[bzoj1013] [JSOI2008] Spherical space generator sphere-[Gaussian elimination element]

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)

This is a Gaussian elimination of the template problem, we have a n+1 point, set the coordinates of the sphere (X1,X2,X3......,XN) so every point to its distance should be equal, so we can get n+1 nonlinear equation

then, using n+1 nonlinear equations, each nonlinear equation except 1 can get a linear equation by subtracting the first nonlinear equation, so that we have an n linearthen move the constant term to the other side of the equal sign to list the determinant using Gaussian elimination. On the Code

1#include <iostream>2#include <cstdio>3#include <cstdlib>4#include <cstring>5 #defineEPS 1e-66 using namespacestd;7 intN;8 structMatrix9 {Ten     Doubled[ the]; One}s[ the],a[ the]; A Doubleans[ the]; - voidWAPs (intXinty) - { the matrix tmp; -tmp=A[x]; -a[x]=A[y]; -a[y]=tmp; + } - DoubleAsbDoublex) + { A     if(x<0)return-x; at     returnx; - } - voidGauss () - { -      for(intI=1, col=1; i<=n;++i) -     { in         intp=i; -          for(intj=i+1; j<=n;++j) to         { +             if(ASB (A[j].d[col])-ASB (A[p].d[col]) >EPS) -             { thep=J; *             } $         }Panax Notoginseng         if(p!=i) - WAPs (p,i); the         if(a[i].d[col]==0) +         { Acol++; thei--; +             Continue; -         } $          for(intj=i+1; j<=n;++j) $         { -             Doublenow=a[i].d[col]/A[j].d[col]; -              for(intk=col;k<=n+1;++k) the             { -a[j].d[k]*=now,a[j].d[k]-=A[i].d[k];Wuyi             } the         } -col++; Wu     } - } About voidGet_ans () $ { -      for(intI=n;i>0;--i) -     { -      for(intj=n;j>i;--j) A     { +a[i].d[n+1]-=a[i].d[j]*Ans[j]; the     } -ans[i]=a[i].d[n+1]/A[i].d[i]; $     } the      for(intI=1; i<n;++i) the     { theprintf"%.3LF", Ans[i]); the     } -printf"%.3LF", Ans[n]); in } the intMain () the { Aboutscanf"%d",&n); the      for(intI=0; i<=n;++i) the      for(intj=1; j<=n;++j) the     { +scanf"%LF",&s[i].d[j]); -     } the      for(intI=1; i<=n;++i)Bayi      for(intj=1; j<=n;++j) the     { thea[i].d[j]=2*s[i].d[j]-2*s[0].d[j]; -a[i].d[n+1]+=s[i].d[j]*s[i].d[j]-s[0].d[j]*s[0].d[j]; -     } the Gauss (); the Get_ans (); the     return 0; the}

Spherical Space Generator

[bzoj1013] [JSOI2008] Spherical space generator sphere-[Gaussian elimination element]