【LOJ】#2532. 「CQOI2018」社交网络

题解

基尔霍夫矩阵，外向树是入度矩阵-邻接矩阵

必须删掉第一行第一列然后再求行列式

代码

#include <bits/stdc++.h>
#define fi first
#define se second
#define pii pair<int, int>
#define pdi pair<db, int>
#define mp make_pair
#define pb push_back
#define enter putchar('\n')
#define space putchar(' ')
#define eps 1e-8
#define mo 974711
#define MAXN 1000005
//#define ivorysi
using namespace std;
typedef long long int64;
typedef double db;
template <class T>
void read(T &res) {
    res = 0;
    char c = getchar();
    T f = 1;
    while (c < '0' || c > '9') {
        if (c == '-') f = -1;
        c = getchar();
    }
    while (c >= '0' && c <= '9') {
        res = res * 10 + c - '0';
        c = getchar();
    }
    res *= f;
}
template <class T>
void out(T x) {
    if (x < 0) {
        x = -x;
        putchar('-');
    }
    if (x >= 10) {
        out(x / 10);
    }
    putchar('0' + x % 10);
}
const int MOD = 10007;
int g[255][255], N, M;
int inc(int a, int b) { return a + b >= MOD ? a + b - MOD : a + b; }
int mul(int a, int b) { return 1LL * a * b % MOD; }
int fpow(int x, int c) {
    int res = 1, t = x;
    while (c) {
        if (c & 1) res = mul(res, t);
        t = mul(t, t);
        c >>= 1;
    }
    return res;
}
int determinant() {
    int res = 1;
    for (int i = 2; i <= N; ++i) {
        int l;
        for (l = i; l <= N; ++l) {
            if (g[l][i]) break;
        }
        if (l != i) {
            res = -res;
            for (int j = i; j <= N; ++j) swap(g[i][j], g[l][j]);
        }
        int inv = fpow(g[i][i], MOD - 2);
        for (int j = i + 1; j <= N; ++j) {
            int t = mul(g[j][i], inv);
            if (t) {
                for (int k = i; k <= N; ++k) {
                    g[j][k] = inc(g[j][k], MOD - mul(t, g[i][k]));
                }
            }
        }
    }
    res = (res + MOD) % MOD;
    for (int i = 2; i <= N; ++i) {
        res = mul(res, g[i][i]);
    }
    return res;
}
void Solve() {
    read(N);
    read(M);
    int u, v;
    for (int i = 1; i <= M; ++i) {
        read(u);
        read(v);
        ++g[u][u];
        --g[v][u];
    }
    for (int i = 1; i <= N; ++i) {
        for (int j = 1; j <= N; ++j) {
            g[i][j] = inc(g[i][j], MOD);
        }
    }
    out(determinant());
    enter;
}
int main() {
#ifdef ivorysi
    freopen("f1.in", "r", stdin);
#endif
    Solve();
    return 0;
}