BZOJ1013(JSOI2008)[球形空间产生器sphere]--高斯消元

【题目链接】

bzoj1013

【解题报告】

设球心坐标为(O1,O2,…,On)。

第i个点坐标为(X(i,1),X(i,2),…,X(i,n))

由题意得

∑(X2(1,i)−2∗X(1,i)∗Oi+O2i)=∑(X2(2,i)−2∗X(2,i)∗Oi+O2i)=...=∑(X2(n+1,i)−2∗X(n+1,i)∗Oi+O2i)

所以∑(2∗(X(2,i)−X(1,i))∗Oi)=∑(X2(2,i)−X2(1,i))

∑(2∗(X(3,i)−X(1,i))∗Oi)=∑(X2(3,i)−X2(1,i))

…

∑(2∗(X(n+1,i)−X(1,i))∗Oi)=∑(X2(n+1,i)−X2(1,i))

就可以用高斯消元解线性方程了

#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
const int maxn=15;
const double P=1e-10;
int n;
double a[maxn][maxn],M[maxn][maxn],ans[maxn];
inline int Read()
{
int res=0;
char ch=getchar();
while (ch<'0'||ch>'9') ch=getchar();
while (ch>='0'&&ch<='9') res=res*10+ch-48,ch=getchar();
return res;
}
bool Fc(double x) {if (x<=P&&x>=-P) return 1; return 0;}
int main()
{
freopen("1013.in","r",stdin);
freopen("1013.out","w",stdout);
n=Read();
for (int i=1; i<=n+1; i++)
for (int j=1; j<=n; j++) scanf("%lf",&a[i][j]);
for (int i=2; i<=n+1; i++)
for (int j=1; j<=n; j++)
M[i-1][j]=(a[i][j]-a[1][j])*2,M[i-1][n+1]+=a[i][j]*a[i][j]-a[1][j]*a[1][j];
for (int i=1; i<=n; i++)
{
int where;
for (int j=i; j<=n; j++)
if (!Fc(M[j][i])) {where=j; break;}
swap(M[where],M[i]);
for (int j=i+1; j<=n; j++) {double num=M[j][i]/M[i][i]; for (int k=i; k<=n+1; k++) M[j][k]-=num*M[i][k];}
}
for (int i=n; i; i--)
{
ans[i]=M[i][n+1];
for (int j=i+1; j<=n; j++) ans[i]-=M[i][j]*ans[j];
ans[i]/=M[i][i];
}
for (int i=1; i<n; i++) printf("%.3lf ",ans[i]); printf("%.3lf\n",ans
);
return 0;
}