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#define _CRT_SECURE_NO_WARNINGS

#include <iostream>
#include <vector>
#include <string>



#define forn(i, n) for(int i = 0; i < int(n); i++)

using namespace std;
const int V = 10;//variant
const int n = 4;
const double k = 1e-2;
using namespace std;


void boost()
{
#ifdef _DEBUG
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
#endif
}
vector< vector< double > > A(n);
vector< double > b(n);

vector< vector< double > > B;

void norm(int k)
{
    double cur = A[k][k];
    b[k] /= cur;
    forn(j, n)
    {
        A[k][j] /= cur;
    }
}
void print()
{
    cout << "\nA = \n";
    forn(i, n)
    {
        forn(j, n)
            cout << A[i][j] << " ";
        cout << endl;
    }
    cout << "\nb = \n";
    forn(i, n)
        cout << b[i] << " ";
    cout << "\n\n";
}


void toZero(int k)
{

    for (int i = k + 1; i < n; ++i)
    {
        double cur = A[i][k] / A[k][k];
        forn(j, n)
        {
            A[i][j] -= A[k][j] * cur;
        }
        b[i] -= b[k] * cur;
    }

}



vector<double> backStep()
{
    vector<double> ans(n);
    ans[n - 1] = b[n - 1];
    for (int i = n - 2; i >= 0; --i)
    {
        double cur = b[i];
        for (int j = n - 1; j > i; --j)
        {
            cur -= ans[j] * A[i][j];
        }
        ans[i] = cur;
    }
    return ans;
}

vector<double> gauss()
{

    forn(i, n - 1) {
        norm(i);
        toZero(i);
        //print();
    }
    norm(n - 1);
    return backStep();


}

void init()
{

    for (int i = 0; i < n; ++i)
    {
        A[i].resize(n);
        A[i][i] = V + i * 2;
    }
    for (int i = 0; i < n; ++i)
    {
        for (int j = 0; j < n; ++j)
        {
            if (i == j)
                continue;
            A[i][j] = (V + i * 2) * k;
        }
    }

    forn(i, n)
    {
        double sum = 0;
        forn(j, n)
        {
            sum += (V + j * 2) * A[i][j];
        }
        b[i] = sum;
    }


}

double det()
{
    forn(i, n - 1)
        toZero(i);
    double res = 1;
    forn(i, n)
        res *= A[i][i];
    return res;
}

void printTransA()
{
    B = vector<vector<double> >(A);
    forn(i, n)
        forn(j, n)
            B[i][j] = A[j][i];
    cout << "\nA^T : \n";
    forn(i, n) {
        forn(j, n)
            cout << B[i][j] << " ";
        cout << endl;
    }
}

int main()
{
    boost();
    init();
    print();
    vector<double> ans = gauss();
    print();
    cout << "\n ans =\n";
    for (auto v : ans)
        cout << v << " ";
    cout << endl;
    forn(i, 15)
        cout << "=";
    cout << endl;
    init();
    cout << "\nDet A = " << det() << endl;
    print();
    forn(i, 15)
        cout << "=";
    init();
    printTransA();


}