【神奇的DP】P2051 [AHOI2009]中国象棋

 1 #include<iostream>
 2 using namespace std;
 3 
 4 int n, m;
 5 const int mod = 9999973;
 6 
 7 inline long long mul(long long x, long long y) 
 8 {
 9     long long res = 0;
10     while (y) 
11     {
12         if (y & 1)res = (res + x) % mod;
13         x = (x << 1) % mod; y >>= 1;
14     }
15     return res;
16 }
17 
18 
19 long long int f[110][110][110];
20 
21 int main()
22 {
23     cin >> n >> m;
24     f[0][0][0] = 1;
25     for (int i = 1; i <= n; i++)
26     {
27         for (int j = 0; j <= m; j++)
28         {
29             for (int k = 0; k <= m - j; k++)
30             {
31                 f[i][j][k] = f[i - 1][j][k];
32                 if (k >= 1) f[i][j][k] += mul(f[i - 1][j + 1][k - 1], 1LL + j);
33                 if (j >= 1) f[i][j][k] += mul(f[i - 1][j - 1][k], 1LL + m - j - k);
34                 if (k >= 2) f[i][j][k] += mul(f[i - 1][j + 2][k - 2], mul((j + 2LL), (j + 1LL)) / 2);
35                 if (k >= 1) f[i][j][k] += mul(mul(f[i - 1][j][k - 1], j), (1LL + m - j - k));
36                 if (j >= 2) f[i][j][k] += mul(f[i - 1][j - 2][k], (2LL + m - j - k) * (1LL + m - j - k) / 2 % mod);
37                 f[i][j][k] %= mod;
38             }
39         }
40     }
41     long long int sum = 0;
42     for (int i = 0; i <= m; i++)
43         for (int j = 0; j <= m; j++)
44         {
45             sum += f[n][i][j];
46             sum %= mod;
47         }
48     cout << sum;
49 }