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  1. /*
  2. Name:Sheikh Md. Showrov Uddin Zishan
  3. Id: 230241003
  4. Report: Gauss Elimination
  5. */
  6.  
  7. #include <iostream>
  8. #include <iomanip>
  9. #include <vector>
  10. #include <cmath>
  11.  
  12. using namespace std;
  13.  
  14. void gaussElimination() {
  15.     int n;
  16.     cout << "Enter the order of square matrix: ";
  17.     cin >> n;
  18.  
  19.     vector<vector<double>> A(n, vector<double>(n + 1));
  20.     vector<double> x(n);
  21.  
  22.     cout << "Enter the elements of augmented matrix row-wise:\n";
  23.     for (int i = 0; i < n; i++) {
  24.         for (int j = 0; j <= n; j++) {
  25.             cin >> A[i][j];
  26.         }
  27.     }
  28.  
  29.  
  30.     for (int j = 0; j < n; j++) {
  31.         // Partial Pivoting
  32.         int maxRow = j;
  33.         for (int i = j + 1; i < n; i++) {
  34.             if (fabs(A[i][j]) > fabs(A[maxRow][j])) {
  35.                 maxRow = i;
  36.             }
  37.         }
  38.         if (A[maxRow][j] == 0) {
  39.             cout << "No unique solution exists (singular matrix)." << endl;
  40.             return;
  41.         }
  42.         if (maxRow != j) {
  43.             swap(A[j], A[maxRow]);
  44.         }
  45.  
  46.         // Eliminate
  47.         for (int i = j + 1; i < n; i++) {
  48.             double factor = A[i][j] / A[j][j];
  49.             for (int k = j; k <= n; k++) {
  50.                 A[i][k] -= factor * A[j][k];
  51.             }
  52.         }
  53.     }
  54.  
  55.  
  56.     for (int i = n - 1; i >= 0; i--) {
  57.         x[i] = A[i][n];
  58.         for (int j = i + 1; j < n; j++) {
  59.             x[i] -= A[i][j] * x[j];
  60.         }
  61.         if (A[i][i] == 0) {
  62.             cout << "No unique solution exists (zero diagonal element)." << endl;
  63.             return;
  64.         }
  65.         x[i] /= A[i][i];
  66.     }
  67.  
  68.  
  69.     cout << "\nThe solution is:\n";
  70.     for (int i = 0; i < n; i++) {
  71.         cout << "x" << i + 1 << " = " << fixed << setprecision(6) << x[i] << endl;
  72.     }
  73. }
  74.  
  75. int main() {
  76.     gaussElimination();
  77.  return 0;
  78. }
Success #stdin #stdout 0.01s 5328KB
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stdin
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2 1 -1 8
-3 -1 2 -11
-2 1 2 -3
stdout
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Enter the order of square matrix: Enter the elements of augmented matrix row-wise:

The solution is:
x1 = 1.500000
x2 = -6.500000
https://ideone.com/kDSJIb
language:
C++14 (gcc 8.3)
created:
17 days ago
visibility:
public

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