Description

題庫鏈接

求 \(n\) 個點以 \(1\) 為根的有向生成樹個數。

\(1\leq n\leq 250\)

Solution

我終於會 \(\texttt{Matrix-Tree}\) 辣！！

寫詳解是不可能的，直接丟鏈接。

註意的是有向圖度數矩陣是入度。

Code

#include <bits/stdc++.h>
using namespace std;
const int N = 250+5, yzh = 10007;

int n, m, u, v, a[N][N];

int gauss() {
    int ans = 1;
    for (int i = 2
 
; i <= n; i++) {
        for (int j = i+1; j <= n; j++)
            while (a[j][i]) {
                int t = a[i][i]/a[j][i];
                for (int k = i; k <= n; k++) (a[i][k] -= a[j][k]*t%yzh) %= yzh;
                swap(a[i], a[j]); ans *= -1;
            }
        (ans *= a[i][i]) %= yzh;
    }
    return
 
 (ans+yzh)%yzh;
}
void work() {
    scanf("%d%d", &n, &m);
    for (int i = 1; i <= m; i++) {
        scanf("%d%d", &v, &u);
        ++a[v][v], --a[u][v];
    }
    printf("%d\n", gauss());
}
int main() {work(); return 0; }

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