【BZOJ 1013】[JSOI2008] 球形空间产生器sphere

Qizy 数论, 解题报告, 高斯消元

题目传送门：http://www.lydsy.com/JudgeOnline/problem.php?id=1013
离线版题目：http://paste.ubuntu.com/18938759/

高斯消元第一题！ 撒花！ *★,°*:.☆\(￣▽￣)/$:*.°★*
1A！ 撒花！ *★,°*:.☆\(￣▽￣)/$:*.°★*
设n维坐标，然后加上一个半径，刚好n+1个未知数
然后一个坐标一个方程，刚好n+1个方程
然后就是高斯消元啦！

#include<iostream>
#include<cstdio>
#define fabs(x) ((x)<0?-(x):(x))
using namespace std;

const int MAXN = 20;

double mat[MAXN][MAXN];
int n;

inline void Gauss(){
	for (int k=1;k<=n;k++){
		int w = k;
		for (int i=k+1;i<=n+1;i++) if (fabs(mat[k][w]) < fabs(mat[k][i])) w = i;
		for (int i=1;i<=n+2;i++) swap(mat[i][k],mat[i][w]);
		for (int i=k+1;i<=n+1;i++){
			double t = mat[k][i]/mat[k][k];
			for (int j=1;j<=n+2;j++)
				mat[j][i] -= mat[j][k]*t;
		}
	}
	for (int k=n+1;k;k--){
		for (int i=n+1;i>k;i--) mat[n+2][k] -= mat[i][k]*mat[n+2][i];
		mat[n+2][k] /= mat[k][k]; 
	}
}

int main(){
	scanf("%d",&n);
	for (int j=1;j<=n+1;j++){
		for (int i=1;i<=n;i++)
			scanf("%lf",&mat[i][j]),
			mat[n+2][j] -= mat[i][j]*mat[i][j],
			mat[i][j] *= -2.0;
		mat[n+1][j] = 1;
	}
	Gauss();
	for (int i=1;i<n;i++) printf("%.3lf ",mat[n+2][i]);
	printf("%.3lf",mat[n+2][n]);
	return 0;
}

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