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QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#846848#7. 主旋律QZJ123456100 ✓971ms15468kbC++141.9kb2025-01-07 15:10:222025-01-07 15:10:27

Judging History

你现在查看的是最新测评结果

  • [2025-01-07 15:10:27]
  • 评测
  • 测评结果:100
  • 用时:971ms
  • 内存:15468kb
  • [2025-01-07 15:10:22]
  • 提交

answer

#include<bits/stdc++.h>
typedef long long ll;
using namespace std;
const ll mod=1e9+7;
int n,m,e[1<<15|5][17],ct[1<<15];
ll f[1<<15|5][17],tmp[1<<15|5][17],pw[505],fac[25],ifac[25],h[1<<15|5],g[1<<15|5];
ll ksm(ll a,ll m,ll p){
	ll ans=1;
	while(m){
		if(m&1)ans=ans*a%mod;
		a=a*a%mod;
		m>>=1;
	}
	return ans;
}
ll Mod(ll v){
	return v-=v>mod?mod:0;
}
typedef unsigned long long ull;
typedef __uint128_t L;
struct FastMod {
	ull b, m;
	FastMod(ull b) : b(b), m(ull((L(1) << 64) / b)) {}
	ull r(ull a) {
		ull q = (ull)((L(m) * a) >> 64);
		ull r = a - q * b; // can be proven that 0 <= r < 2*b
		return r >= b ? r - b : r;
	}
};
FastMod F(2);
int popc[1<<15|5];
int main(){
	F=FastMod(mod);
	scanf("%d%d",&n,&m);
//	n=15,m=0;
	pw[0]=1;
	for(int i=1;i<=m;i++)pw[i]=pw[i-1]*2%mod;
	fac[0]=1;
	for(int i=1;i<=n;i++)fac[i]=fac[i-1]*i%mod;
	for(int i=0;i<=n;i++)ifac[i]=ksm(fac[i],mod-2,mod);
	for(int s=1;s<(1<<n);s++)popc[s]=popc[s>>1]+(s&1);
	while(m--){
		int x,y;
		scanf("%d%d",&x,&y);
		e[1<<(y-1)][x]++;
	}
	for(int i=1;i<=n;i++){
		for(int j=1;j<=n;j++){
			for(int s=1;s<(1<<n);s++){
				if((s>>(j-1))&1)e[s][i]+=e[s^(1<<(j-1))][i];
			}
		}
	}
	f[0][0]=g[0]=1;
	for(int s=1;s<(1<<n);s++){
		for(int s1=s;s1;s1=(s1-1)&s){
			for(int i=0;i<=popc[s^s1];i++){
				f[s][i+1]=F.r(f[s][i+1]+f[s^s1][i]*g[s1]);
			}
		}
		for(int s1=s;s1;s1=(s1-1)&s){
			int u=0;
			for(int i=1;i<=n;i++){
				if((s1>>(i-1))&1)u+=e[s^s1][i];
			}
			for(int i=1;i<=popc[s1];i++){
				if(!f[s1][i])continue;
				tmp[s][i]=F.r(tmp[s][i]+f[s1][i]*pw[u+ct[s^s1]]);
			}
		}
		for(int i=1;i<=n;i++){
			if(i&1)g[s]=(g[s]+tmp[s][i]*ifac[i])%mod;
			else g[s]=(g[s]-tmp[s][i]*ifac[i]%mod+mod)%mod;
		}
		for(int i=1;i<=n;i++){
			if((s>>(i-1))&1)ct[s]+=e[s][i];
		}
		h[s]=g[s];
		g[s]=(pw[ct[s]]-g[s]+mod)%mod;
		f[s][1]=g[s];		
	}
	cout<<g[(1<<n)-1];
	return 0;
}

Details

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Pretests


Final Tests

Test #1:

score: 10
Accepted
time: 0ms
memory: 9808kb

input:

5 15
4 3
4 2
2 5
2 1
1 2
5 1
3 2
4 1
1 4
5 4
3 4
5 3
2 3
1 5
3 1

output:

9390

result:

ok single line: '9390'

Test #2:

score: 10
Accepted
time: 1ms
memory: 7784kb

input:

5 18
4 3
4 2
2 5
2 1
1 2
5 1
3 2
4 1
1 4
5 4
3 4
5 3
2 3
1 5
3 1
1 3
5 2
2 4

output:

100460

result:

ok single line: '100460'

Test #3:

score: 10
Accepted
time: 1ms
memory: 7704kb

input:

8 35
5 1
8 7
7 8
7 6
6 1
2 5
6 5
8 2
7 2
7 5
3 1
6 3
2 3
5 2
8 5
8 3
6 8
2 1
1 6
2 6
7 3
2 4
3 5
3 2
3 7
7 1
8 4
3 4
3 6
6 4
2 7
4 6
6 7
7 4
8 1

output:

299463717

result:

ok single line: '299463717'

Test #4:

score: 10
Accepted
time: 1ms
memory: 7968kb

input:

8 40
5 1
8 7
7 8
7 6
6 1
2 5
6 5
8 2
7 2
7 5
3 1
6 3
2 3
5 2
8 5
8 3
6 8
2 1
1 6
2 6
7 3
2 4
3 5
3 2
3 7
7 1
8 4
3 4
3 6
6 4
2 7
4 6
6 7
7 4
8 1
1 2
4 8
5 8
4 3
5 7

output:

21156439

result:

ok single line: '21156439'

Test #5:

score: 10
Accepted
time: 1ms
memory: 7736kb

input:

8 45
5 1
8 7
7 8
7 6
6 1
2 5
6 5
8 2
7 2
7 5
3 1
6 3
2 3
5 2
8 5
8 3
6 8
2 1
1 6
2 6
7 3
2 4
3 5
3 2
3 7
7 1
8 4
3 4
3 6
6 4
2 7
4 6
6 7
7 4
8 1
1 2
4 8
5 8
4 3
5 7
2 8
1 5
3 8
1 3
4 1

output:

426670664

result:

ok single line: '426670664'

Test #6:

score: 10
Accepted
time: 4ms
memory: 7956kb

input:

10 65
5 10
1 8
7 8
6 2
5 7
9 2
4 7
3 7
1 6
3 10
7 9
8 4
7 1
5 2
1 7
4 2
8 3
8 1
3 9
8 2
2 10
4 3
9 10
5 3
3 8
3 4
6 10
4 8
4 5
5 8
9 5
9 6
10 2
10 5
6 1
2 1
9 4
7 10
5 6
10 7
10 8
5 9
9 7
9 8
4 10
8 9
7 2
2 7
10 1
7 3
6 8
7 6
9 1
6 5
2 4
6 3
2 9
8 10
10 9
8 5
4 1
6 9
2 3
1 3
1 9

output:

931896041

result:

ok single line: '931896041'

Test #7:

score: 10
Accepted
time: 4ms
memory: 9960kb

input:

10 70
5 10
1 8
7 8
6 2
5 7
9 2
4 7
3 7
1 6
3 10
7 9
8 4
7 1
5 2
1 7
4 2
8 3
8 1
3 9
8 2
2 10
4 3
9 10
5 3
3 8
3 4
6 10
4 8
4 5
5 8
9 5
9 6
10 2
10 5
6 1
2 1
9 4
7 10
5 6
10 7
10 8
5 9
9 7
9 8
4 10
8 9
7 2
2 7
10 1
7 3
6 8
7 6
9 1
6 5
2 4
6 3
2 9
8 10
10 9
8 5
4 1
6 9
2 3
1 3
1 9
5 4
1 5
5 1
10 4
10 6

output:

303656759

result:

ok single line: '303656759'

Test #8:

score: 10
Accepted
time: 971ms
memory: 15456kb

input:

15 130
7 10
9 12
4 6
1 10
14 9
4 8
8 9
4 3
15 9
3 9
1 8
2 15
8 4
13 7
3 5
14 13
6 2
14 6
8 3
4 2
8 13
9 2
6 13
12 11
6 4
11 8
15 5
3 8
10 8
15 7
15 6
12 15
8 12
13 9
12 9
8 15
11 6
6 7
10 4
2 8
11 12
7 9
7 12
14 1
5 8
10 9
3 7
7 13
11 9
11 10
1 5
1 3
2 1
2 7
10 1
10 15
7 14
5 6
6 1
15 10
5 15
15 8
5...

output:

717458968

result:

ok single line: '717458968'

Test #9:

score: 10
Accepted
time: 967ms
memory: 15404kb

input:

15 140
7 10
9 12
4 6
1 10
14 9
4 8
8 9
4 3
15 9
3 9
1 8
2 15
8 4
13 7
3 5
14 13
6 2
14 6
8 3
4 2
8 13
9 2
6 13
12 11
6 4
11 8
15 5
3 8
10 8
15 7
15 6
12 15
8 12
13 9
12 9
8 15
11 6
6 7
10 4
2 8
11 12
7 9
7 12
14 1
5 8
10 9
3 7
7 13
11 9
11 10
1 5
1 3
2 1
2 7
10 1
10 15
7 14
5 6
6 1
15 10
5 15
15 8
5...

output:

459157220

result:

ok single line: '459157220'

Test #10:

score: 10
Accepted
time: 952ms
memory: 15468kb

input:

15 150
7 10
9 12
4 6
1 10
14 9
4 8
8 9
4 3
15 9
3 9
1 8
2 15
8 4
13 7
3 5
14 13
6 2
14 6
8 3
4 2
8 13
9 2
6 13
12 11
6 4
11 8
15 5
3 8
10 8
15 7
15 6
12 15
8 12
13 9
12 9
8 15
11 6
6 7
10 4
2 8
11 12
7 9
7 12
14 1
5 8
10 9
3 7
7 13
11 9
11 10
1 5
1 3
2 1
2 7
10 1
10 15
7 14
5 6
6 1
15 10
5 15
15 8
5...

output:

663282473

result:

ok single line: '663282473'