[BZOJ5298][CQOI2018]交错序列(DP+矩阵乘法)

https://blog.csdn.net/dream_maker_yk/article/details/80377490

斯特林数有时并没有用。

 #include<cstdio>
 #include<cstring>
 #include<algorithm>
 #define rep(i,l,r) for (int i=(l); i<=(r); i++)
 typedef long long ll;
 using namespace std;

 const int N=;
 int n,a,b,mod,m,k,ans,fac[N],inv[N];

 struct Mat{
     int a[N][N];
     Mat(){ memset(a,,sizeof(a)); }
 };

 Mat operator *(const Mat &a,const Mat &b){
     Mat c;
     rep(i,,m-) rep(j,,m-) if (a.a[i][j])
         rep(k,,m-) if (b.a[j][k]) c.a[i][k]=(c.a[i][k]+1ll*a.a[i][j]*b.a[j][k])%mod;
     return c;
 }

 Mat ksm(const Mat &a,int b){
     Mat c=a,res;
     rep(i,,m-) res.a[i][i]=;
     for (; b; c=c*c,b>>=)
         if (b & ) res=res*c;
     return res;
 }

 int C(int n,int m){ return n<m ?  : 1ll*fac[n]*inv[m]%mod*inv[n-m]%mod; }

 int ksm(int a,int b){
     int res=;
     for (; b; a=1ll*a*a%mod,b>>=)
         if (b & ) res=1ll*res*a%mod;
     return res;
 }

 int main(){
     scanf("%d%d%d%d",&n,&a,&b,&mod);
     k=a+b+; m=*k;
     fac[]=; rep(i,,m) fac[i]=1ll*fac[i-]*i%mod;
     inv[m]=ksm(fac[m],mod-);
     for (int i=m-; ~i; i--) inv[i]=1ll*inv[i+]*(i+)%mod;
     Mat s; rep(i,,k-) s.a[i][i+k]=;
     rep(i,,k-) rep(j,,i) s.a[j][i]=s.a[j+k][i]=C(i,j);
     s=ksm(s,n); int x=,ans=;
     rep(i,,b) ans=(ans+1ll*C(b,i)*x%mod*(s.a[][a+b-i]+s.a[][a+b-i+k])%mod*(((b-i)&)?-:))%mod,x=1ll*x*n%mod;
     printf("%d\n",(ans+mod)%mod);
     return ;
 }