/*  prog5a.c -- Solve Least Squares Problem by QR Factorization
    Written Mar 30, 2001 by Eric Olson for Mathematics 483

    For more information see Step 27 in First Steps in Numerical 
    Analysis, 2nd Edition, by Hosking, Joe, Joyce and Turner. */

#include <stdio.h>
#include <math.h>

#define N 200
#define m 4

static int n;
static double At[m][N],C[m],Y[N];

double phi(double x,int i){
    switch(i){
case 0:
        return 1;
        break;
case 1:
        return x;
        break;
case 2:
        return x*x;
        break;
case 3:
        return x*x*x;
        break;
default:
        printf("Unknown basis function number %d!\n",i);
        exit(1);
    }
}

writeC(){
    int i;
    printf("C=[ ");
    for(i=0;i<m;i++){
        printf("%lg ",C[i]);
    }
    printf("]\n");
}

QRsolve(){
    double w[N];
    int l;
    for(l=0;l<m;l++){
        {
            double s=0.0;
            {
                int j;
                for(j=l;j<n;j++) s+=At[l][j]*At[l][j];
            }
            s=sqrt(s);
            if(At[l][l]>0) s=-s;
            s+=s;
            {
                double t=sqrt(0.5-At[l][l]/s);
                int j;
                w[l]=t;
                t*=-s;
                for(j=l+1;j<n;j++) w[j]=At[l][j]/t;
            }
        } {
            int i;
            for(i=l;i<m;i++){
                double s=0.0;
                int j;
                for(j=l;j<n;j++) s+=w[j]*At[i][j];
                s+=s;
                for(j=l;j<n;j++) At[i][j]-=w[j]*s;
            }
        } {
            double s=0.0;
            int j;
            for(j=l;j<n;j++) s+=w[j]*Y[j];
            s+=s;
            for(j=l;j<n;j++) Y[j]-=w[j]*s;
        }
    }
    for(l=m-1;l>=0;l--){
        double s=0.0;
        int k;
        for(k=l+1;k<m;k++) s+=At[k][l]*C[k];
        C[l]=(Y[l]-s)/At[l][l];
    }
}

main(){
    int i,j;
    scanf("%d",&n);
    if(n>N){
        printf("Capacity of %d data points exceeded!\n",N);
        exit(2);
    }
    printf("Reading %d data points:\n",n);
    for(j=0;j<n;j++){
        double x,y;
        scanf("%lg %lg",&x,&y);
        for(i=0;i<m;i++) At[i][j]=phi(x,i);
        Y[j]=y;
    }
    QRsolve();
    writeC();
}