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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#56933#4812. Counting SequenceKING_UTAC ✓15369ms229188kbC++202.4kb2022-10-21 22:04:402022-10-21 22:06:38

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2022-10-21 22:06:38]
  • 评测
  • 测评结果:AC
  • 用时:15369ms
  • 内存:229188kb
  • [2022-10-21 22:04:40]
  • 提交

answer

#ifndef LOCAL
#pragma GCC optimize ("Ofast")
#pragma GCC optimize ("unroll-loops")
#endif
#include <bits/stdc++.h>
#define SIZE 40005
#define MX 300
#define MX2 2200
using namespace std;

using ll=long long;

using uint=unsigned;
const uint mod=998244353;
struct mint{
	uint v;
	mint(ll vv=0){s(vv%mod+mod);}
	mint& s(uint vv){
		v=vv<mod?vv:vv-mod;
		return *this;
	}
	mint operator -()const{return mint()-*this;}
	mint& operator+=(const mint&r){return s(v+r.v);}
	mint& operator-=(const mint&r){return s(v+mod-r.v);} 
	mint& operator*=(const mint&r){v=(unsigned ll)v*r.v%mod;return *this;}
	mint& operator/=(const mint&r){return *this*=r.inv();}
	
	mint operator+(const mint&r)const{return mint(*this)+=r;}
	mint operator-(const mint&r)const{return mint(*this)-=r;}
	mint operator*(const mint&r)const{return mint(*this)*=r;}
	mint operator/(const mint&r)const{return mint(*this)/=r;}
	
	mint pow(ll n)const{
		if(n<0)return inv().pow(-n);
		mint res(1),x(*this);
		while(n){
			if(n&1)res*=x;
			x*=x;
			n>>=1;
		}
		return res;
	}
	mint inv()const{return pow(mod-2);}
	
	bool operator<(mint r)const{return v<r.v;}
};
mint dp1[2][SIZE][MX],dp2[2][SIZE][MX];
mint dp[MX2][MX2],bef[MX2][MX2];

int main(){
	int n,c;
	scanf("%d%d",&n,&c);
	int k=min(n,225);
	int pos=0;
	mint ret=0;
	for(int L=1;L<=k;L++){
		int mx=min(n,L*(L+1)/2);
		pos=1-pos;
		if(L==1){
			dp1[pos][1][1]=1;
		} else{
			for(int s=1;s<=mx;s++){
				for(int i=1;i<=min(s,L);i++){
					if(i>1) dp1[pos][s][i]=dp1[pos^1][s-i][i+1]*c;
					else dp1[pos][s][i]=0;
					if(i>1&&(L==2||i>2)) dp1[pos][s][i]+=dp1[pos^1][s-i][i-1];
					dp2[pos][s][i]=dp2[pos^1][s-i][i+1];
					if(i>1) dp2[pos][s][i]+=dp2[pos^1][s-i][i-1]*c;
				}
			}
		}
		for(int s=1;s<=mx;s++){
			for(int i=1;i<=min(s,L);i++){
				dp2[pos][s][1]+=dp1[pos][s][i];
			}
			if((n-s)%L==0){
				for(int i=1;i<=min(s,L);i++){
					ret+=dp2[pos][s][i];
				}
			}
		}
	}
	int mx=n/(k+1)+k;
	//while((k+1)*(2*mx-k)/2>n) mx--;
	//mx+=2;
	for(int s=k;s<=n;s++){
		int id=s%(mx+1);
		for(int i=1;i<=min(mx,s);i++){
			dp[id][i]=dp[(s-i+mx+1)%(mx+1)][i+1];
			if(i>1) dp[id][i]+=dp[(s-i+mx+1)%(mx+1)][i-1]*c;
			if(i<=k&&s<=k*(k+1)/2) bef[id][i]=dp2[pos][s][i];
			else bef[id][i]=0;
			bef[id][i]+=bef[(s-k+mx+1)%(mx+1)][i-1];
			dp[id][i]+=bef[(s-i+mx+1)%(mx+1)][i+1];
			if(i>1) dp[id][i]+=bef[(s-i+mx+1)%(mx+1)][i-1]*c;
			if(s==n) ret+=dp[id][i];
		}
	}
	printf("%u\n",ret.v);
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 31ms
memory: 229096kb

input:

5 3

output:

8

result:

ok 1 number(s): "8"

Test #2:

score: 0
Accepted
time: 44ms
memory: 229040kb

input:

1 0

output:

1

result:

ok 1 number(s): "1"

Test #3:

score: 0
Accepted
time: 449ms
memory: 229088kb

input:

2022 39

output:

273239559

result:

ok 1 number(s): "273239559"

Test #4:

score: 0
Accepted
time: 32ms
memory: 229028kb

input:

1 998244352

output:

1

result:

ok 1 number(s): "1"

Test #5:

score: 0
Accepted
time: 40ms
memory: 229032kb

input:

1 12345678

output:

1

result:

ok 1 number(s): "1"

Test #6:

score: 0
Accepted
time: 59ms
memory: 229184kb

input:

20 998998

output:

643731701

result:

ok 1 number(s): "643731701"

Test #7:

score: 0
Accepted
time: 24ms
memory: 229024kb

input:

23 123

output:

947753998

result:

ok 1 number(s): "947753998"

Test #8:

score: 0
Accepted
time: 32ms
memory: 229096kb

input:

50 5555

output:

745339864

result:

ok 1 number(s): "745339864"

Test #9:

score: 0
Accepted
time: 31ms
memory: 229188kb

input:

60 6666

output:

690992218

result:

ok 1 number(s): "690992218"

Test #10:

score: 0
Accepted
time: 32ms
memory: 229184kb

input:

100 50

output:

169678588

result:

ok 1 number(s): "169678588"

Test #11:

score: 0
Accepted
time: 113ms
memory: 229112kb

input:

500 88888

output:

216149701

result:

ok 1 number(s): "216149701"

Test #12:

score: 0
Accepted
time: 226ms
memory: 229024kb

input:

1000 213456

output:

270989457

result:

ok 1 number(s): "270989457"

Test #13:

score: 0
Accepted
time: 418ms
memory: 229176kb

input:

2000 119988

output:

756425375

result:

ok 1 number(s): "756425375"

Test #14:

score: 0
Accepted
time: 651ms
memory: 229096kb

input:

3000 998244352

output:

71841227

result:

ok 1 number(s): "71841227"

Test #15:

score: 0
Accepted
time: 648ms
memory: 229028kb

input:

3000 555555555

output:

79880116

result:

ok 1 number(s): "79880116"

Test #16:

score: 0
Accepted
time: 897ms
memory: 229096kb

input:

4321 1234

output:

949603993

result:

ok 1 number(s): "949603993"

Test #17:

score: 0
Accepted
time: 1058ms
memory: 229024kb

input:

5000 0

output:

5

result:

ok 1 number(s): "5"

Test #18:

score: 0
Accepted
time: 1080ms
memory: 229104kb

input:

5000 88888777

output:

833064960

result:

ok 1 number(s): "833064960"

Test #19:

score: 0
Accepted
time: 1038ms
memory: 229120kb

input:

5000 35557777

output:

696388498

result:

ok 1 number(s): "696388498"

Test #20:

score: 0
Accepted
time: 2313ms
memory: 229088kb

input:

10000 123456

output:

434296902

result:

ok 1 number(s): "434296902"

Test #21:

score: 0
Accepted
time: 4351ms
memory: 229108kb

input:

20000 555555

output:

34806915

result:

ok 1 number(s): "34806915"

Test #22:

score: 0
Accepted
time: 4628ms
memory: 229184kb

input:

30000 777888999

output:

58443551

result:

ok 1 number(s): "58443551"

Test #23:

score: 0
Accepted
time: 4802ms
memory: 229088kb

input:

50000 2

output:

90102905

result:

ok 1 number(s): "90102905"

Test #24:

score: 0
Accepted
time: 5163ms
memory: 229188kb

input:

70000 77998866

output:

202638568

result:

ok 1 number(s): "202638568"

Test #25:

score: 0
Accepted
time: 5749ms
memory: 228972kb

input:

100000 998244352

output:

360520717

result:

ok 1 number(s): "360520717"

Test #26:

score: 0
Accepted
time: 5722ms
memory: 229140kb

input:

100000 555555555

output:

613886009

result:

ok 1 number(s): "613886009"

Test #27:

score: 0
Accepted
time: 7188ms
memory: 228972kb

input:

150000 233333

output:

381065878

result:

ok 1 number(s): "381065878"

Test #28:

score: 0
Accepted
time: 7143ms
memory: 228972kb

input:

150000 20050117

output:

269891864

result:

ok 1 number(s): "269891864"

Test #29:

score: 0
Accepted
time: 9123ms
memory: 229100kb

input:

200000 114514

output:

262861613

result:

ok 1 number(s): "262861613"

Test #30:

score: 0
Accepted
time: 9246ms
memory: 229144kb

input:

200000 1919810

output:

77872388

result:

ok 1 number(s): "77872388"

Test #31:

score: 0
Accepted
time: 15149ms
memory: 229116kb

input:

300000 0

output:

12

result:

ok 1 number(s): "12"

Test #32:

score: 0
Accepted
time: 14854ms
memory: 229104kb

input:

300000 1

output:

298803948

result:

ok 1 number(s): "298803948"

Test #33:

score: 0
Accepted
time: 14943ms
memory: 229100kb

input:

300000 2

output:

106751203

result:

ok 1 number(s): "106751203"

Test #34:

score: 0
Accepted
time: 14891ms
memory: 229116kb

input:

300000 1234

output:

427045479

result:

ok 1 number(s): "427045479"

Test #35:

score: 0
Accepted
time: 14735ms
memory: 228972kb

input:

300000 2345

output:

441593553

result:

ok 1 number(s): "441593553"

Test #36:

score: 0
Accepted
time: 14681ms
memory: 229024kb

input:

300000 20041115

output:

580367993

result:

ok 1 number(s): "580367993"

Test #37:

score: 0
Accepted
time: 14962ms
memory: 229108kb

input:

300000 20050117

output:

579859619

result:

ok 1 number(s): "579859619"

Test #38:

score: 0
Accepted
time: 15369ms
memory: 229112kb

input:

300000 22223333

output:

596066085

result:

ok 1 number(s): "596066085"

Test #39:

score: 0
Accepted
time: 15220ms
memory: 229144kb

input:

300000 175846372

output:

660364393

result:

ok 1 number(s): "660364393"

Test #40:

score: 0
Accepted
time: 15275ms
memory: 229096kb

input:

299999 9999999

output:

954865020

result:

ok 1 number(s): "954865020"

Test #41:

score: 0
Accepted
time: 14991ms
memory: 229176kb

input:

299998 55556666

output:

904862432

result:

ok 1 number(s): "904862432"

Test #42:

score: 0
Accepted
time: 8849ms
memory: 229108kb

input:

190733 31756136

output:

880544587

result:

ok 1 number(s): "880544587"

Test #43:

score: 0
Accepted
time: 9142ms
memory: 229084kb

input:

198497 463488298

output:

185220207

result:

ok 1 number(s): "185220207"

Test #44:

score: 0
Accepted
time: 14868ms
memory: 229100kb

input:

299997 0

output:

16

result:

ok 1 number(s): "16"

Test #45:

score: 0
Accepted
time: 7810ms
memory: 229184kb

input:

168168 296157813

output:

798716760

result:

ok 1 number(s): "798716760"

Test #46:

score: 0
Accepted
time: 6171ms
memory: 229064kb

input:

114514 1919810

output:

783513290

result:

ok 1 number(s): "783513290"