【JSOI 2008】 球形空间产生器

【题目链接】

             https://www.lydsy.com/JudgeOnline/problem.php?id=1013

【算法】

           高斯消元

【代码】

            

#include<bits/stdc++.h>
using namespace std;
const double eps = 1e-8;
 
int i,j,k,n;
double a[100][100],c[100][100];
double b[100];
double rate;

int main()
{
    
    scanf("%d",&n);
    for (i = 1; i <= n + 1; i++)
    {
        for (j = 1; j <= n; j++)
        {
            scanf("%lf",&a[i][j]);
        }
    }
    for (i = 1; i <= n; i++)
    {
        for (j = 1; j <= n; j++)
        {
            c[i][j] = 2 * (a[i+1][j] - a[i][j]);
            b[i] += a[i+1][j] * a[i+1][j] - a[i][j] * a[i][j];
        }
    }
    for (i = 1; i <= n; i++)
    {
        for (j = i; j <= n; j++)
        {
            if(fabs(c[j][i]) > eps)
            {
                for (k = 1; k <= n; k++) swap(c[i][k],c[j][k]);
                swap(b[i],b[j]);
            }
        }
        for (j = 1; j <= n; j++)
        {
            if (i == j) continue;
            rate = c[j][i] / c[i][i];
            for (k = i; k <= n; k++) c[j][k] -= c[i][k] * rate;
            b[j] -= b[i] * rate;
        }
    }
    for (i = 1; i < n; i++) printf("%.3lf ",b[i]/c[i][i]);
    printf("%.3lf\n",b[n]/c[n][n]);
    
    return 0;
}