883. 高斯消元解线性方程组

https://www.acwing.com/problem/content/submission/code_detail/14020513/

AcWing/883/883.cpp

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