BZOJ1013 [JSOI2008] spherical space generator sphere

Description

There is a spherical space generator capable of producing a hard sphere in n-dimensional space. Now that you're trapped in this n-dimensional sphere, you only know the ball.
The coordinates of the n+1 points on the surface, 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 (1<=n=10). 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 exactly the decimal point.
6 bits, and the 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 accurate to the decimal point
After 3 bits. 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

Tip: Give two definitions: 1, Sphere: points that are equal to any point on the sphere. 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)

Exercises

This question ... Do not ignore the line trailing space ... Damn it...

Anyway, since we want to be equal to each other, and have $n$ an unknown, then we should $n$ a equation.

Set the Sphere $o: (x, Y, ..., W) $, $n +1$ points $p_i: (x_i, Y_i, ..., w_i) $,

We choose $dis (O, p_0) = Dis (o, p_i) (0 < i \leq N) $ this $n$ equation, i.e.

$$ (X-X_0) ^2 + (Y-Y_0) ^2 + ... + (w-w_0) ^2 = (x-x_i) ^2 + (y-y_i) ^2 + ... + (w-w_i) ^2$$

Two-item expansion, move items, merge similar terms, get:

$$2 (X_I-X_0) x + 2 (y_i-y_0) y + ... + 2 (w_i-w_0) w = x_i^2-x_0^2 + y_i^2-y_0^2 + ... + w_i^2-w_0^2$$

Gaussian elimination of the element can be.

Attached code:

#include <algorithm> #include <cstdio>const int n = 15;double a[n][n];void gauss (int n) {for (int i = 0; I &l T N    ++i) {int k = i;    for (int j = i + 1; j < n; ++j) if (A[j][i] > a[k][i]) k = j;    for (int j = i; j <= N; ++j) Std::swap (A[i][j], a[k][j]);  for (k = i + 1, k < n; ++k) for (int j = n; j >= i;--j) a[k][j]-= a[i][j] * A[k][i]/a[i][i];    } for (int i = n-1; ~i; i.) {A[I][N]/= a[i][i];  for (int j = i-1; ~j;--j) a[j][n]-= a[i][n] * A[j][i];  }}double P0[n];int Main () {int N;  scanf ("%d", &n);  for (int i = 0; i < n; ++i) scanf ("%lf", &p0[i]);  Double X;    for (int i = 0; i < n; ++i) {a[i][n] =. 0;      for (int j = 0; J < N; ++j) {scanf ("%lf", &x);      A[I][J] = 2 * (X-p0[j]);    A[i][n] + = x * x-p0[j] * P0[J];  }} gauss (n);  printf ("%.3lf", A[0][n]);  for (int i = 1; i < n; ++i) printf ("%.3lf", A[i][n]);  printf ("\ n"); return 0;}

　　

BZOJ1013 [JSOI2008] spherical space generator sphere