884. 高斯消元解异或线性方程组

https://www.acwing.com/problem/content/submission/code_detail/14082659/

AcWing/884/884.cpp

@@ -0,0 +1,89 @@
+#include <cmath>
+#include <iomanip>
+#include <iostream>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 105;
+
+int n, a[N][N];
+
+int gauss() {
+    int c, r;
+
+    for (c = r = 1; c <= n; c++) {
+        int t = r;
+
+        for (int i = r; i <= n; i++) {
+            if (a[i][c]) t = i;
+        }
+
+        if (!a[t][c]) continue;
+
+        std::swap(a[t], a[r]);
+
+        for (int i = r + 1; i <= n; i++) {
+            if (a[i][c]) {
+                for (int j = n + 1; j >= c; j--) {
+                    a[i][j] ^= a[r][j];
+                }
+            }
+        }
+
+        r++;
+    }
+
+    if (r <= n) {
+        for (int i = r; i <= n; i++) {
+            if (a[i][n + 1]) {
+                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 >> n;
+
+    for (int i = 1; i <= n; i++) {
+        for (int j = 1; j <= n + 1; j++) {
+            cin >> a[i][j];
+        }
+    }
+
+    switch (gauss()) {
+        case 0: {
+            for (int i = 1; i <= n; i++) {
+                cout << a[i][n + 1] << endl;
+            }
+
+            break;
+        }
+        case 1: {
+            cout << "Multiple sets of solutions" << endl;
+
+            break;
+        }
+        case -1: {
+            cout << "No solution" << endl;
+
+            break;
+        }
+    }
+
+    return 0;
+}