[COGS 2353 & 2356] 有标号的DAG计数 容斥原理

 1 #include <cstdio>
 2 #include <cstring>
 3 #include <cstdlib>
 4 #include <cctype>
 5 #define F(i, a, b) for (register int i = (a); i <= (b); i++)
 6 
 7 const int N = 5005;
 8 const int MOD = 10007;
 9 
10 int s, C[N][N], pwr[MOD], f[N];
11 
12 void Prework(void) {
13     C[0][0] = 1;
14     F(i, 1, s) {
15         C[i][0] = 1;
16         F(j, 1, i)
17             C[i][j] = (C[i-1][j] + C[i-1][j-1]) % MOD;
18     }
19     
20     pwr[0] = 1;
21     F(i, 1, MOD)
22         pwr[i] = (pwr[i-1] << 1) % MOD;
23 }
24 inline int Pow(int n) { return pwr[n % (MOD - 1)]; }
25 
26 int main(void) {
27     freopen("DAG.in", "r", stdin);
28     freopen("DAG.out", "w", stdout);
29     
30     scanf("%d", &s), Prework();
31 
32     f[0] = 1;
33     F(n, 1, s)
34         F(k, 1, n)
35             f[n] = (f[n] + (k&1 ? 1LL : -1LL) * C[n][k] * Pow(k*(n-k)) * f[n-k]) % MOD;
36     printf("%d\n", (f[s] + MOD) % MOD);
37     
38     return 0;
39 }