Linear algebra (Gaussian elimination): JSOI2008 spherical space Generator sphere

JSOI2008 Spherical Space Generator sphere

"Title 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 Format"

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 Format"

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"

2  0.0 0.0  -1.0 1.0  1.0 0.0

"Sample Output"

0.500 1.500

Prompted

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)

Column equations, and then subtract from the adjacent two groups, eliminating two of times.

1#include <iostream>2#include <cstring>3#include <cstdio>4#include <cmath>5 using namespacestd;6 Const intmaxn= -;7 Const Doubleeps=1e-8;8 DoubleA[MAXN][MAXN];9 Ten voidSolve (intN) { One      for(intI=1; i<=n;i++){ A         intR=i; -          for(intj=i+1; j<=n;j++) -             if(Fabs (A[j][i])-fabs (A[r][i]) >eps) r=J; the         if(r!=i) { -              for(intj=1; j<=n+1; j + +) - swap (a[i][j],a[r][j]); -         } +         Doublex=A[i][i]; -          for(intj=i;j<=n+1; j + +) a[i][j]/=x; +          for(intj=1; j<=n;j++) A             if(i!=j) { atx=A[j][i]; -                  for(intk=i;k<=n+1; k++) -a[j][k]-=a[i][k]*x; -             }     -     } - } in  - intMain () { to #ifndef Online_judge +Freopen ("bzoj_1013.in","R", stdin); -Freopen ("Bzoj_1013.out","W", stdout); the #endif *     intN; $scanf"%d",&n);Panax Notoginseng      for(intI=1; i<=n+1; i++) -          for(intj=1; j<=n;j++)     thescanf"%LF",&a[i][j]); +                  A      for(intI=1; i<=n;i++){ the          for(intj=1; j<=n;j++){ +a[i][n+1]-=a[i][j]*a[i][j]-a[i+1][j]*a[i+1][j]; -a[i][j]=2* (a[i+1][j]-a[i][j]); $         } $     }             -      - Solve (n); the      -      for(intI=1; i<=n;i++)Wuyiprintf"%.3LF", a[i][n+1]);  theprintf"\ n");  -     return 0;  Wu}

Linear algebra (Gaussian elimination): JSOI2008 spherical space Generator sphere