[JSOI2008]球形空间产生器

注意到给出N + 1个坐标 应该想到压缩方程 转化为n个消去一个变元

sigma (x²) +sigma (y²) - sigma (2xy) = R²

sigma (x_i²) +sigma (y_i²) - sigma (2x_iy_i) = R²

相减

下面给出的是gauss-jordan消去法 稍有不同

#include <cstdio>
#include <cmath>
#define sqr(x) x * x
const int N =300;
int n;
double t[N][N], a[N][N], b[N];
int cho[N];
inline void gauss ()
{
    for (int i = 1; i <= n; i ++)
    {
        double t1 (0);int t2 (0);
        for (int j = 1; j <= n; j ++)
            if (fabs (a[i][j]) > t1)
                t1 = fabs (a[i][j]), t2 = j;cho[t2] = i;
        
        double t = a[i][t2];
        for (int j = 1; j <= n; j ++)
            a[i][j] /= t;
        b[i] /= t;
        
        for (int j = 1; j <= n; j ++)
            if (j != i)
            {
                double t = a[j][t2];
                for (int k = 1; k <= n; k ++)
                    a[j][k] -= a[i][k] * t;
                b[j] -= b[i] * t;
            }
    }
    for (int i = 1; i <= n; i ++)
        printf ("%.3lf ", -b[cho[i]] / a[cho[i]][i]);
}
int main ()
{
    scanf ("%d", &n);
    for (int i = 1; i <= n + 1; i ++)
        for (int j = 1; j <= n; j ++)
            scanf ("%lf", &t[i][j]);
    for (int i = 2; i <= n + 1; i ++)
        for (int j = 1; j <= n; j ++)
            a[i - 1][j] = 2 * (t[1][j] - t[i][j]), b[i - 1] += sqr (t[i][j]) - sqr (t[1][j]);
    gauss ();
    return 0;
}