結果
問題 | No.1392 Don't be together |
ユーザー |
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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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 27 |
ソースコード
#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 998244353using 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];}// 重複組み合わせ:n種類の物から重複を許し,k個選ぶT nHk(int n,int k){return com(n+k-1,k);}// 玉n区別,箱k区別,各箱1個以上O(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;}// 区別できるn人をkチームにわける,チームには最低1人属する// ベン図をイメージ, 包除// 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));}// 区別できるn人をkチーム以下にわける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 rhttps://www.wolframalpha.com/input/?i=sum+combination%28n%2Bx+%2Cx%29%2C+x%3Dl+to+r&lang=jacheck 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 onlyvector<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色以下を使う, dp[i]:=i個の玉を使った数珠の作り方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;}