結果

問題 No.1392 Don't be together
ユーザー milanis48663220
提出日時 2021-02-12 23:01:06
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 565 ms / 2,000 ms
コード長 4,275 bytes
コンパイル時間 1,018 ms
コンパイル使用メモリ 105,796 KB
最終ジャッジ日時 2025-01-18 19:34:56
ジャッジサーバーID
（参考情報） 		judge5 / 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 <iostream>
#include <algorithm>
#include <iomanip>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <numeric>
#include <functional>
#include <cassert>
#define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl;
#define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
using namespace std;
typedef long long ll;
const ll MOD = 998244353;
class ModInt{
    public:
    ll v;
    ModInt(ll _v = 0){
        if(_v >= MOD) _v %= MOD;
        v = _v;
    }
    ModInt operator+(ll n){
        return ModInt((v+n)%MOD);
    }
    ModInt operator-(ll n){
        return ModInt((v-n+MOD)%MOD);
    }
    ModInt operator*(ll n){
        if(n >= MOD) n %= MOD;
        return ModInt((v*n)%MOD);
    }
    ModInt operator/(ll n){
        return ModInt((ModInt(n).inv()*v).v%MOD);
    }
    void operator+=(ll n){
        v = (v+n)%MOD;
    }
    void operator-=(ll n){
        v = (v-n+MOD)%MOD;
    }
    void operator*=(ll n){
        v = (v*n+MOD)%MOD;
    }
    
    
    ModInt operator+(ModInt n){
        return ModInt((v+n.v)%MOD);
    }
    ModInt operator-(ModInt n){
        return ModInt((v-n.v+MOD)%MOD);
    }
    ModInt operator*(ModInt n){
        return ModInt((v*n.v)%MOD);
    }
    ModInt operator/(ModInt n){
        return ModInt((n.inv()*v).v%MOD);
    }
    void operator+=(ModInt n){
        v = (v+n.v)%MOD;
    }
    void operator-=(ModInt n){
        v = (v-n.v+MOD)%MOD;
    }
    void operator*=(ModInt n){
        v = (v*n.v)%MOD;
    }
    void operator=(ModInt n){
        v = n.v;
    }
    bool operator==(ModInt n){
        return v == n.v;
    }
    bool operator!=(ModInt n){
        return v != n.v;
    }
    void operator=(ll n){
        v = n%MOD;
    }
    ModInt inv(){
        if(v == 1) return ModInt(1);
        else return ModInt(MOD-ModInt(MOD%v).inv().v*(MOD/v)%MOD);
    }
};
ostream& operator<<(ostream& os, const ModInt& m){
    os << m.v;
    return os;
}
istream & operator >> (istream &in,  ModInt &m){
    in >> m.v;
    return in;
}
#define N_MAX 200002
ModInt inv[N_MAX],fac[N_MAX],finv[N_MAX];
void init(){
    fac[0]=1;fac[1]=1;
    finv[0]=1;finv[1]=1;
    inv[1]=1;
    for(int i=2;i<N_MAX;i++){
        inv[i]=(ModInt)MOD-inv[MOD%i]*(MOD/i);
        fac[i]=fac[i-1]*(ll) i;
        finv[i]=finv[i-1]*inv[i];
    }
}
ModInt comb(ll n, ll r){
    if(n < r){
        return ModInt(0);
    }else{
        return fac[n]*finv[r]*finv[n-r];
    }
}
struct UnionFind {
    vector<int> data;
    UnionFind(int size) : data(size, -1) {}
    bool unionSet(int x, int y) {
        x = root(x); y = root(y);
        if (x != y) {
        if (data[y] < data[x]) swap(x, y);
        data[x] += data[y]; data[y] = x;
        }
        return x != y;
    }
    bool findSet(int x, int y) {
        return root(x) == root(y);
    }
    int root(int x) {
        return data[x] < 0 ? x : data[x] = root(data[x]);
    }
    int size(int x) {
        return -data[root(x)];
    }
};
ModInt cnt[5005][5005][2];
int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << setprecision(10) << fixed;
    int n, m; cin >> n >> m;
    init();
    for(int i = 2; i <= m; i++){
        cnt[i][1][0] = 0;
        cnt[i][1][1] = i;
        for(int j = 2; j <= n; j++){
            cnt[i][j][0] = cnt[i][j-1][0]*(i-2)+cnt[i][j-1][1]*(i-1);
            cnt[i][j][1] = cnt[i][j-1][0];
        }
    }
    vector<int> p(n);
    UnionFind uf(n);
    for(int i = 0; i < n; i++){
        cin >> p[i]; p[i]--;
        uf.unionSet(i, p[i]);
    }
    vector<int> roots;
    for(int i = 0; i < n; i++){
        if(uf.root(i) == i) {
            roots.push_back(i);
        }
    }
    ModInt ans = 0;
    for(int i = 2; i <= m; i++){
        ModInt tmp = (m-i)%2 == 0 ? ModInt(1) : ModInt(MOD-1);
        for(int r : roots){
            int sz = uf.size(r);
            tmp *= cnt[i][sz][0];
        }
        ans += tmp*comb(m, i);
        // cout << i << ' ' << tmp*comb(m, i) << endl;
    }
    ans *= finv[m];
    cout << ans << endl;
}
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