Bzoj 1013: [JSOI2008] spherical space generator sphere Gaussian elimination element

Subtract the upper and lower two equations and then Gaussian elimination

1013: [JSOI2008] spherical space generator sphere time limit: 1 Sec Memory Limit: 162 MB
Submit: 2901 Solved: 1517
[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

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/* ***********************************************author:ckbosscreated time:2015 May 15 Friday 07:45 04 seconds file Name : bzoj1013.cpp************************************************ * * #include <iostream> #include <cstdio># Include <cstring> #include <algorithm> #include <string> #include <cmath> #include <cstdlib > #include <vector> #include <queue> #include <set> #include <map>using namespace Std;const Double eps=1e-8;const int maxn=40;double a[maxn][maxn],x[maxn];int equ,val;bool Gauss () {int i,j,k,col,max_r;for (k=0, col=0;k<equ&&col<val;k++,col++) {max_r=k;for (i=k+1;i<equ;i++) if (Fabs (A[i][col]) >fabs (a[max_ R][col]) max_r=i;if (Fabs (A[max_r][col]) <eps) return False;if (K!=max_r) {for (int j=col;j<val;j++) swap (A[k][j] , A[max_r][j]); swap (X[k],x[max_r]);} X[k]/=a[k][col];for (j=col+1;j<val;j++) a[k][j]/=a[k][col];a[k][col]=1;for (i=0;i<equ;i++) {if (i!=k) {x[i]-=x [K]*a[i][k];for (j=col+1;j<val;j++) a[i][j]-=a[k][J]*a[i][col];a[i][col]=0;}}} return true;} int n;double Cs[maxn][maxn];int Main () {//freopen ("In.txt", "R", stdin),//freopen ("OUT.txt", "w", stdout), scanf ("%d", &n); for (int i=0;i<n+1;i++) for (int j=0;j<n;j++) scanf ("%lf", &cs[i][j]);//build matrixequ=n; val=n;for (int i=0;i<n;i++) {int ii=i+1;double sum=0;for (int j=0;j<n;j++) {a[i][j]=2* (cs[ii][j]-cs[i][j]); sum+= (Cs[ii][j]-cs[i][j]) * (Cs[ii][j]+cs[i][j]);} X[i]=sum;} Gauss (); for (int i=0;i<val;i++) {printf ("%.3lf%c", X[i], (i==val-1)? '        \ n ': ');} return 0;}

Bzoj 1013: [JSOI2008] spherical space generator sphere Gaussian elimination element