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 ivorysifreopen("f1.in", "r", stdin);
#endifSolve();return 0;
}