[数学] 高斯消元解异或线性方程组(高斯消元+模拟)

1. 高斯消元算法+模板

883. 高斯消元解线性方程组

[数学+模板] 高斯消元算法模板(模板)

重点： 高斯消元

思路：

• 异或运算相当于不进位的加法运算，所以整个过程相对于高斯消元来讲更加简单
• 注意正确判断解的三种情况即可

代码：

#include <iostream>
#include <algorithm>

using namespace std;

const int N = 105;

int n;
int a[N][N];

int gauss() {
    int c = 0, r = 0;
    for (c, r; c < n; ++c) {
        int t = r;
        for (int i = r; i < n; ++i) {
            if (a[i][c]) {
                t = i;
                break;
            }
        }
        if (!a[t][c]) continue;
        
        for (int i = c; i <= n; ++i) swap(a[t][i], a[r][i]);
        
        for (int i = r + 1; i < n; ++i) 
            if (a[i][c])
                for (int j = c; j <= n; ++j)
                    a[i][j] ^= a[r][j];
        
        ++r;
    }
    
    if (r < n) {
        for (int i = r; i < n; ++i)
            if (a[i][n])
                return 2;
        
        return 1;
    }
    
    for (int i = n - 1; i >= 0; --i) 
        for (int j = i + 1; j < n; ++j)
            a[i][n] ^= a[i][j] & a[j][n];
    
    return 0;
}


int main() {
    cin >> n;
    for (int i = 0; i < n; ++i) 
        for (int j = 0; j < n + 1; ++j) 
            cin >> a[i][j];
    
    int res = gauss();
    
    if (res == 0) {
        for (int i = 0; i < n; ++i) cout << a[i][n] << endl;
    } 
    else if (res == 1) puts("Multiple sets of solutions");
    else puts("No solution");
    
    return 0;
}