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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#373654#1262. Justice For Everyone275307894aAC ✓105ms33096kbC++145.7kb2024-04-01 21:25:522024-04-01 21:25:53

Judging History

你现在查看的是最新测评结果

  • [2024-04-01 21:25:53]
  • 评测
  • 测评结果:AC
  • 用时:105ms
  • 内存:33096kb
  • [2024-04-01 21:25:52]
  • 提交

answer

#include<bits/stdc++.h>
#define Gc() getchar()
#define Me(x,y) memset(x,y,sizeof(x))
#define Mc(x,y) memcpy(x,y,sizeof(x))
#define d(x,y) ((m)*(x-1)+(y))
#define R(n) (rnd()%(n)+1)
#define Pc(x) putchar(x)
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define eb emplace_back
#define all(x) x.begin(),x.end()
using namespace std;using ll=long long;using db=double;using lb=long db;using ui=unsigned;using ull=unsigned long long;using pii=pair<int,int>;
const int N=30+5,M=6000+5,K=1000+5,mod=998244353,Mod=mod-1;const db eps=1e-8;const int INF=1e9+7;mt19937 rnd(263082);
#define Tp template<typename T>
#define Ts template<typename T,typename... Ar>
namespace Debug{
	Tp void _debug(char* f,T t){cerr<<f<<'='<<t<<endl;}
	Ts void _debug(char* f,T x,Ar... y){while(*f!=',') cerr<<*f++;cerr<<'='<<x<<",";_debug(f+1,y...);}
	#ifdef LOCAL
	#define gdb(...) _debug((char*)#__VA_ARGS__,__VA_ARGS__)
	#else 
	#define gdb(...) void()
	#endif
}using namespace Debug;

using poly=vector<ll>;
ll mpow(ll x,int y=mod-2){ll ans=1;while(y) y&1&&(ans=ans*x%mod),y>>=1,x=x*x%mod;return ans;}
namespace Poly{
	const int N=1<<21,g=3;
	int tr[N],k,a[N],b[N];ll pw[N];
	void init(int n){
		for(k=2;k<=n;k<<=1);
		for(int i=0;i<k;i++) tr[i]=(tr[i>>1]>>1)|(i&1?k/2:0);
		pw[k/2]=1;pw[k/2+1]=mpow(g,(mod-1)/k);
		for(int i=k/2+2;i<k;i++) pw[i]=pw[i-1]*pw[k/2+1]%mod;
		for(int i=k/2-1;i;i--) pw[i]=pw[i<<1];
	}
	void ntt(int *A,int k,int flag){
		static ull a[N];for(int i=0;i<k;i++) a[tr[i]]=A[i];
		for(int i=2;i<=k;i<<=1){
			ll *e=pw+i/2;
			for(int j=0;j<k;j+=i){
				for(int h=j;h<j+i/2;h++){
					int x=a[h+i/2]*e[h-j]%mod;
					a[h+i/2]=a[h]+mod-x;a[h]+=x;
				}
			}
			if(i==(1<<18)){
				for(int j=0;j<k;j++) a[j]%=mod;
			}
		}
		for(int i=0;i<k;i++) A[i]=a[i]%mod;
		if(flag) return;
		reverse(A+1,A+k);
		ll iv=mpow(k);for(int i=0;i<k;i++) A[i]=A[i]*iv%mod;
	}
	namespace Public{
		poly operator *(const poly &A,const poly &B){
			int n=A.size(),m=B.size(),lim=n+m-1;
			init(lim);
			copy(A.begin(),A.end(),a);fill(a+n,a+k,0);
			copy(B.begin(),B.end(),b);fill(b+m,b+k,0);
			ntt(a,k,1);ntt(b,k,1);
			for(int i=0;i<k;i++) a[i]=1ll*a[i]*b[i]%mod;
			ntt(a,k,0);
			poly c(lim);copy(a,a+lim,c.begin());
			return c;
		}
		poly& operator *=(poly &A,const poly &B){
			return A=A*B;
		}
		poly operator *(const poly &A,const int B){
			poly C=A;for(int i=0;i<C.size();i++) C[i]=1ll*C[i]*B%mod;
			return C;
		}
		poly& operator *=(poly &A,const int &B){
			return A=A*B;
		}
		poly operator +(const poly &A,const poly &B){
			poly C(max(A.size(),B.size()));
			for(int i=0;i<A.size();i++) C[i]=A[i];
			for(int i=0;i<B.size();i++) C[i]=(B[i]+C[i])%mod;
			return C;
		}
		poly& operator +=(poly &A,const poly &B){
			return A=A+B;
		}
		poly operator -(const poly &A,const poly &B){
			poly C(max(A.size(),B.size()));
			for(int i=0;i<A.size();i++) C[i]=A[i];
			for(int i=0;i<B.size();i++) C[i]=(C[i]+mod-B[i])%mod;
			return C;
		}
		poly& operator -=(poly &A,const poly &B){
			return A=A-B;
		}
		poly operator %(const poly &A,const int &B){
			poly C=A;
			if(C.size()>B) C.resize(B);
			return C;
		}
		poly& operator %=(poly &A,const int B){
			return A=A%B;
		}
		poly inve(poly A,int n=-1){
			if(n==-1) n=A.size();
			if(n==1) return poly({(int)mpow(A[0])});
			poly A0=inve(A%(n+1>>1),n+1>>1);
			return A0*(poly({2})-A*A0%n)%n;
		}
		poly sqrt(poly A,int n=-1){
			if(n==-1) n=A.size();
			if(n==1) return poly({1});
			poly A0=sqrt(A%(n+1>>1),n+1>>1);
			return (A0*A0%n+A)*inve(A0,n)%n*(mod+1>>1);
		}
		poly der(poly A){
			poly B(A.size()-1);
			for(int i=1;i<A.size();i++) B[i-1]=1ll*A[i]*i%mod;
			return B;
		}
		poly integ(poly A){
			poly B(A.size()+1);
			static ll inv[N];inv[1]=1;for(int i=2;i<=A.size();i++) inv[i]=(mod-inv[mod%i])*(mod/i)%mod;
			for(int i=0;i<A.size();i++) B[i+1]=inv[i+1]*A[i]%mod;
			return B;
		}
		poly ln(poly A,int n=-1){
			if(n==-1) n=A.size();
			return integ(der(A)*inve(A,n)%n)%n;
		}
		poly exp(poly A,int n=-1){
			if(n==-1) n=A.size();
			if(n==1) return poly({1});
			poly A0=exp(A%(n+1>>1),n+1>>1);
			return A0*(poly({1})-ln(A0,n)+A)%n;
		}
	}
}using namespace Poly::Public;

int n,m,k,A[N],B[N],ans[1<<12],e[N][N][1<<12];ll inv[M],frc[M];
ll w[N][N];
ll Gauss(){
	ll ans=1;
	for(int i=1;i<=n;i++){
		for(int j=i+1;j<=n;j++) if(w[j][i]) {
			swap_ranges(w[i]+i,w[i]+n+1,w[j]+i);
			ans=ans*(mod-1)%mod;break;
		}
		ans=ans*w[i][i]%mod;ll iv=mpow(w[i][i]);
		for(int j=i+1;j<=n;j++){
			int x=mod-w[j][i]*iv%mod;
			for(int h=i;h<=n;h++) w[j][h]=(w[j][h]+x*w[i][h])%mod;
		}
	}
	return ans;
}
void Solve(){
	int i,j,h;scanf("%d",&n);
	for(i=1;i<=n;i++) scanf("%d",&A[i]);
	for(i=1;i<=n;i++) scanf("%d",&B[i]);
	for(i=1;i<=n;i++){
		if(A[i]>B[i]){puts("0");return;}
		k+=B[i]-A[i];
	}
	for(i=1;i<=n;i++) for(j=1;j<=n;j++) if(A[i]<A[j]&&B[j]<B[i]){puts("0");return;}
	if(k&1){puts("0");return;}k>>=1;
	inv[1]=1;for(i=2;i<=2*k;i++) inv[i]=(mod-inv[mod%i])*(mod/i)%mod;
	for(frc[0]=inv[0]=i=1;i<=2*k;i++) frc[i]=frc[i-1]*i%mod,inv[i]=inv[i-1]*inv[i]%mod;
	Poly::init(k+1);
	for(i=1;i<=n;i++)for(j=1;j<=n;j++)if(A[i]<=B[j]){
		for(h=0;2*h<=B[j]-A[i];h++) e[i][j][h]=inv[h]*inv[B[j]-A[i]-2*h]%mod;
		Poly::ntt(e[i][j],Poly::k,1);
	}
	for(i=0;i<Poly::k;i++){
		Me(w,0);for(int x=1;x<=n;x++) for(int y=1;y<=n;y++) w[x][y]=e[x][y][i];
		ans[i]=Gauss();
	}
	Poly::ntt(ans,Poly::k,0);
	ll tot=0;
	for(i=0;i<=k;i++) tot+=(i&1?mod-1:1)*frc[k]%mod*inv[k-i]%mod*frc[2*(k-i)]%mod*ans[i]%mod,gdb(tot%mod);
	tot%=mod;for(i=1;i<=k;i++) tot=tot*(mod+1>>1)%mod;
	printf("%lld\n",tot%mod);
}
int main(){
	int t=1;
	// scanf("%d",&t);
	while(t--) Solve();
	cerr<<clock()*1.0/CLOCKS_PER_SEC<<'\n';
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 0ms
memory: 14184kb

input:

3
1 2 3
3 4 5

output:

1

result:

ok answer is '1'

Test #2:

score: 0
Accepted
time: 0ms
memory: 12228kb

input:

3
1 2 3
7 8 9

output:

42

result:

ok answer is '42'

Test #3:

score: 0
Accepted
time: 0ms
memory: 14248kb

input:

3
1 4 7
3 6 9

output:

6

result:

ok answer is '6'

Test #4:

score: 0
Accepted
time: 2ms
memory: 14400kb

input:

1
1
3

output:

0

result:

ok answer is '0'

Test #5:

score: 0
Accepted
time: 0ms
memory: 14132kb

input:

1
1
1

output:

1

result:

ok answer is '1'

Test #6:

score: 0
Accepted
time: 1ms
memory: 12108kb

input:

2
1 4
4 7

output:

1

result:

ok answer is '1'

Test #7:

score: 0
Accepted
time: 1ms
memory: 7948kb

input:

10
10 9 8 7 6 1 2 3 4 5
11 12 13 114 115 120 129 128 127 126

output:

0

result:

ok answer is '0'

Test #8:

score: 0
Accepted
time: 1ms
memory: 8136kb

input:

30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 131

output:

0

result:

ok answer is '0'

Test #9:

score: 0
Accepted
time: 54ms
memory: 29352kb

input:

30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130

output:

936606510

result:

ok answer is '936606510'

Test #10:

score: 0
Accepted
time: 1ms
memory: 8176kb

input:

30
16 21 33 44 51 60 71 81 91 100 110 122 131 144 155 160 162 171 172 174 177 179 187 188 189 191 192 193 194 199
110 111 112 113 114 115 116 117 118 119 120 122 131 144 155 160 162 171 172 174 177 179 187 188 189 191 192 193 194 199

output:

0

result:

ok answer is '0'

Test #11:

score: 0
Accepted
time: 11ms
memory: 25884kb

input:

30
16 21 33 44 51 60 71 81 91 100 110 122 131 144 155 160 162 171 172 174 177 179 187 188 189 191 192 193 194 199
110 111 112 113 114 115 116 117 118 119 120 122 131 144 155 160 162 171 172 174 177 179 187 188 189 191 192 193 194 200

output:

836228983

result:

ok answer is '836228983'

Test #12:

score: 0
Accepted
time: 0ms
memory: 18360kb

input:

10
10 9 8 7 6 5 4 3 2 1
110 109 108 107 106 105 104 103 102 101

output:

422463757

result:

ok answer is '422463757'

Test #13:

score: 0
Accepted
time: 105ms
memory: 33096kb

input:

30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200

output:

575061951

result:

ok answer is '575061951'