HDU 4623 Crime （状压DP + 数学优化）

#include <bits/stdc++.h>
#define LL long long
#define mem(i, j) memset(i, j, sizeof(i))
#define rep(i, j, k) for(int i = j; i <= k; i++)
#define dep(i, j, k) for(int i = k; i >= j; i--)
#define pb push_back
#define make make_pair
#define INF INT_MAX
#define inf LLONG_MAX
#define PI acos(-1)
using namespace std;

const int N = 2e6 + 5;

short dp[19][N];
int c[30], vis[N], statu[30], bs[30], G[30][30];
int n, mod, up;
int cnt;
int tmp[10] = {2, 3, 5, 7, 11, 13, 17, 19, 23};

int get(int i, int x) {
    int res = (x % bs[i + 1]) / (bs[i]);
    return res;
}

void dfs(int s, int x) {
    if(s == 0) {
        dp[x][0] = 1; return ;
    }
    if(dp[x][s] != -1) return ;
    dp[x][s] = 0;
    rep(i, 1, cnt) {
        if(G[x][i] && get(i, s) >= 1) {
            dfs(s - bs[i], i);
            dp[x][s] = ((int)dp[x][s] + dp[i][s - bs[i]]) % mod;
        }
    }
}

void solve() {

    scanf("%d %d", &n, &mod);
    mem(dp, -1); mem(vis, 0);  mem(statu, 0); mem(c, 0);
    mem(G, 0);
    int ans = 0; cnt = 0;
    statu[++cnt] = 0;
    c[cnt] = 1;

    rep(i, 2, n) { /// 分类
        int st = 0;
        if(i == 17 || i == 19 || i == 23) {
            c[1]++; continue;
        }
        rep(j, 0, 5) {
            if(i % tmp[j] == 0) {
                st |= (1 << j);
            }
        }
        if(!vis[st]) {
            statu[++cnt] = st;
            c[cnt] = 1;
            vis[st] = cnt;
        }
        else c[vis[st]]++;
    }

    rep(i, 1, cnt) rep(j, 1, cnt) { /// 判断是否互质
        if((statu[i] & statu[j]) == 0) G[i][j] = 1;
    }

    up = 0; bs[1] = 1;
    rep(i, 1, cnt) { /// 每一位都有各自的进制
        bs[i + 1] = bs[i] * (c[i] + 1);
        up += bs[i] * c[i];
    }

    rep(i, 1, cnt) {
        dfs(up - bs[i], i);
        ans = ((int)ans + dp[i][up - bs[i]]) % mod;
    }

    rep(i, 1, cnt) {
        while(c[i] > 1) { /// 同一类的还有先取后取之分，要乘 c[i]的阶乘
            ans = ((int)ans * c[i]) % mod;
            c[i]--;
        }
    }

    printf("%d\n", ans);

}

int main() {

    int _; scanf("%d", &_);
    while(_--) solve();


    return 0;

}