P4035 [JSOI2008]球形空间产生器

A,B,球心坐标分别为$(a_1,a_2,a_3....),(b_1,b_2,b_3....),(c_1,c_2,c_3....)$
则$dis{t}^2=(a_1-c_1{)}^2+(a_2-c_2{)}^2+(a_3-c_3{)}^2$...... $=(b_1-c_1{)}^2+(b_2-c_2{)}^2+(b_3-c_3{)}^2$......
所以$(a_1-c_1{)}^2+(a_2-c_2{)}^2+(a_3-c_3{)}^2$...... $=(b_1-c_1{)}^2+(b_2-c_2{)}^2+(b_3-c_3{)}^2$......
所以$(a_1{)}^2-2a_1{c}_1-(c_1{)}^2+(a_2{)}^2-2a_2{c}_2-(c_2{)}^2$...... $=(b_1{)}^2-2b_1{c}_1-(c_1{)}^2+(b_2{)}^2-2b_2{c}_2-(c_2{)}^2$......
移项得$2c_1(a_1-b_1)+2c_2(a_2-b_2)+$......$=(a_1{)}^2-(b_1{)}^2+(a_2{)}^2-(b_2{)}^2$......
式子就酱紫推出来了

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
 
using namespace std;
 
int n;
double tem[12][12],Augmented_matrix[12][12];
 
inline int find_pivot( int column ) {
	int maxn = column;
	for (int i = column + 1; i <= n; ++i) {
		if ( Augmented_matrix[i][column] < Augmented_matrix[maxn][column] ) {
			maxn = i;
		}
	}
	return maxn;
}
 
inline void swap_line( int now , int need ) {
	for (int column = 1; column <= n + 1; ++column) {
		swap( Augmented_matrix[now][column] , Augmented_matrix[need][column] );
	}
	return;
}
 
int main()
{
	scanf ( "%d" , &n );
	for (int i = 1; i <= n + 1; ++i) {
		for (int j = 1; j <= n; ++j) {
			scanf ( "%lf" , &tem[i][j] );
		}
	}
	for (int i = 1; i <= n; ++i) {
		for (int j = 1; j <= n; ++j) {
			Augmented_matrix[i][j] = 2 * ( tem[i][j] - tem[i + 1][j] );
			//因为保证有解 所以不可能出现一列全为0的情况 
			Augmented_matrix[i][n + 1] += pow( tem[i][j] , 2 ) - pow( tem[i + 1][j] , 2 );
		}//化简式子后得到Augmented_martix[i][j]表示的式子 
	}
	for (int line = 1; line <= n; ++line) {
		int pivot = find_pivot( line );
		swap_line( line , pivot ); 
		for ( int tem_line = 1; tem_line <= n; ++tem_line) {
			if ( tem_line != line ) {
				double temp = Augmented_matrix[tem_line][line] / Augmented_matrix[line][line];
				for (int column = line; column <= n + 1; ++column) {
					double temp_number = Augmented_matrix[line][column] * temp;
					Augmented_matrix[tem_line][column] -= temp_number;
				}
			}
		}
	}
	for (int line = 1; line <= n; ++line) {
		Augmented_matrix[line][n + 1] /= Augmented_matrix[line][line];
	}
	//正常高斯消元 
	for (int line = 1; line <= n; ++line) {
		printf ( "%.3lf " , Augmented_matrix[line][n + 1] );
	}
	return 0;
}