
}