BZOJ4555 求和

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推导先放一放吧。。 这道题给我的教育很深刻：

  1. 一定要分清循环的是下标还是长度。FFT的lenlen写成了<n< n，查了很长时间
  2. 谨防填错模板函数参数的数据类型。

Code

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#include "lucida"
using std::swap;
using std::reverse;
const int MAXN=100000+11,P=998244353,MAXL=MAXN<<2,orig=3;
template <class T>
T pow(T base,int index) {
	T res;
	for(res=1;index;base*=base,index>>=1) {
		if(index&1) {
			res*=base;
		}
	}
	return res;
}

namespace modint {
	template <int modu> struct ModInt {
		int64 num;
		ModInt() {}
		ModInt(int64 num):num(num%P) {}
		ModInt inverse() const {
			return pow(*this,modu-2);//modu-1?..	
		}
		friend ModInt operator +(const ModInt &a,const ModInt &b) {
			return ModInt(a.num+b.num);
		}
		friend ModInt operator -(const ModInt &a,const ModInt &b) {
			return ModInt(a.num-b.num);
		}
		friend ModInt operator *(const ModInt &a,const ModInt &b) {
			return ModInt(a.num*b.num);
		}
		friend ModInt operator /(const ModInt &a,const ModInt &b) {
			return a*b.inverse();
		}
	};
}
typedef modint::ModInt<P> ModInt;
ModInt fac[MAXN];
struct _{_(){
	fac[0]=1;
	for(int i=1;i<MAXN;++i) {
		fac[i]=fac[i-1]*i;
	}
}}Auto;
void Trans(ModInt a[],int n,int d) {
	for(int i=1,j=n>>1;i<n-1;++i) {
		if(i<j) swap(a[i],a[j]);
		int k=n>>1;
		while(k<=j) {
			j-=k;
			k>>=1;
		}
		j+=k;
	}
	for(int len=2;len<=n;len<<=1) {//<=n?<n?.
		ModInt rt=pow((ModInt)orig,(P-1)/len);//实例化了int.
		//cos(2*pi*d/len),sin(2*pi*d/len)
		for(int i=0;i<n;i+=len) {
			ModInt w=1;
			for(int j=i;j<i+(len>>1);++j) {
				ModInt u=a[j],t=w*a[j+(len>>1)];
				a[j]=u+t,a[j+(len>>1)]=u-t;
				w*=rt;
			}
		}
	}
	if(d==-1) {
		reverse(a+1,a+n);
		ModInt inv=ModInt(n).inverse();
		for(int i=0;i<n;++i) {
			a[i]*=inv;
		}
	}
}
struct Polynomial {
	int64 a[MAXL],n;
	int64 &operator [](const int &x) {
		return a[x];
	}
	const int64 &operator [](const int &x) const {
		return a[x];
	}
	friend Polynomial operator *(const Polynomial &A,const Polynomial &B) {
		static Polynomial C;
		static ModInt a[MAXL],b[MAXL],c[MAXL];
		int n=1;for(int lim=C.n=A.n+B.n-1;n<lim;n<<=1);
		for(int i=0;i<n;++i) {
			a[i]=i<A.n?A[i]:0;
			b[i]=i<B.n?B[i]:0;
		}
		Trans(a,n,1);Trans(b,n,1);
		for(int i=0;i<n;++i) {
			c[i]=a[i]*b[i];
		}
		Trans(c,n,-1);
		for(int i=0;i<C.n;++i) {
			C[i]=c[i].num;
		}
		return C;
	}
}A,B,C;
int main() {
	freopen("input","r",stdin);
	int n;is>>n;
	A.n=B.n=n+1;
	for(int i=0;i<=n;++i) {
		A[i]=((i&1?-1:1)/fac[i]).num;
	}
	B[0]=1;
	B[1]=n+1;
	for(int i=2;i<=n;++i) {
		B[i]=((1-pow((ModInt)i,n+1))/((1-i)*fac[i])).num;
	}
	C=A*B;
	ModInt res=0;
	for(int i=0;i<=n;++i) {
		res+=pow(ModInt(2),i)*fac[i]*C[i];
	}
	int64 Ans=(res.num+P)%P;
	os<<Ans<<'\n';
	return 0;
}