Parentheses Matrix
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 268 Accepted Submission(s): 101
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
( () )( ((( )))
代码：
#include<bits/stdc++.h>
#define ll long long
using namespace std;
char a[505][505];
int main()
{
int t,i,j,n,m;
cin>>t;
while(t--)
{
cin>>n>>m;
if((n&1)&&(m&1))
{
for(i=0;i<n;i++)
{
for(j=0;j<m;j++)
a[i][j]='(';
}
}
else if(n&1)
{
for(i=0;i<n;i++)
{
for(j=0;j<m;j++)
{
if(j%2)
a[i][j]=')';
else
a[i][j]='(';
}
}
}
else if(m&1)
{
for(i=0;i<m;i++)
{
for(j=0;j<n;j++)
{
if(j%2)
a[j][i]=')';
else
a[j][i]='(';
}
}
}
else
{
if(n==2)
{
for(int i=0;i<m;i++)
{
a[0][i]='(';
a[1][i]=')';
}
}
else if(m==2)
{
for(int i=0;i<n;i++)
{
a[i][0]='(';
a[i][1]=')';
}
}
else if(n==4)
{
for(i=0;i<n;i++)
{
for(int j=0;j<m;j++)
{
if(i==0) a[i][j]='(';
else if(i==n-1) a[i][j]=')';
else if((i&1)&&(j<m/2)) a[i][j]=')';
else if(i&1) a[i][j]='(';
else if(j<m/2) a[i][j]='(';
else a[i][j]=')';
}
}
}
else if(m==4)
{
for(i=0;i<m;i++)
{
for(int j=0;j<n;j++)
{
if(i==0) a[j][i]='(';
else if(i==m-1) a[j][i]=')';
else if((i&1)&&(j<n/2)) a[j][i]=')';
else if(i&1) a[j][i]='(';
else if(j<n/2) a[j][i]='(';
else a[j][i]=')';
}
}
}
else if(n>=m)
{
for(i=0;i<m;i++)
{
for(int j=0;j<n;j++)
{
if(i==0) a[j][i]='(';
else if(i==m-1) a[j][i]=')';
else if((i&1)&&(j&1)) a[j][i]=')';
else if(i&1) a[j][i]='(';
else if(j==0) a[j][i]='(';
else if(j==n-1) a[j][i]=')';
else if(j&1) a[j][i]='(';
else a[j][i]=')';
}
}
}
else
{
for(i=0;i<n;i++)
{
for(int j=0;j<m;j++)
{
if(i==0) a[i][j]='(';
else if(i==n-1) a[i][j]=')';
else if((i&1)&&(j&1)) a[i][j]=')';
else if(i&1) a[i][j]='(';
else if(j==0) a[i][j]='(';
else if(j==m-1) a[i][j]=')';
else if(j&1) a[i][j]='(';
else a[i][j]=')';
}
}
}
}
for(i=0;i<n;i++)
{
for(j=0;j<m;j++)
cout<<a[i][j];
cout<<endl;
}
}
return 0;
}
简洁版：
#include<bits/stdc++.h>
#define f for(int i=0;i<(int)n;i++,puts("")) for(int j=0;j<(int)m;j++)
#define e else if
using namespace std;
void p(char ch){cout<<ch;}
int main(){
int t,n,m;
cin>>t;
while(t--){
cin>>n>>m;
if((n&1)&&(m&1)) f p('(');
e (n&1) f
if(j&1) p(')');
else p('(');
e(m&1) f if(i&1) p(')');
else p('(');
e(n==2) f if(i&1) p(')');
else p('(');
e(m==2) f if(j&1) p(')');
else p('(');
e(n==4) f if(i==0) p('(');
e(i==n-1) p(')');
e((i&1)&&(j<m/2)) p(')');
e(i&1) p('(');
e(j<m/2) p('(');
else p(')');
e(m==4) f if(j==0) p('(');
e(j==m-1) p(')');
e((j&1)&&(i<n/2)) p(')');
e(j&1) p('(');
e(i<n/2) p('(');
else p(')');
e(n>=m) f if(j==0) p('(');
e(j==m-1) p(')');
e((i&1)&&(j&1)) p(')');
e(j&1) p('(');
e(i==0) p('(');
e(i==n-1) p(')');
e(i&1) p('(');
else p(')');
else f if(i==0) p('(');
e(i==n-1) p(')');
e((i&1)&&(j&1)) p(')');
e(i&1) p('(');
e(j==0) p('(');
e(j==m-1) p(')');
e(j&1) p('(');
else p(')');
}
}