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ID题目提交者结果用时内存语言文件大小提交时间测评时间
#239903#6187. Digit Sum ProblemCrysflyAC ✓317ms144076kbC++173.6kb2023-11-05 00:21:252023-11-05 00:21:26

Judging History

你现在查看的是最新测评结果

  • [2023-11-05 00:21:26]
  • 评测
  • 测评结果:AC
  • 用时:317ms
  • 内存:144076kb
  • [2023-11-05 00:21:25]
  • 提交

answer

// what is matter? never mind. 
#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 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=(__int128)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 maxn 200005
#define inf 0x3f3f3f3f

const int N1=(1<<22)+5,N2=4782969+5;
int n,s1,s2,c1,c2,B1,B2,l1,l2;
modint x,y,z,pw2[114],pw3[114];
modint F[N1+N2],G[N1+N2],*f=F+N2,*g=G+N2;

void solveF()
{
	int len1=1,len2=1; f[0]=1;
	while(len1<B1 || len2<B2){
		if(len1<len2){
			Rep(i,len1-1,-len2+1)if(f[i].x)f[i+len1]+=f[i]*y;
			len1*=2;
		}else{
			modint w=qpow(x,len2)*z;
			For(i,-len2+1,len1-1)
				if(f[i].x)f[i-len2]+=f[i]*w,f[i-len2*2]+=f[i]*w*w;
			len2*=3;
		}
	}
}

int cnt2,cnt3,d2[99],d3[99];
void digit(int x){
	int t=x; cnt2=cnt3=0;
	For(j,0,44)cnt2+=(d2[j]=t%2),t/=2;
	For(j,0,28)cnt3+=(d3[j]=x%3),x/=3;
}
void inc(){
	++d2[0],++d3[0],++cnt2,++cnt3;
	For(j,0,44)if(d2[j]==2)d2[j]=0,++d2[j+1],--cnt2; else break;
	For(j,0,28)if(d3[j]==3)d3[j]=0,++d3[j+1],cnt3-=2;else break;
}

void solveG()
{
	// B2j2 - B1j1
	// 枚举 j2
	// += y^{a(j1)}*z^{b(j2)}*x^{j2*B2} 
	digit(0);
	modint xmul=1;
	modint xb2=qpow(x,B2);
	For(i,0,l2-1){
		for(int j=i*B2/B1;j<l1 && i*B2-j*B1>-B2;++j)
			g[i*B2-j*B1]+=xmul*pw3[cnt3]*pw2[__builtin_popcountll(j)];
		xmul*=xb2,inc();
	}
}

signed main()
{
	n=read(),x=read(),y=read(),z=read();
	*pw2=*pw3=1;
	For(i,1,60)pw2[i]=pw2[i-1]*y,pw3[i]=pw3[i-1]*z;
	for(int x=1;x<n;x*=2)++s1;
	for(int x=1;x<n;x*=3)++s2;
	c1=(s1+1)/2,c2=(s2+1)/2,B1=(1ll<<c1),B2=1;
	For(i,1,c2)B2*=3; l1=n/B1,l2=n/B2;
	solveF();
	solveG();
	modint res=0;
	For(i,-B2+1,B1-1) res+=f[i]*g[i];
	res-=1;
	
	int mx=min(l1*B1,l2*B2); digit(mx);
	modint mul=qpow(x,mx%(mod-1));
	For(i,mx,n){
		res+=mul*pw2[cnt2]*pw3[cnt3];
		mul*=x,inc();
	}
	
	cout<<res.x;
	return 0;
}

详细

Test #1:

score: 100
Accepted
time: 10ms
memory: 143860kb

input:

123456 12345 234567 3456789

output:

664963464

result:

ok 1 number(s): "664963464"

Test #2:

score: 0
Accepted
time: 314ms
memory: 143864kb

input:

9876543210987 12816 837595 128478

output:

7972694

result:

ok 1 number(s): "7972694"

Test #3:

score: 0
Accepted
time: 280ms
memory: 144064kb

input:

9196665971964 727160879 966835565 746444639

output:

949890012

result:

ok 1 number(s): "949890012"

Test #4:

score: 0
Accepted
time: 278ms
memory: 143716kb

input:

9361549073598 749653880 965489817 371100607

output:

949904373

result:

ok 1 number(s): "949904373"

Test #5:

score: 0
Accepted
time: 313ms
memory: 144032kb

input:

9567572694963 193332930 544713669 390021151

output:

878781872

result:

ok 1 number(s): "878781872"

Test #6:

score: 0
Accepted
time: 317ms
memory: 143864kb

input:

9769301349033 215825931 425927410 408941695

output:

351574791

result:

ok 1 number(s): "351574791"

Test #7:

score: 0
Accepted
time: 305ms
memory: 144076kb

input:

9975324970399 657749333 5151262 729852127

output:

400022780

result:

ok 1 number(s): "400022780"

Test #8:

score: 0
Accepted
time: 12ms
memory: 143812kb

input:

1 149762920 266126484 107367523

output:

910371791

result:

ok 1 number(s): "910371791"

Test #9:

score: 0
Accepted
time: 95ms
memory: 143808kb

input:

903900971479 969144397 356713678 36786741

output:

414279957

result:

ok 1 number(s): "414279957"

Test #10:

score: 0
Accepted
time: 115ms
memory: 144028kb

input:

1940757501452 72683414 106545701 263512239

output:

786323834

result:

ok 1 number(s): "786323834"

Test #11:

score: 0
Accepted
time: 198ms
memory: 143864kb

input:

2914414844884 174466783 133201789 792227626

output:

187534312

result:

ok 1 number(s): "187534312"

Test #12:

score: 0
Accepted
time: 214ms
memory: 144000kb

input:

3851250038782 553074217 881278164 297532837

output:

847958862

result:

ok 1 number(s): "847958862"

Test #13:

score: 0
Accepted
time: 212ms
memory: 143840kb

input:

4692374803740 352867698 211679787 826248223

output:

426334178

result:

ok 1 number(s): "426334178"

Test #14:

score: 0
Accepted
time: 261ms
memory: 143868kb

input:

5566041306806 454651067 959756163 633543322

output:

842296050

result:

ok 1 number(s): "842296050"

Test #15:

score: 0
Accepted
time: 260ms
memory: 143844kb

input:

6902869060611 556434437 709588186 860268821

output:

897681255

result:

ok 1 number(s): "897681255"

Test #16:

score: 0
Accepted
time: 275ms
memory: 144000kb

input:

7239695301792 356227918 736244273 667563920

output:

726280051

result:

ok 1 number(s): "726280051"

Test #17:

score: 0
Accepted
time: 290ms
memory: 143848kb

input:

8217660029470 458011287 486076297 198034954

output:

967159922

result:

ok 1 number(s): "967159922"