結果

問題 No.1392 Don't be together
ユーザー mugen_1337mugen_1337
提出日時 2021-02-13 00:58:03
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 229 ms / 2,000 ms
コード長 6,092 bytes
コンパイル時間 2,203 ms
コンパイル使用メモリ 208,136 KB
最終ジャッジ日時 2025-01-18 19:58:54
ジャッジサーバーID
(参考情報)
judge3 / judge2
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 27
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include<bits/stdc++.h>
using namespace std;
#define ALL(x) begin(x),end(x)
#define rep(i,n) for(int i=0;i<(n);i++)
#define debug(v) cout<<#v<<":";for(auto x:v){cout<<x<<' ';}cout<<endl;
#define mod 998244353
using ll=long long;
const int INF=1000000000;
const ll LINF=1001002003004005006ll;
int dx[]={1,0,-1,0},dy[]={0,1,0,-1};
// ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
template<class T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;}
template<class T>bool chmin(T &a,const T &b){if(b<a){a=b;return true;}return false;}
struct IOSetup{
IOSetup(){
cin.tie(0);
ios::sync_with_stdio(0);
cout<<fixed<<setprecision(12);
}
} iosetup;
template<typename T>
ostream &operator<<(ostream &os,const vector<T>&v){
for(int i=0;i<(int)v.size();i++) os<<v[i]<<(i+1==(int)v.size()?"":" ");
return os;
}
template<typename T>
istream &operator>>(istream &is,vector<T>&v){
for(T &x:v)is>>x;
return is;
}
template<ll Mod>
struct ModInt{
long long x;
ModInt():x(0){}
ModInt(long long y):x(y>=0?y%Mod:(Mod-(-y)%Mod)%Mod){}
ModInt &operator+=(const ModInt &p){
if((x+=p.x)>=Mod) x-=Mod;
return *this;
}
ModInt &operator-=(const ModInt &p){
if((x+=Mod-p.x)>=Mod)x-=Mod;
return *this;
}
ModInt &operator*=(const ModInt &p){
x=(int)(1ll*x*p.x%Mod);
return *this;
}
ModInt &operator/=(const ModInt &p){
(*this)*=p.inverse();
return *this;
}
ModInt operator-()const{return ModInt(-x);}
ModInt operator+(const ModInt &p)const{return ModInt(*this)+=p;}
ModInt operator-(const ModInt &p)const{return ModInt(*this)-=p;}
ModInt operator*(const ModInt &p)const{return ModInt(*this)*=p;}
ModInt operator/(const ModInt &p)const{return ModInt(*this)/=p;}
bool operator==(const ModInt &p)const{return x==p.x;}
bool operator!=(const ModInt &p)const{return x!=p.x;}
ModInt inverse()const{
int a=x,b=Mod,u=1,v=0,t;
while(b>0){
t=a/b;
swap(a-=t*b,b);swap(u-=t*v,v);
}
return ModInt(u);
}
ModInt pow(long long n)const{
ModInt ret(1),mul(x);
while(n>0){
if(n&1) ret*=mul;
mul*=mul;n>>=1;
}
return ret;
}
friend ostream &operator<<(ostream &os,const ModInt &p){return os<<p.x;}
friend istream &operator>>(istream &is,ModInt &a){long long t;is>>t;a=ModInt<Mod>(t);return (is);}
static int get_mod(){return Mod;}
};
using mint=ModInt<mod>;
template<typename T>
struct Precalc{
vector<T> fact,finv,inv;
int Mod;
Precalc(int MX):fact(MX),finv(MX),inv(MX),Mod(T::get_mod()){
fact[0]=T(1),fact[1]=T(1),finv[0]=T(1),finv[1]=T(1),inv[1]=T(1);
for(int i=2;i<MX;i++){
fact[i]=fact[i-1]*T(i);
inv[i]=T(0)-inv[Mod%i]*(T(Mod/i));
finv[i]=finv[i-1]*inv[i];
}
}
T com(int n,int k){
if(n<k) return T(0);
if(n<0 or k<0) return T(0);
return fact[n]*(finv[k]*finv[n-k]);
}
T fac(int n){
return fact[n];
}
// :nk
T nHk(int n,int k){
return com(n+k-1,k);
}
// nk1O(k)
T F12_dis_dis_one(int n,int k){
if(n<k)return T(0);
T ret=0;
for(int i=0;i<=k;i++){
T add=com(k,i)*(T(i).pow(n));
if((k-i)%2) ret-=add;
else ret+=add;
}
return ret;
}
// nk1
// ,
// require : T(num).pow(k)
T Stirling_number(int n,int k){
T ret=0;
for(int i=0;i<=k;i++) ret+=com(k,i)*T(i).pow(n)*((k-i)%2?(-1):1);
return ret/T(fac(k));
}
// nk
T Bell_number(int n,int k){
T ret=0;
for(int i=1;i<=k;i++) ret+=Stirling_number(n,i);
return ret;
}
T partition_function(int n,int k){
auto table=partition_function_table(n,k);
return table[n][k];
}
vector<vector<T>> partition_function_table(int n,int k){
vector<vector<T>> ret(n+1,vector<T>(k+1,0));
ret[0][0]=1;
for(int i=0;i<=n;i++)for(int j=1;j<=k;j++)if(i or j){
ret[i][j]=ret[i][j-1];
if(i-j>=0) ret[i][j]+=ret[i-j][j];
}
return ret;
}
/* sum combination(n+x, x), x=l to r
https://www.wolframalpha.com/input/?i=sum+combination%28n%2Bx+%2Cx%29%2C+x%3Dl+to+r&lang=ja
check n+x < [COM_PRECALC_MAX] */
T sum_of_comb(int n,int l,int r){
if(l>r)return T(0);
T ret=T(r+1)*com(n+r+1,r+1)-T(l)*com(l+n,l);
ret/=T(n+1);
return ret;
}
};
Precalc<mint> F(500000);
// 0-indexed parmutation only
vector<vector<int>> cycle_partition(const vector<int> &p){
int n=p.size();
vector<vector<int>> ret;
vector<bool> check(n,false);
rep(i,n)if(!check[p[i]]){
vector<int> v;
int pos=p[i];
v.push_back(i);
check[i]=true;
while(pos!=i){
v.push_back(pos);
check[pos]=true;
pos=p[pos];
}
ret.push_back(v);
}
return ret;
}
signed main(){
int n,m;cin>>n>>m;
vector<int> p(n);
cin>>p;
for(auto &x:p) x--;
auto cyc=cycle_partition(p);
vector<int> v;
for(auto &w:cyc) v.emplace_back(w.size());
// x使, dp[i]:=i使
auto f=[&](int x){
vector<mint> a(n+1,0),b(n+1,0),ret(n+1,0);
b[1]=x;
for(int i=1;i<n;i++){
a[i+1]=a[i]*(x-2)+b[i]*(x-1);
b[i+1]=a[i];
}
return a;
};
mint res=0;
for(int i=m;i>=1;i--){
auto w=f(i);
mint add=F.com(m,i);
for(auto sz:v) add*=w[sz];
if((m-i)%2) res-=add;
else res+=add;
}
cout<<res/F.fac(m)<<endl;
return 0;
}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0