code-library/Math/Gaussian Elimination.cpp at main · ShahjalalShohag/code-library · GitHub

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#include<bits/stdc++.h>
using namespace std;

const int N = 3e5 + 9;

const double eps = 1e-9;
int Gauss(vector<vector<double>> a, vector<double> &ans) {
  int n = (int)a.size(), m = (int)a[0].size() - 1;
  vector<int> pos(m, -1);
  double det = 1; int rank = 0;
  for(int col = 0, row = 0; col < m && row < n; ++col) {
    int mx = row;
    for(int i = row; i < n; i++) if(fabs(a[i][col]) > fabs(a[mx][col])) mx = i;
    if(fabs(a[mx][col]) < eps) {det = 0; continue;}
    for(int i = col; i <= m; i++) swap(a[row][i], a[mx][i]);
    if (row != mx) det = -det;
    det *= a[row][col];
    pos[col] = row;
    for(int i = 0; i < n; i++) {
      if(i != row && fabs(a[i][col]) > eps) {
        double c = a[i][col] / a[row][col];
        for(int j = col; j <= m; j++) a[i][j] -= a[row][j] * c;
      }
    }
    ++row; ++rank;
  }
  ans.assign(m, 0);
  for(int i = 0; i < m; i++) {
    if(pos[i] != -1) ans[i] = a[pos[i]][m] / a[pos[i]][i];
  }
  for(int i = 0; i < n; i++) {
    double sum = 0;
    for(int j = 0; j < m; j++) sum += ans[j] * a[i][j];
    if(fabs(sum - a[i][m]) > eps) return -1; //no solution
  }
  for(int i = 0; i < m; i++) if(pos[i] == -1) return 2; //infinte solutions
  return 1; //unique solution
}
int main() {
  int n, m; cin >> n >> m;
  vector< vector<double> > v(n);
  for(int i = 0; i < n; i++) {
    for(int j = 0; j <= m; j++) {
      double x; cin >> x; v[i].push_back(x);
    }
  }
  vector<double> ans;
  int k = Gauss(v, ans);
  if(k) for(int i = 0; i < n; i++) cout << fixed << setprecision(5) << ans[i] << ' ';
  else cout << "no solution\n";
  return 0;
}