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#include <cstdlib>
#include <iomanip>
#include <iostream>
void PrintMatrix(int n, double **a) {
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
std::cout << a[i][j] << ' ';
}
std::cout << '\n';
}
}
void PrintEquation(int n, double **a, double *b) {
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
std::cout << a[i][j] << ' ';
}
std::cout << b[i] << '\n';
}
}
bool HasSolution(int n, double **a, double *b) {
for (int r = 0; r < n; r++) {
bool all_zero = true;
for (int c = 0; c < n; c++) {
if (a[r][c] != 0) {
all_zero = false;
break;
}
}
if (all_zero && b[r] != 0) {
return false;
}
}
return true;
}
void GaussianElimination(int n, double **a, double *b) {
for (int c = 0; c < n; c++) {
int pivot_r = -1;
for (int r = c; r < n; r++) {
if (a[r][c] != 0) {
pivot_r = r;
break;
}
}
if (pivot_r == -1) {
continue;
}
double pivot = a[pivot_r][c];
for (int r = 0; r < n; r++) {
if (r == pivot_r) {
continue;
}
double factor = a[r][c] / pivot;
for (int i = 0; i < n; i++) {
a[r][i] -= factor * a[pivot_r][i];
b[i] -= factor * b[pivot_r];
}
}
for (int i = 0; i < n; i++) {
a[pivot_r][i] /= pivot;
b[pivot_r] /= pivot;
}
}
}
double GetDiff(int n, double *x, double **a, double *b) {
double diff = 0;
for (int r = 0; r < n; r++) {
for (int c = 0; c < n; c++) {
diff += a[r][c] * x[c];
}
diff -= b[r];
}
return diff;
}
int main() {
std::cout << std::showpos << std::fixed << std::setprecision(3);
const int n = 6;
double **a = new double *[n];
double *b = new double[n];
for (int i = 0; i < n; i++) {
a[i] = new double[n];
for (int j = 0; j < n; j++) {
std::cin >> a[i][j];
}
std::cin >> b[i];
}
std::cout << "Equation:\n";
PrintEquation(n, a, b);
GaussianElimination(n, a, b);
std::cout << "After Gaussian Elimination:\n";
PrintEquation(n, a, b);
if (!HasSolution(n, a, b)) {
std::cout << "No solution!\n";
}
if (std::abs(GetDiff(n, b, a, b)) > 1e-6) {
std::cout << "Solution examination failed!\n";
} else {
std::cout << "Solution examination passed!\n";
}
return 0;
}
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