Bzoj 1013 [JSOI2008] Spherical space generator sphere (Gaussian elimination)

1013: [JSOI2008] spherical space generator sphere time limit:1 Sec Memory limit:162 MB
submit:3584 solved:1863
[Submit] [Status] [Discuss] 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)

Source

Ideas

Gaussian elimination element

Column equation: Set two point coordinates of a[],b[], and x[] is the spherical coordinates. is satisfied:

Each of the two adjacent points satisfies this formula to ensure that X is the sphere, so only the n equations need to be solved.

Then the Gaussian elimination equation can be solved.

Code

1#include <cstdio>2#include <cmath>3#include <iostream>4 using namespacestd;5 6typedefDoubleDL;7 Const intN = -;8 9 DL A[n][n],a[n][n];Ten intN; One  A voidGause () { -     intI,j,k,r; -      for(i=0; i<n;i++) {//eliminate Yuan theR=i; -          for(j=i+1; j<n;j++) -             if(Fabs (A[j][i]) >fabs (A[r][i]) r=J; -         if(r!=i) for(j=0; j<=n;j++) Swap (a[r][j],a[i][j]); +          for(j=n;j>=i;j--)//make A[k][i] 0 -              for(k=i+1; k<n;k++) +a[k][j]-=a[k][i]/a[i][i]*A[i][j]; A     } at      for(i=n-1; i>=0; i--) {//Back to Generation -          for(j=i+1; j<n;j++) -a[i][n]-=a[j][n]*A[i][j]; -A[i][n]/=A[i][i]; -     } - } in  - intMain () { toscanf"%d",&n); +      for(intI=0; i<=n;i++) for(intj=0; j<n;j++) -scanf"%LF",&a[i][j]); the      for(intI=0; i<n;i++) {//Tectonic equation set *          for(intj=0; j<n;j++) a[i][j]=2* (a[i+1][j]-a[i][j]); $          for(intj=0; j<n;j++) a[i][n]+=a[i+1][j]*a[i+1][j]-a[i][j]*A[i][j];Panax Notoginseng     } - Gause (); theprintf"%.3LF", a[0][n]);  +      for(intI=1; i<n;i++) printf ("%.3LF", A[i][n]); A     return 0; the}

Bzoj 1013 [JSOI2008] Spherical space generator sphere (Gaussian elimination)