高斯消元与求秩（整数）

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#include<bits/stdc++.h>
using namespace std;
using i64 = long long;
const int INF  =  1e9;
const i64 INFL = 1e18;
const int MAXN = 100 + 3;
const int MOD  = 998244353;
struct Mat{
    int n, m;
    int W[MAXN][MAXN];
    Mat(int _n = 0, int _m = 0){
        n = _n;
        m = _m;
        for(int i = 1;i <= n;++ i)
            for(int j = 1;j <= m;++ j)
                W[i][j] = 0;
    }
};
int power(int a, int b){
    int r = 1;
    while(b){
        if(b & 1) r = 1ll * r * a % MOD;
        b >>= 1,  a = 1ll * a * a % MOD;
    }
    return r;
}
int inv(int x){
    return power(x, MOD - 2);
}
int mat_rank(Mat &a){
    const int &n = a.n;
    const int &m = a.m;
    int cnt = 0;
    for(int i = 1;i <= m;++ i){
        int p = cnt + 1;
        int f = -1;
        for(int j = p;j <= n;++ j){
            if(a.W[j][i] != 0){
                f = j;
                break;
            }
        }
        if(f == -1)
            continue;
        if(f != p){
            for(int j = 1;j <= m;++ j)
                swap(a.W[p][j], a.W[f][j]);
        }
        ++ cnt;
        int invp = inv(a.W[p][i]);
        for(int j = p + 1;j <= n;++ j){
            int rate = 1ll * a.W[j][i] * invp % MOD;
            for(int k = 1;k <= m;++ k){
                a.W[j][k] = (a.W[j][k] - 1ll * rate * a.W[p][k] % MOD + MOD) % MOD;
            }
        }
    }
    return cnt;
}
int X[MAXN];
int main(){
    int n;
    cin >> n;
    Mat A(n, n);
    Mat T(n, n + 1);
    for(int i = 1;i <= n;++ i){
        for(int j = 1;j <= n;++ j)
            cin >> A.W[i][j];
        for(int j = 1;j <= n;++ j)
            T.W[i][j] = A.W[i][j];
        cin >> T.W[i][n + 1];
    }
    int res1 = mat_rank(A);
    int res2 = mat_rank(T);
    if(res1 != res2)
        cout << -1 << endl;
    else
    if(res2 <  n)
        cout << 0 << endl;
    else {
        for(int i = n;i >= 1;-- i){
            int invp = inv(T.W[i][i]);
            X[i] = 1ll * T.W[i][n + 1] * invp % MOD;
            for(int j = i - 1;j >= 1;-- j){
                int rate = 1ll * T.W[j][i] * invp % MOD;
                T.W[j][    i] = (T.W[j][    i] - 1ll * rate * T.W[i][    i] % MOD + MOD) % MOD;
                T.W[j][n + 1] = (T.W[j][n + 1] - 1ll * rate * T.W[i][n + 1] % MOD + MOD) % MOD;
            }
        }
        for(int i = 1;i <= n;++ i)
            cout << "x" << i << "=" << X[i] << endl;
    }
    return 0;
}