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QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#313590#8180. Bridge Eliminationucup-team266#AC ✓370ms63124kbC++204.6kb2024-01-24 20:57:402024-01-24 20:57:40

Judging History

你现在查看的是最新测评结果

  • [2024-01-24 20:57:40]
  • 评测
  • 测评结果:AC
  • 用时:370ms
  • 内存:63124kb
  • [2024-01-24 20:57:40]
  • 提交

answer

/*
Things to notice:
1. do not calculate useless values
2. do not use similar names
 
Things to check:
1. submit the correct file
2. time (it is log^2 or log)
3. memory
4. prove your naive thoughts 
5. long long
6. corner case like n=0,1,inf or n=m
7. check if there is a mistake in the ds or other tools you use
8. fileio in some oi-contest

9. module on time 
10. the number of a same divisor in a math problem
11. multi-information and queries for dp and ds problems
*/
#include<bits/stdc++.h>
using namespace std;
#define int long long
#define fi first
#define se second
#define pii pair<long long,long long>
#define mp make_pair
#define pb push_back
const int mod=998244353;
const int inf=0x3f3f3f3f;
const int INF=1e18;
struct CountGraphs
{
	#define maxn 600005
#define mod 998244353
#define rep(i,j,k) for(int i=(j),LIM=(k);i<=LIM;i++)
#define per(i,j,k) for(int i=(j),LIM=(k);i>=LIM;i--)

int Wl,Wl2,w[maxn]={1},lg[maxn],inv[maxn]={1,1},fac[maxn]={1,1},invf[maxn]={1,1};
int Pow(int b,int k){ int r=1;for(;k;k>>=1,b=1ll*b*b%mod) if(k&1) r=1ll*r*b%mod; return r; }
void init(int n){
	for(Wl=1;n>=Wl<<1;Wl<<=1); w[1]=Pow(3,(mod-1)/(Wl2=Wl<<1));
	rep(i,2,Wl2) w[i]=1ll*w[i-1]*w[1]%mod,lg[i]=lg[i>>1]+1,fac[i]=1ll*fac[i-1]*i%mod,
		inv[i]=1ll*(mod-mod/i)*inv[mod%i]%mod,invf[i]=1ll*invf[i-1]*inv[i]%mod;
}
void NTT(int *A,int n,int tp){
	static int r[maxn];
	rep(i,1,n-1) i<(r[i]=r[i>>1]>>1|(i&1)<<lg[n]-1) && (swap(A[i],A[r[i]]),0);
	for(int L=1,B=Wl;L<n;L<<=1,B>>=1) for(int s=0;s<n;s+=L<<1) for(int k=s,x=0,t;k<s+L;k++,x+=B)
		t=1ll*w[tp^1?Wl2-x:x]*A[k+L]%mod,A[k+L]=(A[k]-t)%mod,A[k]=(A[k]+t)%mod;
	if(tp^1) rep(i,0,n-1) A[i]=1ll*A[i]*inv[n]%mod;
}
void Inv(int *A,int *B,int n){
	B[B[1]=0]=Pow(A[0],mod-2);
	static int t[maxn];
	for(int k=2,L=4;k<(n<<1);k<<=1,L<<=1){
		rep(i,0,L-1) t[i]=i<k?A[i]:B[i]=0;
		NTT(t,L,1),NTT(B,L,1);
		rep(i,0,L-1) B[i]=B[i]*(2-1ll*t[i]*B[i]%mod)%mod;
		NTT(B,L,-1);
		rep(i,min(n,k),L-1) B[i] = 0;
	}
}
void Ln(int *A,int *B,int n){
	static int t[maxn];
	int L = 1 << lg[2*n-2] + 1;
	Inv(A,B,n);
	rep(i,0,L-1) t[i] = i < n-1 ? A[i+1] * (i+1ll) % mod : B[i] = 0;
	NTT(t,L,1),NTT(B,L,1);
	rep(i,0,L-1) t[i] = 1ll * t[i] * B[i] % mod;
	NTT(t,L,-1);
	B[0] = 0;
	rep(i,1,L-1) B[i] = i < n ? 1ll * t[i-1] * inv[i] % mod : 0; 
}
void Exp(int *A,int *B,int n){
	B[B[1] = 0] = 1;
	static int t[maxn];
	for(int k=2,L=4;k<(n<<1);k<<=1,L<<=1){
		Ln(B,t,k);
		rep(i,0,L-1) t[i] = i < k ? ((i == 0) + A[i] - t[i]) % mod : B[i] = 0;
		NTT(t,L,1),NTT(B,L,1);
		rep(i,0,L-1) B[i] = 1ll * t[i] * B[i] % mod;
		NTT(B,L,-1);
		rep(i,min(n,k),L-1) B[i] = 0;
	} 
}

int F[maxn],D[maxn],B[maxn],C[maxn],E[maxn],G[maxn];
int calc(int n)
{
	for(int j=0;j<n;j++)
	C[j] = j < n ? (-1ll * D[j] * n) % mod : 0;
	Exp(C,G,n);
	int ans = 0;
	for(int i=0;i<n;i++)
	ans = (ans + 1ll * G[i] * E[n-1-i]) % mod;
	ans = (1ll * ans * fac[n-1] % mod * inv[n] % mod + mod) % mod;
	return ans;
	
}
void init(){
	init(200000);
	for(int i=0;i<=100000;i++) F[i] = 1ll * Pow(2 , (i * (i-1ll) / 2) % (mod - 1)) * invf[i] % mod;
	Ln(F,D,100001);
	for(int i=0;i<=100000;i++) D[i] = 1ll * D[i] * i % mod;
	for(int i=0;i<100000;i++) E[i] = 1ll * D[i+1] * (i+1) % mod;
	
}
}cg;
int fpow(int x,int b)
{
	if(x==0) return 0;
	if(b==0) return 1;
	int res=1;
	while(b>0)
	{
		if(b&1)	res=1LL*res*x%mod;
		x=1LL*x*x%mod;
		b>>=1;
	}
	return res;
}
int fac[300005],ifac[300005];
int C(int x,int y)
{
	if(y>x) return 0;
	if(x==y||y==0) return 1;
	return 1LL*fac[x]*ifac[x-y]%mod*ifac[y]%mod;
}
void init(int x)
{
	fac[0]=fac[1]=1;
	for(int i=2;i<=x;i++) fac[i]=1LL*fac[i-1]*i%mod;
	ifac[x]=fpow(fac[x],mod-2);  // x should be less than mod!!!
	for(int i=x-1;i>=0;i--) ifac[i]=1LL*ifac[i+1]*(i+1)%mod;
}
int F[405],a[405];
int g[405][405],h[405][405];
void solve()
{
	init(100000); 
	cg.init();
	for(int i=1;i<=400;i++) F[i]=cg.calc(i);
	int n;
	cin>>n;
	for(int i=1;i<=n;i++) cin>>a[i];
	for(int i=1;i<=n;i++) g[i][1]=F[i]*i%mod;
	g[n][1]=F[n]; 
	for(int k=1;k<n;k++) for(int i=k;i<n;i++) if(g[i][k])
	{
		for(int d=1;i+d<=n;d++) g[i+d][k+1]=(g[i+d][k+1]+g[i][k]*C(i+d-k-1,i-k)%mod*d%mod*F[d])%mod;
	} 
	h[0][0]=1;
	for(int i=1;i<=n;i++) for(int j=1;j<=i;j++) for(int lst=0;lst<i;lst++) h[i][j]=(h[i][j]+h[lst][j-1]*a[i])%mod;
	int ans=0;
	for(int k=1;k<=n;k++)
	{
		int nw=0;
		for(int i=k;i<=n;i++) nw=(nw+h[i][k])%mod; 
//		cout<<nw<<" ";
		nw=nw*g[n][k]%mod;
		if(k>=3) nw=nw*fpow(n,k-2)%mod; 
//		cout<<" "<<g[n][k]<<"\n";
		ans=(ans+nw)%mod;
	}
	cout<<ans<<"\n";
}
signed main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	int _=1;
//	cin>>_;
	while(_--) solve();
	return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 201ms
memory: 62392kb

input:

3
8 5 9

output:

1102

result:

ok "1102"

Test #2:

score: 0
Accepted
time: 200ms
memory: 57320kb

input:

5
4 2 1 3 10

output:

63860

result:

ok "63860"

Test #3:

score: 0
Accepted
time: 210ms
memory: 62448kb

input:

7
229520041 118275986 281963154 784360383 478705114 655222915 970715006

output:

35376232

result:

ok "35376232"

Test #4:

score: 0
Accepted
time: 278ms
memory: 62520kb

input:

300
7 8 2 8 6 5 5 3 2 3 8 0 6 0 1 0 10 7 10 0 1 0 6 7 2 6 4 7 9 4 6 5 5 9 8 5 4 5 3 5 4 4 10 2 4 9 7 5 2 2 5 6 3 6 8 2 8 3 6 2 5 1 10 3 0 7 1 9 6 5 10 0 3 0 2 4 2 7 6 10 1 0 0 9 4 3 5 5 2 6 1 8 5 4 0 0 5 8 8 1 3 9 9 9 8 1 4 10 7 4 8 5 0 4 3 4 4 8 1 6 1 10 9 3 2 5 0 0 5 2 7 5 4 10 3 5 10 10 7 6 10 3 ...

output:

409590176

result:

ok "409590176"

Test #5:

score: 0
Accepted
time: 295ms
memory: 59932kb

input:

335
4 3 7 7 8 1 4 7 8 8 4 3 5 5 6 8 8 9 3 7 2 4 6 6 6 3 0 7 8 4 6 1 9 10 9 9 0 7 10 3 3 4 10 5 10 4 10 3 7 7 1 9 8 4 0 3 8 1 10 10 7 5 2 7 6 0 4 7 5 9 1 4 10 3 2 9 2 0 1 5 3 5 5 9 9 3 5 6 10 6 9 5 10 10 8 10 5 9 6 1 10 6 7 1 0 7 10 1 6 7 8 2 2 10 1 3 4 1 5 3 3 2 4 10 3 5 8 0 10 0 9 4 9 2 7 3 8 7 4 7...

output:

997747

result:

ok "997747"

Test #6:

score: 0
Accepted
time: 216ms
memory: 58132kb

input:

84
2 5 3 4 5 8 10 5 2 10 7 6 10 10 7 7 3 2 1 7 8 5 9 10 7 5 6 1 2 8 2 8 6 5 4 6 9 0 3 9 3 2 0 2 9 0 4 4 8 10 3 4 6 10 10 5 8 1 10 8 2 7 3 10 8 8 3 2 8 7 4 10 2 6 9 9 3 6 3 3 9 0 7 6

output:

182929290

result:

ok "182929290"

Test #7:

score: 0
Accepted
time: 208ms
memory: 62316kb

input:

54
9 2 1 10 6 6 10 4 7 6 0 3 8 10 5 7 8 6 1 10 9 6 1 8 0 4 2 7 4 0 9 8 5 3 0 4 3 6 1 8 4 1 4 9 6 6 8 0 8 0 0 7 6 9

output:

43066240

result:

ok "43066240"

Test #8:

score: 0
Accepted
time: 209ms
memory: 57976kb

input:

32
0 8 6 8 1 3 9 5 9 0 4 2 4 4 3 10 2 3 1 8 2 6 5 3 9 5 0 0 5 2 1 4

output:

718335570

result:

ok "718335570"

Test #9:

score: 0
Accepted
time: 201ms
memory: 55620kb

input:

1
998244352

output:

998244352

result:

ok "998244352"

Test #10:

score: 0
Accepted
time: 370ms
memory: 57596kb

input:

400
998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244...

output:

764763555

result:

ok "764763555"

Test #11:

score: 0
Accepted
time: 215ms
memory: 62524kb

input:

85
998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 9982443...

output:

360553407

result:

ok "360553407"

Test #12:

score: 0
Accepted
time: 222ms
memory: 56852kb

input:

191
998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244352 998244...

output:

991556265

result:

ok "991556265"

Test #13:

score: 0
Accepted
time: 206ms
memory: 60616kb

input:

5
998244352 998244352 998244352 998244352 998244352

output:

998243313

result:

ok "998243313"

Test #14:

score: 0
Accepted
time: 214ms
memory: 62552kb

input:

1
1

output:

1

result:

ok "1"

Test #15:

score: 0
Accepted
time: 360ms
memory: 62868kb

input:

400
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ...

output:

304058802

result:

ok "304058802"

Test #16:

score: 0
Accepted
time: 355ms
memory: 57088kb

input:

386
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ...

output:

874115996

result:

ok "874115996"

Test #17:

score: 0
Accepted
time: 278ms
memory: 58644kb

input:

313
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ...

output:

597837845

result:

ok "597837845"

Test #18:

score: 0
Accepted
time: 251ms
memory: 62700kb

input:

268
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ...

output:

419739297

result:

ok "419739297"

Test #19:

score: 0
Accepted
time: 209ms
memory: 59048kb

input:

54
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

output:

643244867

result:

ok "643244867"

Test #20:

score: 0
Accepted
time: 205ms
memory: 57812kb

input:

48
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

output:

338935899

result:

ok "338935899"

Test #21:

score: 0
Accepted
time: 197ms
memory: 57300kb

input:

12
1 1 1 1 1 1 1 1 1 1 1 1

output:

530659406

result:

ok "530659406"

Test #22:

score: 0
Accepted
time: 214ms
memory: 58876kb

input:

16
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

output:

873741770

result:

ok "873741770"

Test #23:

score: 0
Accepted
time: 314ms
memory: 61384kb

input:

358
1115290 857418774 525660612 441235960 968251556 195367707 499270374 150410361 311616821 559224631 56376437 943235745 210570297 973440142 173148033 156186709 113638344 240700037 220654177 232430149 10319333 895951986 632968612 969427208 953160305 662164174 33843437 666747237 34205190 811103418 41...

output:

286780900

result:

ok "286780900"

Test #24:

score: 0
Accepted
time: 311ms
memory: 58876kb

input:

344
210579027 582997879 503991744 614640417 67235757 419878515 164535437 554084256 51607125 652025880 891447125 13583488 80121136 152736049 421847155 801187930 34239618 40500488 767047613 353848772 24784010 319866280 913730443 802405315 9245074 512437704 262407695 883841184 511503173 334945884 19176...

output:

217532565

result:

ok "217532565"

Test #25:

score: 0
Accepted
time: 287ms
memory: 61300kb

input:

325
630363144 393404219 366794662 459012744 644644744 90410787 930109789 246555884 917192211 5371492 414476764 571657222 667592533 200323050 421503836 125424416 264941519 988742481 275608116 281878470 441716151 276997372 469030579 287933529 258099275 745817136 121648206 734858183 6675212 48521173 17...

output:

805089310

result:

ok "805089310"

Test #26:

score: 0
Accepted
time: 364ms
memory: 60120kb

input:

400
823489320 406308599 710963770 183707427 192930969 941365774 318564299 391028855 945374838 651744270 515755727 220857626 599403217 214957584 335628890 771694833 40989299 34892948 630275822 869708185 432704750 924850167 707864789 232688853 406616372 529994171 782650336 979286144 653704962 98275198...

output:

227120863

result:

ok "227120863"

Test #27:

score: 0
Accepted
time: 355ms
memory: 61292kb

input:

400
805673855 954340879 768398694 792304488 160627816 690839001 634355243 680917132 889295686 174793413 162216449 663827931 792641124 536196712 718524372 416336507 377989502 506596252 498339899 205499242 720836814 666357765 542341092 715613501 108264501 828631634 378880723 4945299 472651139 36366555...

output:

197153359

result:

ok "197153359"

Test #28:

score: 0
Accepted
time: 362ms
memory: 57252kb

input:

400
573858409 158564131 626297515 95107209 839325592 131488841 262394741 598473086 279712965 923126037 768477685 872125938 43550359 350073805 625331165 631979459 231780563 364979372 994161997 417207682 561100817 652033756 620534272 372707170 800776175 349668140 135175766 794164905 319904460 23767601...

output:

309947167

result:

ok "309947167"

Test #29:

score: 0
Accepted
time: 219ms
memory: 57684kb

input:

161
454284697 718044840 911733869 788445829 374976576 283555956 330659567 534673219 763772621 533686340 997431381 315009839 801324614 867648208 840434404 84390366 444646874 652727596 245127393 429009611 491221735 782941712 766298213 670004861 389539042 58372655 501168063 678515082 901575199 7964062 ...

output:

871565443

result:

ok "871565443"

Test #30:

score: 0
Accepted
time: 216ms
memory: 63124kb

input:

162
151292163 943012123 167343147 819676643 584819196 603260437 344227100 217480474 257123917 755733732 306150953 58563430 585700931 430100762 23364684 779598621 281842628 501243718 739611077 892539286 74267401 75305112 125317256 859095786 751541515 405943984 918972027 808877799 705127200 721405494 ...

output:

273432531

result:

ok "273432531"

Test #31:

score: 0
Accepted
time: 261ms
memory: 56708kb

input:

286
600838530 575651850 385279426 475664485 619069265 780822783 860939782 184686123 193863774 466950919 765401970 705574987 282843644 717393988 375193483 210523577 335822289 399592519 691770149 949281236 374732311 386267435 94137955 739197796 853274439 85692571 391770291 584612694 455182007 64033146...

output:

581998699

result:

ok "581998699"

Test #32:

score: 0
Accepted
time: 214ms
memory: 57384kb

input:

61
453833616 501467684 4992671 214825639 871776849 218199413 42498305 303731723 912156523 129282295 439845605 182960525 185237067 162024603 36559317 688854981 935232225 246423320 92982685 695989722 630828913 551225463 167009365 765939546 822255011 178394229 882957486 3774194 362820770 200498412 9203...

output:

455579427

result:

ok "455579427"

Test #33:

score: 0
Accepted
time: 204ms
memory: 62316kb

input:

25
900307596 286223988 229751451 948490346 250323590 175633754 171483351 707853698 603512678 51411170 126676903 326582510 111531585 521302732 467030281 284302822 453471425 898992972 344271140 632092014 841124127 159268130 234849517 332336122 538047172

output:

641428561

result:

ok "641428561"

Test #34:

score: 0
Accepted
time: 211ms
memory: 62284kb

input:

50
893955548 5432673 340595831 583427119 94992225 787645123 311038284 546749098 933218937 561482178 527027577 871516321 329687526 96875316 862464008 320975040 435140352 951500073 831730146 242883780 961810021 310011134 441489680 217976348 203907166 525210038 295522145 713990656 44280374 492792810 10...

output:

474987173

result:

ok "474987173"

Test #35:

score: 0
Accepted
time: 203ms
memory: 60780kb

input:

17
726738121 723815755 532257301 649033140 817058831 665912348 585846647 472719308 53020833 679093694 601943548 536712177 917063040 137577090 676474390 447455603 55046910

output:

205253339

result:

ok "205253339"

Test #36:

score: 0
Accepted
time: 201ms
memory: 57936kb

input:

13
319526944 707203324 397137993 712092752 253972256 682960643 636749775 764641774 359483944 695780350 619279205 717907790 322375408

output:

301609478

result:

ok "301609478"

Test #37:

score: 0
Accepted
time: 202ms
memory: 60756kb

input:

15
673123463 250231589 715576329 413978055 995958701 401244843 682058967 349009605 504949036 838330837 739330277 480154478 764761812 434210368 470676772

output:

460419982

result:

ok "460419982"

Extra Test:

score: 0
Extra Test Passed