P2455 [SDOI2006]线性方程组

https://www.luogu.com.cn/record/89160212

Luogu/P2455/P2455.cpp

@@ -0,0 +1,87 @@
+#include <iostream>
+#include <iomanip>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 55;
+const double eps = 1e-6;
+
+int n;
+double a[N][N];
+
+int gauss() {
+    int r, c;
+
+    for (r = c = 1; c <= n; c++) {
+        int t = r;
+
+        for (int i = r; i <= n; i++) {
+            if (std::abs(a[i][c]) > std::abs(a[t][c])) t = i;
+        }
+
+        if (std::abs(a[t][c]) < eps) continue;
+
+        std::swap(a[t], a[r]);
+
+        for (int i = n + 1; i >= c; i--) {
+            a[r][i] /= a[r][c];
+        }
+
+        for (int i = r + 1; i <= n; i++) {
+            if (std::abs(a[i][c]) > eps) {
+                for (int j = n + 1; j >= c; j--) {
+                    a[i][j] -= a[i][c] * a[r][j];
+                }
+            }
+        }
+
+        r++;
+    }
+
+    if (r <= n) {
+        for (int i = r; i <= n; i++) {
+            if (std::abs(a[i][n + 1]) > eps) {
+                return -1;
+            }
+        }
+
+        return 1;
+    }
+
+    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];
+        }
+    }
+
+    return 0;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    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 == 1) {
+        cout << 0 << endl;
+    } else if (r == -1) {
+        cout << -1 << endl;
+    } else {
+        for (int i = 1; i <= n; i++) {
+            cout << 'x' << i << '=' << std::fixed << std::setprecision(2) << (std::abs(a[i][n + 1]) < eps ? 0.0 : a[i][n + 1]) << endl;
+        }
+    }
+
+    return 0;
+}