LOJ#3042. 「ZJOI2019」麻将
如何判定一个集合牌有没有胡的子集是不是胡的
就用一个(dp[j][k][0/1])表示有j个连续两个的串，有k个连续1个串，有没有对子，再记一下这个集合里的牌大于等于2的花色数有几个
我们把(dp[j][k][0/1])和大于等于2的花色数作为一副牌的状态，然后给每个状态标号，做一个dp
(f[i][j][S])表示考虑到第(i)种花色，有(j)张牌，状态标号是(S)的方案数，记录到第(j)张牌还没赢的方案数是(S(j))，那么期望就是(frac{sum_{j = 13}^{infty} S(j)}{(4n- 13)!})
#include <bits/stdc++.h>
#define fi first
#define se second
#define pii pair<int,int>
#define mp make_pair
#define pb push_back
#define space putchar(' ')
#define enter putchar('
')
#define eps 1e-10
#define MAXN 200005
#define ba 47
//#define ivorysi
using namespace std;
typedef long long int64;
typedef unsigned int u32;
typedef double db;
template<class T>
void read(T &res) {
res = 0;T f = 1;char c = getchar();
while(c < '0' || c > '9') {
if(c == '-') f = -1;
c = getchar();
}
while(c >= '0' && c <= '9') {
res = res * 10 +c - '0';
c = getchar();
}
res *= f;
}
template<class T>
void out(T x) {
if(x < 0) {x = -x;putchar('-');}
if(x >= 10) {
out(x / 10);
}
putchar('0' + x % 10);
}
const int MOD = 998244353;
int inc(int a,int b) {
return a + b >= MOD ? a + b - MOD : a + b;
}
int mul(int a,int b) {
return 1LL * a * b % MOD;
}
void update(int &x,int y) {
x = inc(x,y);
}
void upmax(int &x,int y) {
x = max(x,min(4,y));
}
int fpow(int x,int c) {
int res = 1,t = x;
while(c) {
if(c & 1) res = mul(res,t);
t = mul(t,t);
c >>= 1;
}
return res;
}
int N;
int cnt[105];
struct state {
int d[3][3];
state() {memset(d,-1,sizeof(d));}
friend state trans(const state &a,int t) {
state c;
for(int j = 0 ; j <= 2 ; ++j) {
for(int k = 0 ; k <= 2 ; ++k) {
if(a.d[j][k] == -1) continue;
for(int i = 0 ; i <= min(2,t - j - k) ; ++i) {
upmax(c.d[k][i],a.d[j][k] + j + (t - j - k - i) / 3);
}
}
}
return c;
}
friend state Max(const state &a,const state &b) {
state t;
for(int j = 0 ; j <= 2 ; ++j) {
for(int k = 0 ; k <= 2 ; ++k) {
t.d[j][k] = max(a.d[j][k],b.d[j][k]);
}
}
return t;
}
friend bool operator == (const state &a,const state &b) {
for(int j = 0 ; j <= 2 ; ++j) {
for(int k = 0 ; k <= 2 ; ++k) {
if(a.d[j][k] != b.d[j][k]) return false;
}
}
return true;
}
friend bool operator != (const state &a,const state &b) {
return !(a == b);
}
friend bool operator < (const state &a,const state &b) {
for(int j = 0 ; j <= 2 ; ++j) {
for(int k = 0 ; k <= 2 ; ++k) {
if(a.d[j][k] != b.d[j][k]) return a.d[j][k] < b.d[j][k];
}
}
return false;
}
};
struct MJ {
state dp[2];int cnt;
MJ() {cnt = 0;dp[0].d[0][0] = 0;}
friend MJ Trans(const MJ &a,int t) {
MJ c;
c.dp[1] = trans(a.dp[1],t);
if(t >= 2) c.dp[1] = Max(trans(a.dp[0],t - 2),c.dp[1]);
c.dp[0] = trans(a.dp[0],t);
if(t >= 2) c.cnt = min(a.cnt + 1,7);
else c.cnt = a.cnt;
return c;
}
friend bool operator == (const MJ &a,const MJ &b) {
for(int i = 0 ; i < 2 ; ++i) if(a.dp[i] != b.dp[i]) return false;
if(a.cnt != b.cnt) return false;
return true;
}
friend bool operator < (const MJ &a,const MJ &b) {
for(int i = 0 ; i < 2 ; ++i) if(a.dp[i] != b.dp[i]) return a.dp[i] < b.dp[i];
if(a.cnt != b.cnt) return a.cnt < b.cnt;
return false;
}
bool win() {
if(cnt >= 7) return true;
for(int i = 0 ; i <= 2 ; ++i) {
for(int j = 0 ; j <= 2 ; ++j) {
if(dp[1].d[i][j] >= 4) return true;
}
}
return false;
}
void print() {
out(cnt);enter;
for(int p = 0 ; p <= 1 ; ++p) {
for(int j = 0 ; j <= 2 ; ++j) {
for(int k = 0 ; k <= 2 ; ++k) {
out(dp[p].d[j][k]);space;
}
enter;
}
}
}
}pool[100006];
map<MJ,int> zz;
int tot;
int dp[2][405][5005],cur,fac[405],invfac[405];
void dfs(MJ a) {
if(zz.count(a)) return;
if(a.win()) return;
zz[a] = ++tot;pool[tot] = a;
for(int i = 0 ; i <= 4 ; ++i) {
dfs(Trans(a,i));
}
}
int C(int n,int m) {
if(n < m) return 0;
return mul(fac[n],mul(invfac[m],invfac[n - m]));
}
void Solve() {
read(N);
int w,a;
for(int i = 1 ; i <= 13 ; ++i) {
read(w);read(a);
cnt[w]++;
}
MJ t;
dfs(t);
dp[0][0][zz[t]] = 1;cur = 0;
fac[0] = 1;
for(int i = 1 ; i <= 400 ; ++i) fac[i] = mul(fac[i - 1],i);
invfac[400] = fpow(fac[400],MOD - 2);
for(int i = 399 ; i >= 0 ; --i) invfac[i] = mul(invfac[i + 1],i + 1);
for(int i = 1 ; i <= N ; ++i) {
memset(dp[cur ^ 1],0,sizeof(dp[cur ^ 1]));
for(int j = 0 ; j <= 4 * (i - 1) ; ++j) {
for(int h = 1 ; h <= tot ; ++h) {
if(!dp[cur][j][h]) continue;
for(int k = max(cnt[i],0) ; k <= 4 ; ++k) {
MJ nxt = Trans(pool[h],k);
if(nxt.win()) continue;
update(dp[cur ^ 1][j + k][zz[nxt]],mul(dp[cur][j][h],C(4 - cnt[i],k - cnt[i])));
}
}
}
cur ^= 1;
}
int ans = 0;
for(int j = 13 ; j <= 4 * N ; ++j) {
for(int h = 1 ; h <= tot ; ++h) {
update(ans,mul(dp[cur][j][h],mul(fac[j - 13],fac[4 * N - j])));
}
}
ans = mul(ans,invfac[4 * N - 13]);
out(ans);enter;
}
int main() {
#ifdef ivorysi
freopen("f1.in","r",stdin);
#endif
Solve();
return 0;
}