結果

問題 No.1392 Don't be together
ユーザー gazellegazelle
提出日時 2021-02-12 22:37:21
言語 C++17
(gcc 13.2.0 + boost 1.83.0)
結果
AC  
実行時間 608 ms / 2,000 ms
コード長 5,908 bytes
コンパイル時間 2,319 ms
コンパイル使用メモリ 210,492 KB
実行使用メモリ 207,036 KB
最終ジャッジ日時 2023-09-27 05:23:11
合計ジャッジ時間 12,505 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge14
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 175 ms
206,640 KB
testcase_01 AC 175 ms
206,132 KB
testcase_02 AC 175 ms
206,712 KB
testcase_03 AC 175 ms
206,712 KB
testcase_04 AC 175 ms
206,216 KB
testcase_05 AC 175 ms
206,180 KB
testcase_06 AC 207 ms
206,568 KB
testcase_07 AC 608 ms
207,036 KB
testcase_08 AC 278 ms
206,644 KB
testcase_09 AC 227 ms
206,556 KB
testcase_10 AC 352 ms
206,556 KB
testcase_11 AC 410 ms
206,640 KB
testcase_12 AC 321 ms
206,664 KB
testcase_13 AC 342 ms
206,636 KB
testcase_14 AC 473 ms
206,972 KB
testcase_15 AC 412 ms
206,908 KB
testcase_16 AC 315 ms
206,708 KB
testcase_17 AC 359 ms
206,648 KB
testcase_18 AC 348 ms
206,640 KB
testcase_19 AC 405 ms
206,900 KB
testcase_20 AC 303 ms
206,704 KB
testcase_21 AC 222 ms
206,612 KB
testcase_22 AC 305 ms
206,612 KB
testcase_23 AC 271 ms
206,660 KB
testcase_24 AC 261 ms
206,600 KB
testcase_25 AC 254 ms
206,652 KB
testcase_26 AC 207 ms
206,636 KB
testcase_27 AC 202 ms
206,604 KB
testcase_28 AC 278 ms
206,568 KB
testcase_29 AC 221 ms
206,704 KB
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 # 

#include <bits/stdc++.h>
#define FOR(i, n, m) for(ll i = (n); i < (ll)(m); i++)
#define REP(i, n) FOR(i, 0, n)
#define ALL(v) v.begin(), v.end()
#define pb push_back
using namespace std;
using ll = long long;
using ld = long double;
using P = pair<ll, ll>;
constexpr ll inf = 1000000000;
constexpr ll mod = 998244353;
constexpr long double eps = 1e-6;
 
template<typename T1, typename T2>
ostream& operator<<(ostream& os, pair<T1, T2> p) {
    os << to_string(p.first) << " " << to_string(p.second);
    return os;
}
template<typename T>
ostream& operator<<(ostream& os, vector<T>& v) {
    REP(i, v.size()) {
        if(i) os << " ";
        os << v[i];
    }
    return os;
}
 
struct modint {
    ll n;
public:
    modint(const ll n = 0) : n((n % mod + mod) % mod) {}
    static modint pow(modint a, int m) {
        modint r = 1;
        while(m > 0) {
            if(m & 1) { r *= a; }
            a = (a * a); m /= 2;
        }
        return r;
    }
    modint &operator++() { *this += 1; return *this; }
    modint &operator--() { *this -= 1; return *this; }
    modint operator++(int) { modint ret = *this; *this += 1; return ret; }
    modint operator--(int) { modint ret = *this; *this -= 1; return ret; }
    modint operator~() const { return (this -> pow(n, mod - 2)); } // inverse
    friend bool operator==(const modint& lhs, const modint& rhs) {
        return lhs.n == rhs.n;
    }
    friend bool operator<(const modint& lhs, const modint& rhs) {
        return lhs.n < rhs.n;
    }
    friend bool operator>(const modint& lhs, const modint& rhs) {
        return lhs.n > rhs.n;
    }
    friend modint &operator+=(modint& lhs, const modint& rhs) {
        lhs.n += rhs.n;
        if (lhs.n >= mod) lhs.n -= mod;
        return lhs;
    }
    friend modint &operator-=(modint& lhs, const modint& rhs) {
        lhs.n -= rhs.n;
        if (lhs.n < 0) lhs.n += mod;
        return lhs;
    }
    friend modint &operator*=(modint& lhs, const modint& rhs) {
        lhs.n = (lhs.n * rhs.n) % mod;
        return lhs;
    }
    friend modint &operator/=(modint& lhs, const modint& rhs) {
        lhs.n = (lhs.n * (~rhs).n) % mod;
        return lhs;
    }
    friend modint operator+(const modint& lhs, const modint& rhs) {
        return modint(lhs.n + rhs.n);
    }
    friend modint operator-(const modint& lhs, const modint& rhs) {
        return modint(lhs.n - rhs.n);
    }
    friend modint operator*(const modint& lhs, const modint& rhs) {
        return modint(lhs.n * rhs.n);
    }
    friend modint operator/(const modint& lhs, const modint& rhs) {
        return modint(lhs.n * (~rhs).n);
    }
};
istream& operator>>(istream& is, modint m) { is >> m.n; return is; }
ostream& operator<<(ostream& os, modint m) { os << m.n; return os; }
 
#define MAX_N 1010101
long long extgcd(long long a, long long b, long long& x, long long& y) {
    long long d = a;
    if (b != 0) {
        d = extgcd(b, a % b, y, x);
        y -= (a / b) * x;
    } else {
        x = 1; y = 0;
    }
    return d;
}
long long mod_inverse(long long a, long long m) {
    long long x, y;
    if(extgcd(a, m, x, y) == 1) return (m + x % m) % m;
    else return -1;
}
vector<long long> fact(MAX_N+1, inf);
long long mod_fact(long long n, long long& e) {
    if(fact[0] == inf) {
        fact[0]=1;
        if(MAX_N != 0) fact[1]=1;
        for(ll i = 2; i <= MAX_N; ++i) {
            fact[i] = (fact[i-1] * i) % mod;
        }
    }
    e = 0;
    if(n == 0) return 1;
    long long res = mod_fact(n / mod, e);
    e += n / mod;
    if((n / mod) % 2 != 0) return (res * (mod - fact[n % mod])) % mod;
    return (res * fact[n % mod]) % mod;
}
// return nCk
long long mod_comb(long long n, long long k) {
    if(n < 0 || k < 0 || n < k) return 0;
    long long e1, e2, e3;
    long long a1 = mod_fact(n, e1), a2 = mod_fact(k, e2), a3 = mod_fact(n - k, e3);
    if(e1 > e2 + e3) return 0;
    return (a1 * mod_inverse((a2 * a3) % mod, mod)) % mod;
}
 
using mi = modint;
 
mi mod_pow(mi a, ll n) {
    mi ret = 1;
    mi tmp = a;
    while(n > 0) {
        if(n % 2) ret *= tmp;
        tmp = tmp * tmp;
        n /= 2;
    }
    return ret;
}

ll mod_pow(ll a, ll n, ll m) {
    ll ret = 1;
    ll tmp = a;
    while(n > 0) {
        if(n % 2) ret *= tmp;
        ret %= m;
        tmp = tmp * tmp;
        tmp %= m;
        n /= 2;
    }
    return ret % m;
}
 
ll gcd(ll a, ll b) {
    if (b == 0) return a;
    return gcd(b, a % b);
}

vector<vector<mi>> memo(5001, vector<mi>(5001));
mi dfs(ll m, ll k) {
    if(memo[m][k].n != -1) {
        return memo[m][k];
    }

    if(k == 1) {
        return memo[m][k] = m;
    } else if(k == 2) {
        return memo[m][k] = m * (m - 1);
    } else if(k == 3) {
        return memo[m][k] = ((m * (m - 1)) % mod) * (m - 2);
    } else {
        return memo[m][k] = (m - 1) * dfs(m, k - 2) + (m - 2) * dfs(m, k - 1);
    }
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    REP(i, 5001) REP(j, 5001) {
        memo[i][j].n = -1;
    }

    int n, m;
    cin >> n >> m;

    vector<int> p(n);

    REP(i, n) {
        cin >> p[i];
        p[i] -= 1;
    }

    if(m == 1) {
        cout << 0 << endl;
        return 0;
    }

    vector<bool> used(n, false);
    vector<int> cycle;

    REP(i, n) {
        if(not used[i]) {
            int cnt = 0;
            int pos = i;
            while(not used[pos]) {
                used[pos] = true;
                cnt += 1;
                pos = p[pos];
            }
            cycle.pb(cnt);
        }
    }

    mi ans = 0;

    vector<mi> dp(m + 1, 1);

    for(int i = 2; i <= m; i += 1) {
        for(auto c: cycle) {
            dp[i] *= dfs(i, c);
        }
        if((m - i) % 2) ans -= mod_comb(m, i) * dp[i];
        else ans += mod_comb(m, i) * dp[i];
        // cout << dp[i] << endl;
    }

    mi fct = 1;
    FOR(i, 1, m + 1) fct *= i;

    cout << ans / fct << endl;

    return 0;
}
0