結果

問題 No.1392 Don't be together
ユーザー tokusakurai
提出日時 2021-02-12 22:16:28
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 236 ms / 2,000 ms
コード長 6,654 bytes
コンパイル時間 2,750 ms
コンパイル使用メモリ 207,836 KB
最終ジャッジ日時 2025-01-18 18:47:39
ジャッジサーバーID
（参考情報） 		judge3 / judge1
このコードへのチャレンジ
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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 rep(i, n) for(int i = 0; i < n; i++)
#define rep2(i, x, n) for(int i = x; i <= n; i++)
#define rep3(i, x, n) for(int i = x; i >= n; i--)
#define each(e, v) for(auto &e: v)
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
//const int MOD = 1000000007;
const int MOD = 998244353;
const int inf = (1<<30)-1;
const ll INF = (1LL<<60)-1;
template<typename T> bool chmax(T &x, const T &y) {return (x < y)? (x = y, true) : false;};
template<typename T> bool chmin(T &x, const T &y) {return (x > y)? (x = y, true) : false;};
struct io_setup{
    io_setup(){
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
    }
} io_setup;
template<int mod>
struct Mod_Int{
    int x;
    Mod_Int() : x(0) {}
    Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
    Mod_Int &operator += (const Mod_Int &p){
        if((x += p.x) >= mod) x -= mod;
        return *this;
    }
    Mod_Int &operator -= (const Mod_Int &p){
        if((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }
    Mod_Int &operator *= (const Mod_Int &p){
        x = (int) (1LL * x * p.x % mod);
        return *this;
    }
    Mod_Int &operator /= (const Mod_Int &p){
        *this *= p.inverse();
        return *this;
    }
    Mod_Int &operator ++ () {return *this += Mod_Int(1);}
    Mod_Int operator ++ (int){
        Mod_Int tmp = *this;
        ++*this;
        return tmp;
    }
    Mod_Int &operator -- () {return *this -= Mod_Int(1);}
    Mod_Int operator -- (int){
        Mod_Int tmp = *this;
        --*this;
        return tmp;
    }
    Mod_Int operator - () const {return Mod_Int(-x);}
    Mod_Int operator + (const Mod_Int &p) const {return Mod_Int(*this) += p;}
    Mod_Int operator - (const Mod_Int &p) const {return Mod_Int(*this) -= p;}
    Mod_Int operator * (const Mod_Int &p) const {return Mod_Int(*this) *= p;}
    Mod_Int operator / (const Mod_Int &p) const {return Mod_Int(*this) /= p;}
    bool operator == (const Mod_Int &p) const {return x == p.x;}
    bool operator != (const Mod_Int &p) const {return x != p.x;}
    Mod_Int inverse() const {
        assert(*this != Mod_Int(0));
        return pow(mod-2);
    }
    Mod_Int pow(long long k) const{
        Mod_Int now = *this, ret = 1;
        for(; k > 0; k >>= 1, now *= now){
            if(k&1) ret *= now;
        }
        return ret;
    }
    friend ostream &operator << (ostream &os, const Mod_Int &p){
        return os << p.x;
    }
    friend istream &operator >> (istream &is, Mod_Int &p){
        long long a;
        is >> a;
        p = Mod_Int<mod>(a);
        return is;
    }
};
using mint = Mod_Int<MOD>;
template<int mod>
struct Combination{
    using T = Mod_Int<mod>;
    vector<T> _fac, _ifac;
    Combination(int n){
        _fac.resize(n+1), _ifac.resize(n+1);
        _fac[0] = 1;
        for(int i = 1; i <= n; i++) _fac[i] = _fac[i-1]*i;
        _ifac[n] = _fac[n].inverse();
        for(int i = n; i >= 1; i--) _ifac[i-1] = _ifac[i]*i;
    }
    T fac(int k) const {return _fac[k];}
    T ifac(int k) const {return _ifac[k];}
    T comb(int n, int k) const{
        if(k < 0 || n < k) return 0;
        return fac(n)*ifac(n-k)*ifac(k);
    }
    T comb2(int x, int y) const {return comb(x+y, x);}
    T perm(int n, int k) const{
        if(k < 0 || n < k) return 0;
        return fac(n)*ifac(n-k);
    }
    T second_stirling_number(int n, int k) const{ //n個の区別できる玉を、k個の区別しない箱に、各箱に1個以上玉が入るように入れる場合の数
        T ret = 0;
        for(int i = 0; i <= k; i++){
            T tmp = comb(k, i)*T(i).pow(n);
            ret += ((k-i)&1)? -tmp : tmp;
        }
        return ret*ifac(k);
    }
    T bell_number(int n, int k) const{ //n個の区別できる玉を、k個の区別しない箱に入れる場合の数
        if(n == 0) return 1;
        k = min(k, n);
        vector<T> pref(k+1);
        pref[0] = 1;
        for(int i = 1; i <= k; i++){
            if(i&1) pref[i] = pref[i-1]-ifac(i);
            else pref[i] = pref[i-1]+ifac(i);   
        }
        T ret = 0;
        for(int i = 1; i <= k; i++){
            ret += T(i).pow(n)*ifac(i)*pref[k-i];
        }
        return ret;
    }
};
using comb = Combination<MOD>;
struct Union_Find_Tree{
    vector<int> data;
    const int n;
    
    Union_Find_Tree(int n) : n(n){
        data.assign(n, -1);
    }
    
    int root(int x){
        if(data[x] < 0) return x;
        return data[x] = root(data[x]);
    }
    int operator [] (int i) {return root(i);}
    
    bool unite(int x, int y){
        x = root(x), y = root(y);
        if(x == y) return false;
        if(data[x] > data[y]) swap(x, y);
        data[x] += data[y], data[y] = x;
        return true;
    }
    
    int size(int x) {return -data[root(x)];}
    
    bool same(int x, int y) {return root(x) == root(y);}
    
    void clear() {fill(begin(data), end(data), -1);}
};
struct Graph{
    vector<vector<int>> es;
    const int n;
    vector<int> d;
    Graph(int n) : n(n){
        es.resize(n), d.resize(n);
    }
    void add_edge(int from, int to, bool directed = false){
        es[from].pb(to);
        if(!directed) es[to].pb(from);
    }
    void dfs(int now, int pre){
        if(pre == -1) d[now] = 0;
        else d[now] = d[pre]+1;
        each(e, es[now]){
            if(e != pre) dfs(e, now);
        }
    }
};
int main(){
    int N, M; cin >> N >> M;
    vector<int> p(N);
    rep(i, N) {cin >> p[i]; p[i]--;}
    vector<int> v;
    Union_Find_Tree uf(N);
    Graph G(N);
    rep(i, N){
        if(!uf.unite(i, p[i])) v.eb(i);
        else G.add_edge(i, p[i], false);
    }
    vector<int> d(N);
    each(e, v){
        G.dfs(e, -1);
        d[e] = G.d[p[e]];
    }
    int n = 0;
    rep(i, N){
        if(uf[i] == i) n++;
    }
    mint ans = 0;
    comb C(M);
    rep2(i, 2, M){
        vector<mint> dp1(N), dp2(N);
        dp1[0] = 1, dp2[0] = 0;
        mint P = mint(1)/mint(i-1);
        rep(i, N-1){
            dp1[i+1] = dp2[i]*P;
            dp2[i+1] = dp1[i]+dp2[i]*(-P+1);
        }
        dp2[1] = 1;
        mint tmp = mint(i).pow(n)*mint(i-1).pow(N-n);
        each(e, v) tmp *= dp2[d[e]];
        tmp *= C.comb(M, i);
        if(i%2 == M%2) ans += tmp;
        else ans -= tmp;
    }
    cout << ans*C.ifac(M) << '\n';
}
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