Wannafly Winter Camp 2020 Day 7D 方阵的行列式 - 数学

于是去弄了个板子来

#include <bits/stdc++.h>
using namespace std;
#define int long long

const int mod = 998244353;
const int N = 505;

int qpow(int p,int q) {return ((q&1)?p:1) * (q?qpow(p*p%mod,q>>1):1) % mod;}

int n, Q;

// Input: a[][],n
// Method: build() modify(i,j,x)
// Output: inv[][], ans
struct matrix {
    int a[N][N], st[N][N], inv[N][N], ans, n;
    void build() {
        ans=1;
        for(int i=1;i<=n;i++) {
            for(int j=1;j<=n;j++) {
                st[i][j]=a[i][j];
            }
        }
        for (int i = 1; i <= n; i++) inv[i][i] = 1;
        for (int i = 1; i <= n; i++) {
            for (int j = i; j <= n; j++) {
                if (a[j][i]) {
                    for (int k = 1; k <= n; k++) {
                        swap(a[i][k], a[j][k]);
                        swap(inv[i][k], inv[j][k]);
                    }
                    if (j > i) ans = (mod - ans) % mod;
                    break;
                }
            }
            int K = qpow(a[i][i], mod-2);
            for (int j = i+1; j <= n; j++) {
                int tmp = K * a[j][i] % mod;
                for (int k = 1; k <= n; k++) {
                    a[j][k] = (a[j][k] + mod - tmp * a[i][k] % mod) % mod;
                    inv[j][k] = (inv[j][k] + mod - tmp * inv[i][k] % mod) % mod;
                }
            }
        }
        for (int i = n; i >= 1; i--) {
            int K = qpow(a[i][i], mod-2);
            ans = ans * a[i][i] % mod;
            for (int j = 1; j <= n; j++) {
                a[i][j] = a[i][j] * K % mod;
                inv[i][j] = inv[i][j] * K % mod;
            }
            for (int j = 1; j < i; j++) {
                int tmp = a[j][i];
                for (int k = 1; k <= n; k++) {
                    a[j][k] = (a[j][k] + mod - tmp * a[i][k] % mod) % mod;
                    inv[j][k] = (inv[j][k] + mod - tmp * inv[i][k] % mod) % mod;
                }
            }
        }
    }
    void modify(int x,int y,int z) {
        int t = (z + mod - st[x][y]) % mod;
        st[x][y] = z;
        for (int i = 1; i <= n; i++) {
            a[i][y] = (a[i][y] + t * inv[i][x] % mod) % mod;
        }
        {
            int i = y;
            int K = qpow(a[i][i], mod-2);
            ans = ans * a[i][i] % mod;
            for (int j = 1; j <= n; j++) {
                a[i][j] = a[i][j] * K % mod;
                inv[i][j] = inv[i][j] * K % mod;
            }
            for (int j = 1; j <= n; j++) {
                if (j == i) continue;
                int tmp = a[j][i];
                for (int k = 1; k <= n; k++) {
                    a[j][k] = (a[j][k] + mod - tmp * a[i][k] % mod) % mod;
                    inv[j][k] = (inv[j][k] + mod - tmp * inv[i][k] % mod) % mod;
                }
            }
        }
    }
} mat;

signed main() {
    scanf("%d%d", &n, &Q);
    mat.n = n;
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= n; j++) {
            scanf("%d", &mat.a[i][j]);
        }
    }
    mat.build();

    while(Q--) {
        int t1,t2,t3;
        scanf("%d%d%d", &t1, &t2, &t3);
        mat.modify(t1,t2,t3);
        printf("%d\n", mat.ans);
    }
}

/*
2 3
0 1
1 0
1 1 1
2 1 2
2 2 1
[Output]
998244352
998244351
998244352
*/