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QOJ
ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#97668 | #6323. Range NEQ | yangjl | TL | 120ms | 27552kb | C++20 | 8.1kb | 2023-04-17 20:57:08 | 2023-04-17 20:57:12 |
Judging History
answer
#include<iostream>
#include<cmath>
#include<cstring>
#include<cassert>
#include<string>
#include<queue>
#include<deque>
#include<stack>
#include<algorithm>
#include<unordered_map>
#include<map>
#include<vector>
#include<set>
#include<unordered_set>
#include<bitset>
#include<climits>
#include<numeric>
#include<functional>
#include<iomanip>
#include<random>
#ifdef YJL
#include<debug.h>
#else
#define debug(args...)0
#define debug_n(a,n)0
#endif
using namespace std;
typedef long long ll;
template<int P>
struct MInt {
int x;
MInt(): x(0){}
MInt(ll x): x(norm(x%P)){}
static int norm(int x) {
if(x<0) x+=P;
else if(x>=P) x-=P;
return x;
}
MInt pow(ll b) const{
MInt res=1,a=*this;
for(; b; b>>=1,a*=a)
if(b&1) res*=a;
return res;
}
MInt inv() const{
return pow(P-2);
}
MInt operator-() const{
return MInt()-*this;
}
MInt& operator+=(const MInt& a) {
x=norm(x+a.x);
return *this;
}
MInt& operator-=(const MInt& a) {
x=norm(x-a.x);
return *this;
}
MInt& operator*=(const MInt& a) {
x=(ll)x*a.x%P;
return *this;
}
MInt& operator/=(const MInt& a) {
return *this*=a.inv();
}
friend MInt operator+(MInt l,const MInt& r) {
return l+=r;
}
friend MInt operator-(MInt l,const MInt& r) {
return l-=r;
}
friend MInt operator*(MInt l,const MInt& r) {
return l*=r;
}
friend MInt operator/(MInt l,const MInt& r) {
return l/=r;
}
friend istream& operator>>(istream& is,MInt& a) {
ll v;
is>>v;
a=MInt(v);
return is;
}
friend ostream& operator<<(ostream& os,const MInt& a) {
return os<<a.x;
}
};
const int P=998244353;
using Z=MInt<P>;
namespace NTT {
using Poly=vector<Z>;
Poly mulxk(Poly a,int k) {
a.insert(a.begin(),k,0);
return a;
}
Poly divxk(const Poly& a,int k) {
if(a.size()<=k) return Poly();
return Poly(a.begin()+k,a.end());
}
Poly modxk(const Poly& a,int k) {
k=min(k,(int)a.size());
return Poly(a.begin(),a.begin()+k);
}
Poly operator+(const Poly& a,const Poly& b) {
Poly c(a);
c.resize(max(a.size(),b.size()));
for(int i=0; i<b.size(); ++i)
c[i]+=b[i];
return c;
}
Poly operator-(const Poly& a,const Poly& b) {
Poly c(a);
c.resize(max(a.size(),b.size()));
for(int i=0; i<b.size(); ++i)
c[i]-=b[i];
return c;
}
Poly operator-(Poly a) {
for(auto& x:a)
x=-x;
return a;
}
#if fftTag==3
using FFT::operator*;
#else
void dft(Poly& a) {
static vector<int> rev;
int n=a.size();
if(rev.size()!=n) {
rev.resize(n);
for(int i=1; i<n; ++i)
rev[i]=rev[i>>1]>>1|(i&1?n>>1:0);
}
for(int i=0; i<n; ++i)
if(i<rev[i])
swap(a[i], a[rev[i]]);
// w[i]=w(highbit(i)*2, i-highbit(i))
static vector<Z> w{0,1};
if(w.size()<n) {
int k=__builtin_ctz(w.size());
w.resize(n);
for(; (1<<k)<n; ++k) {
// w(1<<(k+1),1)
Z e=Z(3).pow((P-1)>>(k+1));
for(int i=(1<<(k-1)); i<(1<<k); ++i) {
w[i<<1]=w[i];
w[i<<1|1]=w[i]*e;
}
}
}
for(int m=1; m<n; m<<=1)
for(int i=0; i<n; i+=m<<1)
for(int j=0; j<m; ++j) {
Z B=a[i+j], C=a[i+m+j]*w[m+j];
a[i+j]=B+C, a[i+m+j]=B-C;
}
}
void idft(Poly& a) {
dft(a);
reverse(a.begin()+1,a.end());
Z inv=(1-P)/(int)a.size();
for(auto& x:a)
x*=inv;
}
Poly operator*(Poly a,Poly b) {
if(a.empty()||b.empty()) return Poly();
int len=1, sz=a.size()+b.size()-1;
while(len<sz)
len<<=1;
a.resize(len), dft(a);
b.resize(len), dft(b);
for(int i=0; i<len; ++i)
a[i]*=b[i];
idft(a);
a.resize(sz);
return a;
}
#endif
Poly operator*(Poly a,Z b) {
for(auto& x:a) x*=b;
return a;
}
Poly operator*(Z a,Poly b) {
return b*a;
}
Poly operator+=(Poly& a,const Poly& b) {
return a=a+b;
}
Poly operator-=(Poly& a,const Poly& b) {
return a=a-b;
}
template<class T>
Poly operator*=(Poly& a,const T& b) {
return a=a*b;
}
Poly Deriv(Poly a) {
for(int i=0; i+1<a.size(); ++i)
a[i]=a[i+1]*(i+1);
if(a.size())
a.pop_back();
return a;
}
Poly Integ(Poly a) {
a.push_back(0);
for(int i=(int)a.size()-1; i>0; --i)
a[i]=a[i-1]/i;
a[0]=0;
return a;
}
Poly Inv(const Poly& a,int m=-1) {
assert(a[0].x!=0);
if(m==-1) m=a.size();
Poly f{a[0].inv()};
int k=1;
while(k<m) {
k<<=1;
f=modxk(f*(Poly{2}-f*modxk(a,k)),k);
// 非MTT优化:两次变一次
// Poly x=f; x.resize(k); x.resize(k<<1);
// Poly y=a; y.resize(k); y.resize(k<<1);
// dft(x), dft(y);
// for(int i=0; i<x.size(); ++i)
// x[i]=x[i]*(2-x[i]*y[i]);
// idft(x);
// f=modxk(x,k);
}
return modxk(f,m);
}
namespace Cipolla {
Z w,a;
struct CP {
Z x,y;
CP(Z x,Z y): x(x),y(y) {}
CP operator*(const CP& b) const{
return CP(x*b.x+y*b.y*w,x*b.y+y*b.x);
}
CP pow(int b) const{
CP ans(1,0), a(*this);
for(; b; b>>=1,a=a*a)
if(b&1) ans=ans*a;
return ans;
}
};
int sqrt(Z n) {
if(!n.x) return 0;
if(n.pow((P-1)>>1).x==P-1)
return -1;// 非二次剩余
while(true) {
a=rand(), w=a*a-n;
if(w.pow((P-1)>>1).x==P-1)
return CP(a,1).pow((P+1)>>1).x.x;
}
return -1;
}
}
Poly Sqrt(const Poly& a,int m=-1) {
int x=Cipolla::sqrt(a[0]);
assert(x!=-1);
if(m==-1) m=a.size();
Poly f{min(x,P-x)};
int k=1;
while(k<m) {
k<<=1;
f=(f+modxk(modxk(a,k)*Inv(f,k),k))*((1+P)>>1);
}
return modxk(f,m);
}
Poly Ln(const Poly& a,int m=-1) {
assert(a[0].x==1);
if(m==-1) m=a.size();
return modxk(Integ(Deriv(a)*Inv(a,m)),m);
}
Poly Exp(const Poly& a,int m=-1) {
assert(a[0].x==0);
if(m==-1) m=a.size();
Poly f{1};
int k=1;
while(k<m) {
k<<=1;
f=modxk(f*(Poly{1}-Ln(f,k)+modxk(a,k)),k);
}
return modxk(f,m);
}
Poly Pow(const Poly& a,ll k,int m=-1) {
if(m==-1) m=a.size();
int i=0;
while(i<a.size() && !a[i].x) i++;
if(i==a.size()||i*k>=m) return Poly(m);
Z val=a[i].pow(k);// val*x^(ik)
Poly b=divxk(a,i)*a[i].inv();
return mulxk(Exp(k*Ln(b,m-i*k),m-i*k),i*k)*val;
}
Poly mulSub(const Poly& a,Poly b) {// 减法卷积
if(b.empty()) return Poly();
reverse(b.begin(), b.end());
return divxk(a*b,b.size()-1);
}
} using namespace NTT;
namespace {
const int MAXN=2e6+10;
Z inv[MAXN],fac[MAXN],infac[MAXN];
int initFac=[](int n=MAXN-1) {
n=min(n,P-1);
inv[1]=fac[0]=infac[0]=1;
for(int i=1; i<=n; ++i) {
fac[i]=fac[i-1]*i;
if(i>1) inv[i]=(P-P/i)*inv[P%i];
infac[i]=infac[i-1]*inv[i];
}
return 0;
}();
Z binom(int n,int m) {// n,m<P
if(m<0||n<m) return 0;
return fac[n]*infac[m]*infac[n-m];
}
}
int main() {
ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
int n,m;
cin>>n>>m;
Poly f(m+1);
for(int i=0; i<=m; ++i) {
f[i]=binom(m,i)*binom(m,i)*fac[i];
}
f=Pow(f,n,n*m+1);
Z ans=0;
for(int i=0; i<=n*m; ++i) {
ans+=(i&1?-1:1)*fac[n*m-i]*f[i];
}
cout<<ans;
return 0;
}
/*
*/
詳細信息
Test #1:
score: 100
Accepted
time: 35ms
memory: 26892kb
input:
2 2
output:
4
result:
ok 1 number(s): "4"
Test #2:
score: 0
Accepted
time: 42ms
memory: 26824kb
input:
5 1
output:
44
result:
ok 1 number(s): "44"
Test #3:
score: 0
Accepted
time: 120ms
memory: 27552kb
input:
167 91
output:
284830080
result:
ok 1 number(s): "284830080"
Test #4:
score: 0
Accepted
time: 32ms
memory: 26872kb
input:
2 1
output:
1
result:
ok 1 number(s): "1"
Test #5:
score: 0
Accepted
time: 31ms
memory: 26888kb
input:
2 3
output:
36
result:
ok 1 number(s): "36"
Test #6:
score: 0
Accepted
time: 36ms
memory: 26824kb
input:
2 4
output:
576
result:
ok 1 number(s): "576"
Test #7:
score: 0
Accepted
time: 36ms
memory: 26828kb
input:
3 1
output:
2
result:
ok 1 number(s): "2"
Test #8:
score: 0
Accepted
time: 31ms
memory: 26796kb
input:
3 2
output:
80
result:
ok 1 number(s): "80"
Test #9:
score: 0
Accepted
time: 30ms
memory: 26888kb
input:
3 3
output:
12096
result:
ok 1 number(s): "12096"
Test #10:
score: 0
Accepted
time: 30ms
memory: 26864kb
input:
3 4
output:
4783104
result:
ok 1 number(s): "4783104"
Test #11:
score: 0
Accepted
time: 30ms
memory: 26872kb
input:
4 1
output:
9
result:
ok 1 number(s): "9"
Test #12:
score: 0
Accepted
time: 36ms
memory: 26860kb
input:
4 2
output:
4752
result:
ok 1 number(s): "4752"
Test #13:
score: 0
Accepted
time: 30ms
memory: 26868kb
input:
4 3
output:
17927568
result:
ok 1 number(s): "17927568"
Test #14:
score: 0
Accepted
time: 30ms
memory: 26832kb
input:
4 4
output:
776703752
result:
ok 1 number(s): "776703752"
Test #15:
score: 0
Accepted
time: 38ms
memory: 26864kb
input:
5 2
output:
440192
result:
ok 1 number(s): "440192"
Test #16:
score: 0
Accepted
time: 31ms
memory: 26808kb
input:
5 3
output:
189125068
result:
ok 1 number(s): "189125068"
Test #17:
score: 0
Accepted
time: 31ms
memory: 26784kb
input:
5 4
output:
975434093
result:
ok 1 number(s): "975434093"
Test #18:
score: -100
Time Limit Exceeded
input:
1000 1000