HYSBZ 1013: [JSOI2008] Spherical space generator sphere (Gaussian elimination template)

Title Link: http://www.lydsy.com/JudgeOnline/problem.php?id=1013

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 Input2
0.0 0.0
-1.0 1.0
1.0 0.0Sample Output0.500 1.500HINT

Data size:

For 40% of data, 1<=n<=3

For 100% of data, 1<=n<=10

Tip: Give two definitions:

1, the ball sphere: to the spherical surface any point distance is equal points.

2, Distance: Set two n for Space point A, B coordinates (a1, a2, ..., an), (B1, B2, ..., BN), then AB distance is defined as: dist = sqrt ((A1-B1) ^2 + (A2-B2) ^2 + ... + (an-bn) ^2)

Ps:

Gaussian elimination!

Set the center of the circle (x, y), and then use the radius equal! Using the distance formula we can get n equations, and then use the Gaussian elimination to solve the equation!

Set the circle on a point for (a B) to get: (a-x) ^2+ (b-y) ^2 = a^2-2ax+x^2+b^2-2by+y^2;

Set the circle on a point for (A1,B1) Get: (a-x) ^2+ (b-y) ^2 = a^2-2ax+x^2+b^2-2by+y^2;

Radii equal to get:

2 (a1-a) x+2 (b1-b) y = a1^2-a^2+b1^2-b^2;

The code is as follows:

#include <cstdio> #include <cstring> #include <cmath> #include <iostream>using namespace std; int n; #define EPS 1e-9const int maxn = 220;double a[maxn][maxn],x[maxn];//equation to the left of the matrix and equation to the right of the value, after the solution x is the result int equ,var;//    The number of equations and the number of unknowns/** return 0 for no solution, 1 for the solution */int Gauss () {int i,j,k,col,max_r;        for (k=0,col=0; k<equ&&col<var; k++,col++) {max_r=k;        for (i=k+1; i<equ; i++) if (Fabs (A[i][col]) >fabs (A[max_r][col])) max_r=i;        if (Fabs (A[max_r][col]) <eps) return 0;            if (K!=max_r) {for (j=col; j<var; j + +) Swap (a[k][j],a[max_r][j]);        Swap (X[k],x[max_r]);        } X[k]/=a[k][col];        for (j=col+1; j<var; j + +) A[k][j]/=a[k][col];        A[k][col]=1;                for (i=0; i<equ; i++) if (i!=k) {x[i]-=x[k]*a[i][k];                for (j=col+1; j<var; j + +) A[i][j]-=a[k][j]*a[i][col];            a[i][col]=0; }} return 1;}    int main () {double S[MAXN];        while (~SCANF ("%d", &n)) {memset (x,0,sizeof (x));        Equ = var = n;        for (int i = 0; i < n; i++) {scanf ("%lf", &s[i]);        } double TT; for (int i = 0; i < n; i++) {for (int j = 0; J < N; j + +) {scanf ("%lf", &A                MP;TT);                A[I][J] = (tt-s[j]);            X[I]+=TT*TT-S[J]*S[J];                }} int ans = Gauss ();        printf ("%.3lf", x[0]);        for (int i = 1; i < n; i++) {printf ("%.3lf", X[i]);    } printf ("\ n"); } return 0;}

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HYSBZ 1013: [JSOI2008] Spherical space generator sphere (Gaussian elimination template)