//Name : Babiceanu Florin-Daniel
//Date : 22/03/2019

#include <stdio.h>
#include <stdlib.h>

#define L_MAX 30

int main()
/*
Datele vor fii memorate in matrice incepand cu pozitia [1][1].
Nu se verifica diagonal dominanta => algoritmul nu este stabil.
*/
{
    FILE* input_file;
    FILE* output_file;

    input_file=fopen("data.in", "r");
    output_file=fopen("data.out", "w");

    int n;
    int i=0;
    int j=0;

    float a[L_MAX][L_MAX+1];

    fscanf(input_file,"%d", &n);

    for(i=1; i<=n; i++)
    {
        for(j=1; j<=n+1; j++)
        {
            fscanf(input_file, "%f", &a[i][j]);
        }
    }

    a[1][2]=a[1][2]/a[1][1];// primul R

    for(i=2; i<=n; i++)
    {
        if(a[i][i]==0)
        {
            fprintf(output_file,"Sistemul nu are solutie unica !");
            return 0;
        }
        a[i][i]=a[i][i]-a[i][i-1]*a[i-1][i]; //L
        if(i+1<=n)
        {
            a[i][i+1]=a[i][i+1]/a[i][i];//r
        }
    }

    a[1][1]=a[1][n+1]/a[1][1];

    for(i=2; i<=n ; i++)
    {
       a[i][i] = (a[i][n+1]-a[i][i-1]*a[i-1][i-1])/a[i][i];
    }

    if(a[n][n]==0)
    {
        fprintf(output_file,"Sistemul nu are solutie unica ! 2");
        return 0;
    }
    for(i=n-1;i>=1;i--)
    {
        a[i][n]=a[i][i]-a[i][i+1]*a[i+1][n];
    }

    for(i=1; i<=n; i++)
    {
        fprintf(output_file,"X%d = %f\n", i, a[i][n]);
    }

    fclose(input_file);
    fclose(output_file);

    return 0;
}