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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#273217#7886. Not Another Eulerian Number Problem_set_AC ✓8ms16384kbC++177.8kb2023-12-02 22:06:152023-12-02 22:06:16

Judging History

你现在查看的是最新测评结果

  • [2023-12-02 22:06:16]
  • 评测
  • 测评结果:AC
  • 用时:8ms
  • 内存:16384kb
  • [2023-12-02 22:06:15]
  • 提交

answer

// what is matter? never mind. 
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,sse4,popcnt,abm,mmx,avx,avx2") 
#include<bits/stdc++.h>
#define For(i,a,b) for(int i=(a);i<=(b);++i)
#define Rep(i,a,b) for(int i=(a);i>=(b);--i)
#define ll long long
#define ull unsigned long long
#define i128 __int128
//#define int long long
using namespace std;
inline int read()
{
	char c=getchar();int x=0;bool f=0;
	for(;!isdigit(c);c=getchar())f^=!(c^45);
	for(;isdigit(c);c=getchar())x=(x<<1)+(x<<3)+(c^48);
	if(f)x=-x;return x;
}

#define mod 998244353
struct modint{
	int x;
	modint(int o=0){x=o;}
	modint &operator = (int o){return x=o,*this;}
	modint &operator +=(modint o){return x=x+o.x>=mod?x+o.x-mod:x+o.x,*this;}
	modint &operator -=(modint o){return x=x-o.x<0?x-o.x+mod:x-o.x,*this;}
	modint &operator *=(modint o){return x=1ll*x*o.x%mod,*this;}
	modint &operator ^=(int b){
		modint a=*this,c=1;
		for(;b;b>>=1,a*=a)if(b&1)c*=a;
		return x=c.x,*this;
	}
	modint &operator /=(modint o){return *this *=o^=mod-2;}
	friend modint operator +(modint a,modint b){return a+=b;}
	friend modint operator -(modint a,modint b){return a-=b;}
	friend modint operator *(modint a,modint b){return a*=b;}
	friend modint operator /(modint a,modint b){return a/=b;}
	friend modint operator ^(modint a,int b){return a^=b;}
	friend bool operator ==(modint a,int b){return a.x==b;}
	friend bool operator !=(modint a,int b){return a.x!=b;}
	bool operator ! () {return !x;}
	modint operator - () {return x?mod-x:0;}
	bool operator <(const modint&b)const{return x<b.x;}
};
inline modint qpow(modint x,int y){return x^y;}

vector<modint> fac,ifac,iv;
inline void initC(int n)
{
	if(iv.empty())fac=ifac=iv=vector<modint>(2,1);
	int m=iv.size(); ++n;
	if(m>=n)return;
	iv.resize(n),fac.resize(n),ifac.resize(n);
	For(i,m,n-1){
		iv[i]=iv[mod%i]*(mod-mod/i);
		fac[i]=fac[i-1]*i,ifac[i]=ifac[i-1]*iv[i];
	}
}
inline modint C(int n,int m){
	if(m<0||n<m)return 0;
	return initC(n),fac[n]*ifac[m]*ifac[n-m];
}
inline modint sign(int n){return (n&1)?(mod-1):(1);}

#define fi first
#define se second
#define pb push_back
#define mkp make_pair
typedef pair<int,int>pii;
typedef vector<int>vi;

#define poly vector<modint>
const modint G=3,Ginv=modint(1)/3;
inline poly one(){poly a;a.push_back(1);return a;}
vector<int>rev;
int rts[2100000];
inline int ext(int n){
	int k=0;
	while((1<<k)<n)++k;return k; 
}
inline void init(int k){
	int n=1<<k;
	rts[0]=1,rts[1<<k]=qpow(31,1<<(21-k)).x;
	Rep(i,k,1)rts[1<<(i-1)]=1ull*rts[1<<i]*rts[1<<i]%mod;
	For(i,1,n-1)rts[i]=1ull*rts[i&(i-1)]*rts[i&-i]%mod;
}

void ntt(poly&a,int k,int typ){
	int n=1<<k;
	static ull tmp[2100000];
	for(int i=0;i<n;++i)tmp[i]=a[i].x;
	if(typ==1){
		for(int l=n>>1;l>=1;l>>=1){
			ull*k=tmp;
			for(int*g=rts;k<tmp+n;k+=(l<<1),++g){
				for(ull*x=k;x<k+l;++x){
					int o=x[l]%mod*(*g)%mod;
					x[l]=*x+mod-o,*x+=o;
				}
			}
		}
		for(int i=0;i<n;++i)a[i].x=tmp[i]%mod;
	}else{
		for(int l=1;l<n;l<<=1){
			ull*k=tmp;
			for(int*g=rts;k<tmp+n;k+=(l<<1),++g){
				for(ull*x=k;x<k+l;++x){
					int o=x[l]%mod;
					x[l]=(*x+mod-o)*(*g)%mod,*x+=o;
				}
			}
		}
		int iv=qpow(n,mod-2).x;
		for(int i=0;i<n;++i)a[i].x=tmp[i]%mod*iv%mod;
		reverse(a.begin()+1,a.end());
	}
}
 
poly operator +(poly a,poly b){
	int n=max(a.size(),b.size());a.resize(n),b.resize(n);
	For(i,0,n-1)a[i]+=b[i];return a;
}
poly operator -(poly a,poly b){
	int n=max(a.size(),b.size());a.resize(n),b.resize(n);
	For(i,0,n-1)a[i]-=b[i];return a;
}
poly operator *(poly a,modint b){
	int n=a.size();
	For(i,0,n-1)a[i]*=b;return a;
} 
poly operator *(poly a,poly b){
	if(!a.size()||!b.size())return {};
	if((int)a.size()<=32 || (int)b.size()<=32){
		poly c(a.size()+b.size()-1,0);
		for(int i=0;i<a.size();++i)for(int j=0;j<b.size();++j)c[i+j]+=a[i]*b[j];
		return c; 
	}
	int n=(int)a.size()+(int)b.size()-1,k=ext(n);
	a.resize(1<<k),b.resize(1<<k);
	ntt(a,k,1),ntt(b,k,1);
	For(i,0,(1<<k)-1)a[i]*=b[i];
	ntt(a,k,-1),a.resize(n);return a;
}

poly Tmp;
poly pmul(poly a,poly b,int n,bool ok=0)
{
	int k=ext(n);
	a.resize(1<<k),ntt(a,k,1);
	if(!ok) b.resize(1<<k),ntt(b,k,1),Tmp=b;
	For(i,0,(1<<k)-1)a[i]*=Tmp[i];
	ntt(a,k,-1),a.resize(n);
	return a;
}
poly inv(poly a,int n)
{
	a.resize(n);
	if(n==1){
		poly f(1,1/a[0]);
		return f;
	}
	poly f0=inv(a,(n+1)>>1),f=f0;
	poly now=pmul(a,f0,n,0);
	for(int i=0;i<f0.size();++i)now[i]=0;
	now=pmul(now,poly(0),n,1);
	f.resize(n);
	for(int i=f0.size();i<n;++i)f[i]=-now[i];
	return f;
}
poly inv(poly a){return inv(a,a.size());}

poly deriv(poly a){
	int n=(int)a.size()-1;
	For(i,0,n-1)a[i]=a[i+1]*(i+1);
	a.resize(n);return a;
}
poly inter(poly a){
	int n=a.size()+1;a.resize(n); initC(n+1);
	Rep(i,n-1,1)a[i]=a[i-1]*iv[i];
	a[0]=0;return a;
}
poly ln(poly a){
	int n=a.size();
	a=inter(deriv(a)*inv(a));
	a.resize(n);return a;
}
poly exp(poly a,int k){
	int n=1<<k;a.resize(n);
	if(n==1)return one();
	poly f0=exp(a,k-1);f0.resize(n);
	return f0*(one()+a-ln(f0)); 
}
poly exp(poly a){
	int n=a.size(); a[0]=0;
	a=exp(a,ext(n));a.resize(n);return a;
}
poly div(poly a,poly b){
	int n=a.size(),m=b.size(),k=ext(n-m+1);
	reverse(a.begin(),a.end()),reverse(b.begin(),b.end());
	a.resize(n-m+1),b.resize(n-m+1);
	a=a*inv(b),a.resize(n-m+1),reverse(a.begin(),a.end()); return a;
}
poly modulo(poly a,poly b){
	if(b.size()>a.size())return a;
	int n=b.size()-1;
	a=a-div(a,b)*b;a.resize(n);return a;
}
poly mulx(poly f){
	int n=f.size(); f.resize(n+1);
	Rep(i,n,1)f[i]=f[i-1]; f[0]=0; return f;
}
poly divx(poly f){
	int n=f.size();
	For(i,0,n-2) f[i]=f[i+1]; f.pop_back(); return f;
}
poly qpow(poly a,int b){
	assert(a[0].x==1);
	return exp(ln(a)*b);
}

#define maxn 200005
#define inf 0x3f3f3f3f

int a,n,m,m0,n0;

poly newton(int n){
	if(n==1)return {0};
	if(n==2)return {0,1};
	poly f0=newton((n+1)>>1); f0.resize(n+1);
//	cout<<"solve "<<n<<"\n";
	poly I=qpow(one()-f0,mod-a);
	poly a=I*f0*(::a-2)+I; a.resize(n);
	poly b=f0*f0; b.resize(n+1); b=b*I*(1-::a+mod); b.resize(n);
	b=divx(b); b.resize(n);
	For(i,1,n-1)a[i]*=iv[i];
	a=exp(a);
	b=b*inv(a),b.resize(n);
	For(i,1,n-1)b[i]*=iv[i];
	b[0]=1;
	poly res=mulx(a*b); res.resize(n);
//	for(auto x:res)cout<<x.x<<" ";cout<<" res\n";
	return res;
}
/*
u'(v) = 1/v'(x)

u(v) = u'(v) * v / ((1-v)^(a-1))
x = 1/v'(x) * v / ((1-v)^(a-1))
1/v'(x) * v / ((1-v)^(a-1)) - x = 0

v / ((1-v)^(a-1)) - x*v' = 0
((a-2)v+1)/((1-v)^a) - x*v''

how??

https://vfleaking.blog.uoj.ac/blog/43

v' = (v / ((1-v)^(a-1))) / x
*/

signed main()
{
	init(21),initC(1<<18|5);
	a=read(),n=read(),m=read(),n0=read();
	int lst=0;
	For(i,1,n0*a){
		int x=read();
		m0+=(lst>x),lst=x;
	}
	if(m<m0)puts("0"),exit(0);
	if(a==1){
		modint res=0;
		For(i,m0,m){
			modint t=qpow(i+1,n-n0)*C(i-m0+n0,n0);
			// * (1-x)^{n+1}
			int nd=m-i;
			t*=sign(nd)*C(n+1,nd);
			res+=t;
		}
		cout<<res.x;
		exit(0);
	}
	// u = u' * x/(1-x)^{a-1}
	// calc u^<-1>
	poly ui=newton(m-m0+3);
//	ui= {0,1,2,499122182,332748135,707089809,798595693,691839573,595780532};
//	poly tmp=ui*qpow(one()-ui,mod-(a-1))-mulx(deriv(ui)); tmp.resize(ui.size());
//	for(auto x:tmp)cout<<x.x<<" ";cout<<" tmp\n";
	
	// G_{n0} = x^{m0+1} / (1-x)^{n0+1}
	ui.resize(m-m0+2);
	poly ux=divx(ui); ux.pb(0);
	
	poly F1=ln(ux),F2=ln(one()-ui);
	poly h=(F1*(m0+1)-F2*((1ll*a*n0+1)%mod));
	h=exp(h);
	h.resize(m-m0+1);
//	for(auto x:h)cout<<x.x<<" ";
	For(i,0,m-m0)h[i]*=qpow(i+m0+1,n-n0);
	h=h*exp(F2*((1ll*a*n+1)%mod));
	h.resize(m-m0+1);
	
//	for(auto x:h)cout<<x.x<<" ";cout<<"\n";
	// need h(u(i))[x^{m+1}]
	// lagrange inversion
	++m;
	modint res=0;
	poly g=exp(F1*(mod-m));
	For(i,0,m-m0-1) res+=h[i]*(i+m0+1)*g[m-m0-1-i];
	res/=m;
	cout<<res.x;
	return 0;
}
/*
3 8 8 1
2 3 1
*/

这程序好像有点Bug,我给组数据试试?

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 8ms
memory: 15632kb

input:

1 4 2 2
2 1

output:

7

result:

ok 1 number(s): "7"

Test #2:

score: 0
Accepted
time: 8ms
memory: 14824kb

input:

2 4 2 2
1 2 2 1

output:

19

result:

ok 1 number(s): "19"

Test #3:

score: 0
Accepted
time: 8ms
memory: 14812kb

input:

1 1 0 1
1

output:

1

result:

ok 1 number(s): "1"

Test #4:

score: 0
Accepted
time: 7ms
memory: 15600kb

input:

3 1 0 1
1 1 1

output:

1

result:

ok 1 number(s): "1"

Test #5:

score: 0
Accepted
time: 7ms
memory: 15592kb

input:

4 1 0 1
1 1 1 1

output:

1

result:

ok 1 number(s): "1"

Test #6:

score: 0
Accepted
time: 8ms
memory: 14816kb

input:

5 1 0 1
1 1 1 1 1

output:

1

result:

ok 1 number(s): "1"

Test #7:

score: 0
Accepted
time: 0ms
memory: 15616kb

input:

10 1 0 1
1 1 1 1 1 1 1 1 1 1

output:

1

result:

ok 1 number(s): "1"

Test #8:

score: 0
Accepted
time: 4ms
memory: 15360kb

input:

1 3 2 1
1

output:

1

result:

ok 1 number(s): "1"

Test #9:

score: 0
Accepted
time: 2ms
memory: 15272kb

input:

3 3 2 3
2 2 2 3 3 3 1 1 1

output:

0

result:

ok 1 number(s): "0"

Test #10:

score: 0
Accepted
time: 8ms
memory: 15932kb

input:

3 3 2 2
1 1 2 2 2 1

output:

5

result:

ok 1 number(s): "5"

Test #11:

score: 0
Accepted
time: 8ms
memory: 16184kb

input:

3 3 2 1
1 1 1

output:

15

result:

ok 1 number(s): "15"

Test #12:

score: 0
Accepted
time: 8ms
memory: 16112kb

input:

3 3 1 2
2 2 2 1 1 1

output:

2

result:

ok 1 number(s): "2"

Test #13:

score: 0
Accepted
time: 4ms
memory: 14352kb

input:

1 4 0 4
4 2 1 3

output:

0

result:

ok 1 number(s): "0"

Test #14:

score: 0
Accepted
time: 0ms
memory: 14216kb

input:

2 4 1 4
1 4 4 3 3 2 2 1

output:

0

result:

ok 1 number(s): "0"

Test #15:

score: 0
Accepted
time: 0ms
memory: 15648kb

input:

2 4 2 4
1 3 3 2 2 4 4 1

output:

1

result:

ok 1 number(s): "1"

Test #16:

score: 0
Accepted
time: 0ms
memory: 15596kb

input:

2 4 2 1
1 1

output:

58

result:

ok 1 number(s): "58"

Test #17:

score: 0
Accepted
time: 4ms
memory: 15132kb

input:

2 4 1 2
1 1 2 2

output:

14

result:

ok 1 number(s): "14"

Test #18:

score: 0
Accepted
time: 8ms
memory: 15928kb

input:

1 8 7 3
2 1 3

output:

0

result:

ok 1 number(s): "0"

Test #19:

score: 0
Accepted
time: 8ms
memory: 15620kb

input:

1 8 0 4
1 2 3 4

output:

1

result:

ok 1 number(s): "1"

Test #20:

score: 0
Accepted
time: 7ms
memory: 14868kb

input:

1 8 4 4
4 3 1 2

output:

771

result:

ok 1 number(s): "771"

Test #21:

score: 0
Accepted
time: 7ms
memory: 16144kb

input:

1 8 1 4
4 3 2 1

output:

0

result:

ok 1 number(s): "0"

Test #22:

score: 0
Accepted
time: 8ms
memory: 16384kb

input:

1 8 7 1
1

output:

1

result:

ok 1 number(s): "1"

Test #23:

score: 0
Accepted
time: 7ms
memory: 15060kb

input:

1 9 2 5
4 3 1 5 2

output:

0

result:

ok 1 number(s): "0"

Test #24:

score: 0
Accepted
time: 4ms
memory: 15608kb

input:

1 9 7 8
6 5 8 3 4 7 2 1

output:

0

result:

ok 1 number(s): "0"

Test #25:

score: 0
Accepted
time: 0ms
memory: 14744kb

input:

1 9 7 7
5 3 2 4 7 6 1

output:

0

result:

ok 1 number(s): "0"

Test #26:

score: 0
Accepted
time: 0ms
memory: 15608kb

input:

1 9 7 6
2 1 3 5 6 4

output:

0

result:

ok 1 number(s): "0"

Test #27:

score: 0
Accepted
time: 4ms
memory: 14828kb

input:

1 9 3 3
1 2 3

output:

20420

result:

ok 1 number(s): "20420"

Test #28:

score: 0
Accepted
time: 3ms
memory: 15092kb

input:

1 10 0 10
5 6 10 1 3 2 4 7 8 9

output:

0

result:

ok 1 number(s): "0"

Test #29:

score: 0
Accepted
time: 4ms
memory: 15628kb

input:

1 10 7 2
2 1

output:

30973

result:

ok 1 number(s): "30973"

Test #30:

score: 0
Accepted
time: 8ms
memory: 15532kb

input:

1 10 1 6
6 3 5 2 4 1

output:

0

result:

ok 1 number(s): "0"

Test #31:

score: 0
Accepted
time: 4ms
memory: 15636kb

input:

1 10 2 1
1

output:

47840

result:

ok 1 number(s): "47840"

Test #32:

score: 0
Accepted
time: 7ms
memory: 14332kb

input:

1 10 5 2
2 1

output:

689155

result:

ok 1 number(s): "689155"

Extra Test:

score: 0
Extra Test Passed