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883. 高斯消元解线性方程组
https://www.acwing.com/problem/content/submission/code_detail/14020513/
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AcWing/883/883.cpp
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96
AcWing/883/883.cpp
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#include <cmath>
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#include <iomanip>
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#include <iostream>
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using std::cin;
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using std::cout;
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const char endl = '\n';
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const int N = 105;
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const double eps = 1e-6;
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int n;
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double a[N][N];
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int gauss() {
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int c, r;
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for (c = 1, r = 1; c <= n; c++) {
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// 找到绝对值最大的一行
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int t = r;
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for (int i = r; i <= n; i++) {
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if (std::abs(a[i][c]) > std::abs(a[t][c])) t = i;
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}
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// 非零
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if (std::abs(a[t][c]) < eps) continue;
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// 将该行移至顶部
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for (int i = c; i <= n + 1; i++) {
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std::swap(a[t][i], a[r][i]);
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}
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// 将该行第一个非零的数变成 1
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for (int i = n + 1; i >= c; i--) {
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a[r][i] /= a[r][c];
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}
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// 将下方所有行的第 c 列变成 0
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for (int i = r + 1; i <= n; i++) {
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if (std::abs(a[i][c]) > eps) { // 非零
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for (int j = n + 1; j >= c; j--) {
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a[i][j] -= a[r][j] * a[i][c];
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}
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}
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}
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r++;
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}
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if (r <= n) {
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for (int i = r; i <= n; i++) {
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if (std::abs(a[i][n + 1]) > eps)
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// 无解
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return -1;
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}
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// 无穷多组解
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return 1;
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}
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// 将系数矩阵化为对角矩阵
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for (int i = n; i; i--) {
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for (int j = i + 1; j <= n; j++) {
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a[i][n + 1] -= a[i][j] * a[j][n + 1];
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}
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}
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// 有解
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return 0;
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}
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int main() {
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std::ios::sync_with_stdio(false);
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cin >> n;
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for (int i = 1; i <= n; i++) {
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for (int j = 1; j <= n + 1; j++) {
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cin >> a[i][j];
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}
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}
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int r = gauss();
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if (r == 0) {
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for (int i = 1; i <= n; i++) {
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if (std::abs(a[i][n + 1]) < eps) a[i][n + 1] = 0;
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cout << std::fixed << std::setprecision(2) << a[i][n + 1] << endl;
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}
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} else if (r == 1) {
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cout << "Infinite group solutions" << endl;
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} else { // r == -1
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cout << "No solution" << endl;
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}
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return 0;
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}
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