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QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#106580#5827. 异或图sichengzhou30 176ms5344kbC++143.0kb2023-05-18 07:25:022023-05-18 07:25:06

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.
  • [2023-05-18 07:25:06]
  • 评测
  • 测评结果:30
  • 用时:176ms
  • 内存:5344kb
  • [2023-05-18 07:25:02]
  • 提交

answer

#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const int N=15,mod=998244353;
int n,m;
LL C,a[N],c[1<<N],f[1<<N],cnt1[1<<N];
int mi[1<<N];
bool e[1<<N];
vector<pair<int,LL> >dp[1<<N];
int lowbit(int x)
{
	return x&(-x);
}
LL ny[N<<2];
LL solve(int x)
{
	LL ret=0;
	bool extra=true;
	for(int j=59;j>=0;j--)
	{
		bool v=C>>j&1;
		for(int i=0;i<n;i++)
		{
			if(x>>i&1)
			{
			v^=(a[i]>>j&1);
			}
		}
		LL m=1,m0=1,m1=0;
	    for(int i=0;i<n;i++)
	    {
	    	if(x>>i&1)
	    	{
	    		LL x=(a[i]%(1ll<<j)+1)%mod,y=(1ll<<j)%mod;
	    		m*=x;m%=mod;
	    		LL n0=m0,n1=m1;
	    		m0*=x;m0%=mod;
	    		m1*=x;m1%=mod;
	    		if(a[i]>>j&1)
	    		{
	    			m1+=n0*y%mod;m1%=mod;
	    			m0+=n1*y%mod;m0%=mod;
				}
			}
		}
	//	cout<<j<<' '<<ret<<' '<<m<<' '<<m0<<' '<<m1<<endl;
		if(v)
		{
			ret+=m1*ny[j]%mod;
			ret%=mod;
			extra=false;
			break;
		}else{
			ret+=(m0-m+mod)*ny[j]%mod;
			ret%=mod;
		}
	}
	if(extra)
	{
		ret=(ret+1)%mod;
	}
//	cout<<x<<"->"<<ret<<endl;
	return ret;
}
int main()
{
	LL ans=0;
	int u,v;
	scanf("%d%d%lld",&n,&m,&C);
	for(int i=0;i<n;i++)
	{
		scanf("%lld",&a[i]);
	}
	ny[0]=1;
	for(int i=1;i<=59;i++)
	{
		ny[i]=ny[i-1]*(mod+1)/2%mod;
	}
	for(int i=1;i<=m;i++)
	{
		scanf("%d%d",&u,&v);
		u--;v--;
		e[(1<<u)+(1<<v)]=1;
	}
	for(int i=0;i<(1<<n);i++)
	{
		for(int j=0;;j=(j/lowbit(i-j)+1)*lowbit(i-j))
		{
			e[i]|=e[j];
			if(j==i)
			{
				break;
			}
		}
	}
	for(int i=0;i<(1<<n);i++)
	{
		c[i]=1-e[i];
		int l=i-lowbit(i);
		for(int j=0;j<l;j=(j/lowbit(l-j)+1)*lowbit(l-j))
		{
			c[i]-=c[j+lowbit(i)]*(1-e[l-j])-mod;
			c[i]%=mod;
		}
	//	printf("c[%d]=%lld\n",i,c[i]);
	}
	for(int i=0;i<(1<<n);i++)
	{
		for(int j=0;j<n;j++)
		{
			if(i>>j&1)
			{
				continue;
			}
			cnt1[i+(1<<j)]=cnt1[i]+1;
			if(i==0)
			{
				mi[i+(1<<j)]=j;
			}else{
				if(a[mi[i]]<a[j])
				{
					mi[i+(1<<j)]=mi[i];
				}else{
					mi[i+(1<<j)]=j;
				}
			}
		}
	}
	dp[0].push_back(make_pair(0,1));
	for(int i=1;i<(1<<n);i++)
	{
		for(int j=0;j<=i;j++)
		{
			f[j]=0;
		}
		int l=i-lowbit(i);
	//	cout<<i<<endl;
		for(int j=0;j<=l;j=(j/lowbit(l-j)+1)*lowbit(l-j))
		{
			for(int k=0;k<dp[j].size();k++)
			{
				int x=dp[j][k].first;
				LL y=dp[j][k].second;
			//	cout<<x<<'*'<<y<<endl;
				if(cnt1[i-j]&1)
				{
					f[x+(1<<mi[i-j])]+=y*c[i-j]%mod;
					f[x+(1<<mi[i-j])]%=mod;
				}else{
				//	cout<<"**";
					f[x]+=y*c[i-j]%mod*(a[mi[i-j]]+1)%mod;
					f[x]%=mod;
				}
			//	cout<<f[x]<<endl;
			}
			if(j==l)
			{
				break;
			}
		}
	//	cout<<i<<endl;
		for(int j=0;j<=i;j++)
		{
			if(f[j])
			{
			//	cout<<j<<' '<<f[j]<<endl;
				dp[i].push_back(make_pair(j,f[j]));
			}
		}
	//	cout<<endl;
	}
	for(int i=0;i<dp[(1<<n)-1].size();i++)
	{
		int x=dp[(1<<n)-1][i].first;
		LL y=dp[(1<<n)-1][i].second;
	//	cout<<y<<endl;
		ans+=y*solve(x)%mod;
		ans%=mod;
	}
	printf("%lld\n",ans);
	return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Subtask #1:

score: 20
Accepted

Test #1:

score: 20
Accepted
time: 0ms
memory: 4368kb

input:

4 6 2
7 11 14 0
1 2
1 3
2 3
2 4
4 1
4 3

output:

44

result:

ok 1 number(s): "44"

Test #2:

score: 0
Accepted
time: 0ms
memory: 4448kb

input:

4 4 6
12 14 14 5
4 2
1 4
3 2
1 2

output:

798

result:

ok 1 number(s): "798"

Test #3:

score: 0
Accepted
time: 2ms
memory: 4608kb

input:

3 3 2
10 4 11
2 1
3 2
1 3

output:

33

result:

ok 1 number(s): "33"

Test #4:

score: 0
Accepted
time: 2ms
memory: 4368kb

input:

4 0 4
9 8 5 2

output:

148

result:

ok 1 number(s): "148"

Test #5:

score: 0
Accepted
time: 2ms
memory: 4348kb

input:

5 6 14
12 15 13 13 12
3 1
2 4
2 5
2 1
5 3
4 5

output:

21337

result:

ok 1 number(s): "21337"

Test #6:

score: 0
Accepted
time: 2ms
memory: 4308kb

input:

4 5 5
5 2 4 13
2 1
3 4
1 4
4 2
3 2

output:

42

result:

ok 1 number(s): "42"

Test #7:

score: 0
Accepted
time: 2ms
memory: 4368kb

input:

4 4 3
13 7 8 12
4 1
3 1
2 4
4 3

output:

552

result:

ok 1 number(s): "552"

Test #8:

score: 0
Accepted
time: 2ms
memory: 4444kb

input:

4 2 12
1 12 4 11
2 1
3 1

output:

70

result:

ok 1 number(s): "70"

Test #9:

score: 0
Accepted
time: 2ms
memory: 4392kb

input:

5 5 6
10 7 8 2 13
1 5
1 3
2 1
4 3
5 3

output:

1231

result:

ok 1 number(s): "1231"

Test #10:

score: 0
Accepted
time: 2ms
memory: 4392kb

input:

5 7 9
6 7 13 15 12
1 3
5 3
5 2
4 5
4 3
4 1
3 2

output:

6223

result:

ok 1 number(s): "6223"

Test #11:

score: 0
Accepted
time: 2ms
memory: 4384kb

input:

3 0 3
15 7 12

output:

104

result:

ok 1 number(s): "104"

Test #12:

score: 0
Accepted
time: 0ms
memory: 4368kb

input:

3 2 9
10 6 5
1 2
1 3

output:

17

result:

ok 1 number(s): "17"

Test #13:

score: 0
Accepted
time: 0ms
memory: 4388kb

input:

5 5 11
7 9 15 9 9
5 4
5 1
5 2
1 3
3 4

output:

5224

result:

ok 1 number(s): "5224"

Test #14:

score: 0
Accepted
time: 2ms
memory: 4428kb

input:

5 0 12
9 8 14 11 2

output:

3006

result:

ok 1 number(s): "3006"

Test #15:

score: 0
Accepted
time: 2ms
memory: 4592kb

input:

3 1 1
6 10 4
3 1

output:

30

result:

ok 1 number(s): "30"

Subtask #2:

score: 0
Wrong Answer

Dependency #1:

100%
Accepted

Test #16:

score: 0
Wrong Answer
time: 3ms
memory: 4604kb

input:

9 27 705410105529944560
929827299070190972 733413770730537329 473007347105710981 190062421504120247 918561152768663129 196040702922254016 981530663192980241 203295856357272834 337150461958783092
2 8
7 9
8 9
2 3
9 2
2 7
9 5
9 4
4 8
1 7
6 3
6 1
4 1
6 5
2 4
2 1
9 3
9 6
7 3
7 5
5 2
4 5
2 6
3 1
3 8
4 3
8 6

output:

241590823

result:

wrong answer 1st numbers differ - expected: '5392583', found: '241590823'

Subtask #3:

score: 10
Accepted

Test #47:

score: 10
Accepted
time: 176ms
memory: 5344kb

input:

14 0 731833687287532167
157552918690640051 900457311668526045 111217720157614956 84140984111060473 814012186135880499 784848789620248379 958953377683017264 105083874298571687 104921429970878846 44983041675142735 871013110538758030 686733907990421995 98063590462078176 495161493555059993

output:

231790380

result:

ok 1 number(s): "231790380"

Test #48:

score: 0
Accepted
time: 7ms
memory: 4548kb

input:

11 0 101435837408688522
638776638580507479 933944392115323974 19098604312360490 142362319980029593 419910251764515410 275591812677260089 770239593400917018 928344484461634421 67340905784404712 378109786925249078 110881245457449811

output:

242383534

result:

ok 1 number(s): "242383534"

Test #49:

score: 0
Accepted
time: 3ms
memory: 4416kb

input:

9 0 100988561775675251
622570387572403506 684352103903274038 784649864569409753 270298495621205212 56183537059869110 346856482529145989 86639702870530669 607198038565138736 14747634008501988

output:

20893166

result:

ok 1 number(s): "20893166"

Test #50:

score: 0
Accepted
time: 4ms
memory: 4480kb

input:

10 0 839910859917247463
611237879350518457 292219463776059962 548211857317940894 822255554598388425 335628456629874391 774414280870858683 882480367082748768 654587410087321403 74330774886125511 22894883233341926

output:

61697734

result:

ok 1 number(s): "61697734"

Subtask #4:

score: 0
Skipped

Dependency #1:

100%
Accepted

Dependency #2:

0%