Task №4

#include "iostream"
#include "math.h"

using namespace std;
double **directFlow (double **mtrx, double *vector, int n, int *&otv)
{
    double **M=new double *[n];
    for(int i=0;i<n;i++)
        M[i]=new double [n+1];
    for (int i=0;i<n;i++)
        for (int j=0;j<n;j++)
            M[i][j]=mtrx[i][j];
    for (int i=0;i<n;i++)
        M[i][n]=vector[i];
//____________________________________//



    int i_max, j_max;
    double ax;
    for(int k=0;k<n+1;k++)
    {
        i_max = k, j_max = k;
        for (int i = k; i < n; i++ )
            for (int j = k; j < n; j++ )
                if ( fabs( M[i_max] [j_max] ) < fabs( M[i] [j] ) )
                {
                    i_max = i;
                    j_max = j;
                }
  //Переставляем строки
                for (int j = k; j < n+1 && k<n; j++ )
                {
                    ax = M[k][j];
                    M[k] [j] = M[i_max] [j];
                    M[i_max] [j] = ax;
                }
  //Переставляем столбцы
                for ( int i = 0; i < n; i++ )
                {
                    ax = M[i] [k];
    M[i] [k] = M[i] [j_max];
    M[i] [j_max] = ax;
  }
  //Учитываем изменение порядка корней
  int m = otv[k];
  otv[k] = otv[j_max];
  otv[j_max] = m;

        for (int i=1;i+k<n;i++)
        {
            ax=M[i+k][k]/M[k][k];
            for(int j=0;j+k<n+1;j++)
            {
                M[i+k][k+j]-=ax*M[k][k+j];
            }
        }
    }
//____________________________________//


        return M;
}



double *reverseFlow(double **mtrx, int n, int *&otv)
{
    double **M=new double *[n];
    for(int i=0;i<n;i++)
        M[i]=new double [n+1];
    for (int i=0;i<n;i++)
        for (int j=0;j<n+1;j++)
            M[i][j]=mtrx[i][j];
    double c;
    for(int i=0;i<n;i++)
    {
        c=M[i][i];
        for (int j=i;j<n+1;j++)
        {
            M[i][j]/=c;
        }
    }
        double *x=new double [n];
        for(int i=0;i<n;i++)
        {
                x[i]=0;
        }
        x[n-1]=M[n-1][n];
        for(int i=n-2;i>=0;i--)
        {
            x[i]=M[i][n];
            for( int j=1;j+i<n;j++)
                x[i]-=x[i+j]*M[i][i+j];
        }


        return x;
}

double *check (double **mtrx, int n,  double *x)
{
    double **M=new double *[n];
        for(int i=0;i<n;i++)
            M[i]=new double [n];
        for (int i=0;i<n;i++)
            for (int j=0;j<n;j++)
                M[i][j]=mtrx[i][j];
        double *X=new double [n];
            for(int i=0;i<n;i++)
                for (int j=0;j<n;j++)
                    X[j]=x[j];
        double *B=new double [n];
            for(int i=0;i<n;i++)
                for(int j=0;j<n;j++)
                    B[i]+=M[i][j]*X[j];
            return B;

}

int main()
{
    double det=1, c;
    int n;
    cout<<"n="<<endl;
    cin>>n;
    double **a=new double *[n];
    for(int i=0;i<n;i++)
        a[i]=new double [n];
    for (int i=0;i<n;i++)
        for (int j=0;j<n;j++)
        {
            cout<<"a["<<i<<"]["<<j<<"]=";
            cin>>a[i][j];
        }
        double *b=new double [n];
        for (int i=0;i<n;i++)
        {
            cout<<"b["<<i<<"]=";
            cin>>b[i];
        }

        int *otv=new int [n];
        for ( int i = 0; i < n ; i++ )
        otv[i] = i;

        directFlow(a,b,n, otv);
        for(int i=0;i<n;i++)
            det*=directFlow(a,b,n, otv)[i][i];
        cout<<"det="<<det<<endl;
        double *x=new double [n];
                for (int i=0;i<n;i++)
                {
                    x[i]=reverseFlow(directFlow(a,b,n, otv), n, otv)[i];
                }

         for(int i=0;i<n-1;i++)
                for(int j=n-1;j>i;j--)
                    if(otv[j]<otv[j-1])
                                                {
                                                        c=otv[j];
                                                        otv[j]=otv[j-1];
                                                        otv[j-1]=c;
                                                        c=x[j];
                                                        x[j]=x[j-1];
                                                        x[j-1]=c;

                                                }
    for ( int j = 0; j < n; j++ )
        cout<<"x["<<j<<"]="<<x[j]<<endl;


    for(int i=0;i<n;i++)
    cout<<check(a,n,x)[i]<<endl;
        return 0;
}