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P2051 [AHOI2009] 中国象棋

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https://www.luogu.com.cn/record/85999692
This commit is contained in:
Baoshuo Ren 2022-09-06 16:54:42 +08:00
parent 2a7f05b968
commit 7f893ac0ff
Signed by: baoshuo
GPG Key ID: 00CB9680AB29F51A
1 changed files with 87 additions and 0 deletions
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Luogu/P2051/P2051.cpp Normal file
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#include <iostream>
using std::cin;
using std::cout;
const char endl = '\n';
const int N = 105;
const int mod = 9999973;
int n, m;
long long f[N][N][N]{1}, ans;
long long C(long long x) {
return x * (x - 1) / 2;
}
int main() {
std::ios::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n >> m;
for (int i = 1; i <= n; i++) {
// 不增加炮
for (int j = 0; j <= m; j++) {
for (int k = 0; j + k <= m; k++) {
f[i][j][k] = f[i - 1][j][k];
}
}
// 增加 1 个炮
//
// 从 1 个炮增加到 2 个炮
for (int j = 0; j <= m; j++) {
for (int k = 1; j + k <= m; k++) {
f[i][j][k] = (f[i][j][k] + f[i - 1][j + 1][k - 1] * (j + 1) % mod) % mod;
}
}
// 增加 1 个炮
//
// 从 0 个炮增加到 1 个炮
for (int j = 1; j <= m; j++) {
for (int k = 0; j + k <= m; k++) {
f[i][j][k] = (f[i][j][k] + f[i - 1][j - 1][k] * (m - j - k + 1) % mod) % mod;
}
}
// 增加 2 个炮
//
// 一列从 0 个炮增加到 1 个炮
// 一列从 1 个炮增加到 2 个炮
for (int j = 0; j <= m; j++) {
for (int k = 1; j + k <= m; k++) {
f[i][j][k] = (f[i][j][k] + f[i - 1][j][k - 1] * j * (m - j - k + 1) % mod) % mod;
}
}
// 增加 2 个炮
//
// 两列从 0 个炮增加到 1 个炮
for (int j = 2; j <= m; j++) {
for (int k = 0; j + k <= m; k++) {
f[i][j][k] = (f[i][j][k] + f[i - 1][j - 2][k] * C(m - j - k + 2) % mod) % mod;
}
}
// 增加 2 个炮
//
// 两列从 1 个炮增加到 2 个炮
for (int j = 0; j <= m; j++) {
for (int k = 2; j + k <= m; k++) {
f[i][j][k] = (f[i][j][k] + f[i - 1][j + 2][k - 2] * C(j + 2) % mod) % mod;
}
}
}
for (int i = 0; i <= m; i++) {
for (int j = 0; i + j <= m; j++) {
ans = (ans + f[n][i][j]) % mod;
}
}
cout << ans << endl;
return 0;
}