CF#230 B题 Three matrices

n × n matrix W, consisting of integers, and you should find two n × n matrices A and B, all the following conditions must hold:

• Aij = Aji, for all i, j (1 ≤ i, j ≤ n);
• Bij =  - Bji, for all i, j (1 ≤ i, j ≤ n);
• Wij = Aij + Bij, for all i, j (1 ≤ i, j ≤ n).

Can you solve the problem?

Input

n (1 ≤ n ≤ 170). Each of the following n lines contains n integers. The j-th integer in the i-th line is Wij(0 ≤ |Wij| < 1717).

Output

n lines must contain matrix A. The next n lines must contain matrix B. Print the matrices in the format equal to format of matrix Win input. It is guaranteed that the answer exists. If there are multiple answers, you are allowed to print any of them.

10 - 4.

Sample test(s)

input

2 1 4 3 2

output

1.00000000 3.50000000 3.50000000 2.00000000 0.00000000 0.50000000 -0.50000000 0.00000000

input

3 1 2 3 4 5 6 7 8 9

output

1.00000000 3.00000000 5.00000000 3.00000000 5.00000000 7.00000000 5.00000000 7.00000000 9.00000000 0.00000000 -1.00000000 -2.00000000 1.00000000 0.00000000 -1.00000000 2.00000000 1.00000000 0.00000000

#include <stdio.h>
#include <string.h>
double a[180][180], b[180][180];
int c[180][180];
int main()
{
    int n, i, j;
    scanf("%d",&n);
    for(i=0; i<n; i++)
    {
        for(j=0; j<n; j++)
        {
            scanf("%d",&c[i][j]);
            if(i==j)
            {
                b[i][j]=0;
                a[i][j]=c[i][j]-b[i][j];
            }
        }
    }
    for(i=0; i<n; i++)
    {
        for(j=0; j<n; j++)
        {
            b[i][j]=(c[i][j]-c[j][i])*1.0/2;
            b[j][i]=-b[i][j];
            a[i][j]=c[i][j]-b[i][j];
            a[j][i]=c[i][j]-b[i][j];
        }
    }
    for(i=0;i<n;i++)
    {
        for(j=0;j<n;j++)
        {
            if(j==n-1)
                printf("%.6lf\n",a[i][j]);
            else
                printf("%.6lf ",a[i][j]);
        }
    }
    for(i=0;i<n;i++)
    {
        for(j=0;j<n;j++)
        {
            if(j==n-1)
                printf("%.6lf\n",b[i][j]);
            else
                printf("%.6lf ",b[i][j]);
        }
    }
    return 0;
}