"Gaussian elimination Element" "Jsoi 2008" "Bzoj 1013" spherical space generator sphere

1013: [JSOI2008] spherical space generator sphere

Time Limit: 1 Sec  Memory Limit: 162 MBSubmit: 3211  Solved: 1685

Description

There is a spherical space generator capable of producing a hard sphere in n-dimensional space. Now that you are trapped in this n-dimensional sphere, you only know the coordinates of the n+1 points on the sphere, and you need to determine the spherical coordinates of the n-dimensional sphere as quickly as you can to destroy the sphere space generator.

Input

The first line is an integer, N. The next n+1 line, each row has n real numbers, representing the n-dimensional coordinates of a point on the sphere. Each real number is accurate to 6 digits after the decimal point, and its absolute value is no more than 20000.

Output

With only one row, the n-dimensional coordinates (n real numbers) of the globe are given in turn, and two real numbers are separated by a space. Each real number is exactly 3 digits after the decimal point. Data is guaranteed to be solvable. Your answer must be the same as the standard output in order to score.

Sample Input

20.0 0.0-1.0 1.01.0 0.0

Sample Output

0.500 1.500

HINT

Data size:

对于40%的数据，1<=n<=3对于100%的数据，1<=n<=10

Tips:

给出两个定义：1、 球心：到球面上任意一点距离都相等的点。2、 距离：设两个n为空间上的点A, B的坐标为(a1, a2, …, an), (b1, b2, …, bn)，则AB的距离定义为：dist = sqrt( (a1-b1)^2 + (a2-b2)^2 + … + (an-bn)^2 )

Exercises

Gaussian elimination of the naked problem.
According to the hint can be used as a point of entry, because the n+1 points, so you can use a point as a datum point, and other n points to form n equations.

Code:

#include <iostream>#include <cstdio>#include <cstdlib>#include <cmath>#include <cstring>#include <algorithm>using namespace STD;intNDoublea[ -][ -]={0},b[ -]={0},c[ -][ -]={0};intMain () {scanf("%d", &n); for(intI=1; i<=n+1; i++) for(intj=1; j<=n; J + +)scanf("%LF", &c[i][j]);Doublex=0; for(intI=1; i<=n; i++) { for(intj=1; j<=n; J + +) {a[i][j]=2* (c[i][j]-c[i+1][J]); x+= (C[i][j]*c[i][j])-(c[i+1][j]*c[i+1][J]); } a[i][n+1]=x; x=0; } for(intI=1; i<=n; i++) {if(a[i][i]==0){ for(intj=i+1; j<=n; J + +) {if(a[j][i]!=0){ for(intk=1; k<=n+1; k++) Swap (a[i][k],a[j][k]); Break; }            }        } for(intj=i+1; j<=n; J + +) {X=a[j][i]/a[i][i]; for(intk=1; k<=n+1;        k++) a[j][k]-=a[i][k]*x; }    } for(intI=n; i>=1; i--) {b[i]=a[i][n+1]/a[i][i]; for(intj=i-1; j>=1; j--) {a[j][n+1]-=a[j][i]*b[i]; a[j][i]=0; }    } for(intI=1; i<n; i++)printf("%.3f", B[i]);printf("%.3f\n", B[n]);return 0;}

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"Gaussian elimination" "Jsoi 2008" "Bzoj 1013" spherical space generator sphere