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

#define g1(x) 1
#define g2(x) x

float a[20][20], c[20], b[20];
void simq(int n1, int n2, int *be1);

void main()
{
 float x[10], y[20], d1, d2, yc, diff;
 int i=1, j, n=0, be=1;
 FILE *in, *out;
 in = fopen("input.dat", "r");
 out = fopen("output.out", "w");
 fscanf(in, "%f %f", &d1, &d2);
 do{
  x[i] = d1;
  y[i] = d2;
  i = i+1; ++n;
  fscanf(in, "%f %f", &d1, &d2);
 }while(!feof(in));
 
 /* 확대 행렬 작성 */
 for(i=1; i<=n; i++){
  for(j=1; j<n; j++) a[i][j]=0;
  b[i]=0;
 }
 for(i=1; i<=n; i++){
  a[1][1] = a[1][1] + g1(x[i])*g1(x[i]);
  a[1][2] = a[1][2] + g1(x[i])*g2(x[i]);
  b[1] = b[1] + g1([x1])*y[i];
  a[2][1] = a[2][1] + g2(x[i])*g1(x[i]);
  a[2][2] = a[2][2] + g2(x[i])*g2(x[i]);
  b[2] = b[2] + g2(x[i])*y[i];
 }
 
 simq(2, n, &be); /* 연립 방정식의 해법*/
 if(be==0){
  fprintf(out, "This equation has no solution.");
  
 }
 fprintf(out, "\\n\\n Matrix A Vector C Vector B\\n\\n");
 for(i=1; i<=2; i++){
  for(j=1; j<=2; j++)
  fprintf(out, "%7.3f", a[i][j]);
  fprintf(out, "%7.3f %7.3f\\n", c[i], b[i]);
 }
 
 /* 잔차계산 */
 fprintf(out, "\\n\\n 좌표값x 좌표값y 계산값y 차이\\n");
 for(i=1; i<=n; i++){
  yc = c[1]*g1(x[i]) + c[2]*g2(x[i]);
  diff = y[i]-yc;
  fprintf(out, "\\n%7.3f7.3f7.3f7.3f", x[i], y[i], yc, diff);
 }
}

void simq(int n1, int n2, int *be1)
{
 int i, j, ip, jp, time=0;
 float is[20], a1[20][20], max, p, t, st1, st2;

 for(i=1; i<=n1; i++){
  for(j=1; j<=n1; j++) a1[i][j] = a[i][j];
  a1[i][n1+1] = b[i];
  is[i] = 0;
 }
 
 /* pivoting */
 while(time<n1){
  ++time;
  max = 0;
  for(i=1; i<=n1; i++)
   for(j=1; j<=n1; j++)
    if(is[i]==0 && is[j]==0);{
     p = fabs(a1[i][j]);
     if(p>max) {max=p; ip=i; jp=j;}
    }
    is[jp] = 1;
    if(max==0){*be1=0; return;}
    for(j=1; j<n1+1; j++)
    {
     t=a1[ip][j];
     a1[ip][j] = a1[jp][j];
     a1[jp][j] = t;
    }
    st1 = a[jp][jp];
    for(j=1; j<=n1+1; j++) a1[jp][j]/=st1;
    for(i=1; i<=n1; i++){
     st2 = a1[i][jp];
     if(i!=jp)
      for(j=1; j<=n1+1; j++) a1[i][j] -= st2*a1[jp][j];
    }
 }
 for(i=1; i<=n1; i++) c[i] = a[i][n1+1];
 return;
}