Bzoj 1013 [JSOI2008] spherical space generator sphere

1013: [JSOI2008] spherical space generator sphere time limit:1 Sec Memory limit:162 MB
submit:3074 solved:1614
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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

Exercises

We set the sphere to X (x1,x2,..., xn)

Suppose there are two points a (a1,a2,..., an) and B (B1,b2,..., bn)

Then we can get two equations.

(X1-A1) ^2+ (X2-A2) ^2+...+ (Xn-an) ^2=r^2

(X1-B1) ^2+ (X2-B2) ^2+...+ (xn-bn) ^2=r^2

These equations are all two times and cannot be applied to Gaussian elimination

But we can do some processing. Subtract the above two equations to get a

(A1-B1) x1+ (A2-B2) x2+...+ (an-bn) xn=[(a1^2-b1^2) + (a2^2-b2^2) +...+ (an^2-bn^2)]/2

R is eliminated, n equations, n unknowns can be applied to Gaussian elimination template

The template sleeve is Huang long ...

1#include <iostream>2#include <cstdio>3#include <cmath>4#include <algorithm>5#include <queue>6#include <cstring>7 #definePAU Putchar (")8 #defineENT Putchar (' \ n ')9 using namespacestd;TenInlineintRead () { One     intx=0, sig=1;CharCh=GetChar (); A      while(!isdigit (CH)) {if(ch=='-') sig=-1; ch=GetChar ();} -      while(IsDigit (CH)) x=Ten*x+ch-'0', ch=GetChar (); -     returnx*=Sig; the } -InlinevoidWriteintx) { -     if(x==0) {Putchar ('0');return;}if(x<0) Putchar ('-'), x=-x; -     intlen=0, buf[ the]; while(x) buf[len++]=x%Ten, x/=Ten; +      for(inti=len-1; i>=0; i--) Putchar (buf[i]+'0');return; - } + using namespacestd; A Const intmaxn= -+5;Const Doubleeps=1e-7; at intNDoubleF[MAXN],A[MAXN][MAXN]; - DoubleSqrDoublex) {returnx*x;} - voidIni () { -n=read (); -      for(intI=1; i<=n;i++) scanf ("%LF",&f[i]); -      for(intI=1; i<=n;i++) in          for(intj=1; j<=n;j++){ -             DoubleT; toscanf"%LF",&t); +a[i][j]=2* (tf[j]); -a[i][n+1]+=SQR (t)-Sqr (F[j]); the         } * } $ BOOLGauss () {Panax Notoginseng     intnow=1, to; -      for(intI=1; i<=n;i++){ the          for(to=now;to<=n;to++)if(Fabs (A[to][i]) >eps) Break;if(to>n)Continue; +         if(To!=now) for(intj=1; j<=n+1; j + +) Swap (a[to][j],a[now][j]); A         Doublet=A[now][i]; the          for(intj=1; j<=n+1; j + +) a[now][j]/=T; +          for(intj=1; j<=n;j++)if(j!=Now ) { -T=a[j][i]; for(intk=1; k<=n+1; k++) a[j][k]-=t*A[now][k]; $}now++; $     } -      for(inti=now;i<=n;i++)if(Fabs (a[i][n+1]) >eps)return false; -     return true; the } - voidinit () {Wuyi ini (); the     return; - } Wu voidWork () { - Gauss (); About     return; $ } - voidprint () { -      for(intI=1; i<n;i++) printf ("%.3LF", a[i][n+1]); -printf"%.3LF", a[n][n+1]); A     return; + } the intMain () { -Init (); work ();p rint ();return 0; $}

Bzoj 1013 [JSOI2008] spherical space generator sphere