# 1013: [JSOI2008] spherical space generator sphere

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1013: [JSOI2008] spherical space generator sphere time limit:1 Sec Memory limit:162 MB
submit:6517 solved:3381
[Submit] [Status] [Discuss] 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 on the point A, B

Coordinates for (A1, A2, ..., an), (B1, B2, ..., bn), the distance of AB is defined as: dist = sqrt ((A1-B1) ^2 + (A2-B2) ^2 +

... + (AN-BN) ^2)

Analysis

There is a ball in an n-dimensional space, and then the center of the circle is calculated. The n+1 points on the ball are given.

This n+1 point is equal to the distance of the sphere. Set the Circle Center \$ (a_1,a_2...a_n) \$, then for each ball on the point \$ (x_1,x_2...x_n) \$, there are

\$ (x_1-a_1) ^2+ (x_2-a_2) ^2+...+ (x_n-a_n) ^2=r^2\$

22 Merge, then get a linear equation, using Gaussian elimination element.

Code
`1#include <cstdio>2#include <cmath>3#include <algorithm>4 5 using namespacestd;6 Const intN = the;7 DoubleA[n][n],c[n];8 intN;9 Ten voidGauss () { One      for(intk=1; k<=n; ++k) { A         //Select line R and line I interchange -         intR =K; -          for(inti=k+1; i<=n; ++i) the             if(Fabs (a[i][k]) > Fabs (a[r][k])) R =i; -         if(r! = k) for(intj=1; j<=n+1; ++j) Swap (A[r][j],a[k][j]); -         //eliminate Yuan -          for(inti=k+1; i<=n; ++i) { +             Doublet = a[i][k]/A[k][k]; -              for(intJ=k; j<=n+1; ++J) a[i][j]-= t*A[k][j]; +         } A     } at     //Back to Generation -      for(intI=n; i>=1; --i) { -          for(intj=i+1; j<=n; ++j) -a[i][n+1]-= a[j][n+1]*A[i][j]; -a[i][n+1] /=A[i][i]; -     } in } - intMain () { to     Doublex; +scanf"%d",&n); -      for(intI=1; i<=n; ++i) thescanf"%LF",&c[i]); *      for(intI=1; i<=n; ++i) \$          for(intj=1; j<=n; ++j) {Panax Notoginsengscanf"%LF",&x); -A[I][J] = (x*2-c[j]*2); thea[i][n+1] + = (x*x-c[j]*c[j]); +         } A Gauss (); the      for(intI=1; i<n; ++i) +printf"%.3LF", a[i][n+1]); -printf"%.3LF", a[n][n+1]); \$     return 0; \$}`

1013: [JSOI2008] spherical space generator sphere

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