true_gauss.cpp

#include <vector>
#include <iostream>
#include <iomanip>
#include <cmath>
#include <fstream>

using namespace std;

ifstream fin ("in.txt");
ofstream fout ("out.txt");

const double eps = 10e-9;

void print(const vector<vector<double>> & v) {
    for (auto & row : v) {
        for (auto & it : row)
            fout << setw(12) << (fabs(it) > eps ? it : 0);
        fout << endl;
    }
}

vector<double> solve(vector<vector<double>> & D) {
    fout << "Input:" << endl;
    print(D);
    fout << endl;

    int m = D.size(), n = D.front().size(), now = 0;
    for (int j = 0, i; j < n-1; ++j) {
        int max = now;
        for (i = now+1; i < m; ++i)
            if (fabs(D[i][j]) > fabs(D[max][j]))
                max = i;

        if ( fabs(D[max][j]) < 10e-9 ) continue;

        swap(D[max], D[now]);

        for (i = now+1; i < m; ++i) {
            if ( !D[i][j] ) continue;
            double c = D[i][j] / D[now][j];
            for (int k = j; k < n; ++k)
                D[i][k] -= c * D[now][k];
        }
        ++now;
    }

    fout << "First:" << endl;
    print(D);
    fout << endl;

    now = m-1;

    for (int j = n-2; j >= 0; --j, --now) {
        if ( !D[now][j] ) continue;

        for (int i = now-1; i >= 0; --i) {
            if ( !D[i][j] ) continue;
            double c = D[i][j] / D[now][j];
            for (int k = n-1; k >= 0; --k)
                D[i][k] -= c * D[now][k];
        }
    }

    fout << "Second:" << endl;
    print(D);
    fout << endl;

    vector<double> answer(m, 0);
    for (int i = 0; i < m; ++i)
        if ( D[i][i] ) {
            D[i].back() /= D[i][i];
            D[i][i] = 1;
            answer[i] = D[i].back();
        }

    return answer;
}

int main() {
    int n;
    fin >> n;
    vector<vector<double>> s(n, vector<double>(n+1, 0));

    for (auto & row : s)
        for (auto & it : row)
            fin >> it;


    auto a = solve(s);

    fout << "Answer:" << endl;
    for (auto & it : a)
        fout << setw(12) << (fabs(it) > eps ? it : 0);
    fout << endl;

    return 0;
}