結果

問題 No.1392 Don't be together
ユーザー rniyarniya
提出日時 2021-02-12 23:48:06
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 1,608 ms / 2,000 ms
コード長 9,615 bytes
コンパイル時間 2,444 ms
コンパイル使用メモリ 212,768 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-07-20 01:44:05
合計ジャッジ時間 18,486 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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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 1 ms
5,248 KB
testcase_01 AC 2 ms
5,376 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 2 ms
5,376 KB
testcase_05 AC 1 ms
5,376 KB
testcase_06 AC 687 ms
5,376 KB
testcase_07 AC 1,064 ms
5,376 KB
testcase_08 AC 1,133 ms
5,376 KB
testcase_09 AC 1,608 ms
5,376 KB
testcase_10 AC 643 ms
5,376 KB
testcase_11 AC 1,040 ms
5,376 KB
testcase_12 AC 602 ms
5,376 KB
testcase_13 AC 858 ms
5,376 KB
testcase_14 AC 961 ms
5,376 KB
testcase_15 AC 630 ms
5,376 KB
testcase_16 AC 1,031 ms
5,376 KB
testcase_17 AC 673 ms
5,376 KB
testcase_18 AC 936 ms
5,376 KB
testcase_19 AC 884 ms
5,376 KB
testcase_20 AC 322 ms
5,376 KB
testcase_21 AC 122 ms
5,376 KB
testcase_22 AC 529 ms
5,376 KB
testcase_23 AC 357 ms
5,376 KB
testcase_24 AC 213 ms
5,376 KB
testcase_25 AC 379 ms
5,376 KB
testcase_26 AC 97 ms
5,376 KB
testcase_27 AC 144 ms
5,376 KB
testcase_28 AC 431 ms
5,376 KB
testcase_29 AC 234 ms
5,376 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 # 

#define LOCAL
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
typedef __int128_t i128;
typedef unsigned int uint;
typedef unsigned long long ull;
#define ALL(x) (x).begin(), (x).end()

template <typename T> istream& operator>>(istream& is, vector<T>& v) {
    for (T& x : v) is >> x;
    return is;
}
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, typename U> ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << '(' << p.first << ',' << p.second << ')';
    return os;
}
template <typename T, typename U, typename V> ostream& operator<<(ostream& os, const tuple<T, U, V>& t) {
    os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ')';
    return os;
}
template <typename T, typename U, typename V, typename W> ostream& operator<<(ostream& os, const tuple<T, U, V, W>& t) {
    os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ',' << get<3>(t) << ')';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const multiset<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const unordered_set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const deque<T>& v) {
    for (int i = 0; i < (int)v.size(); i++) {
        os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
    }
    return os;
}

void debug_out() { cerr << '\n'; }
template <class Head, class... Tail> void debug_out(Head&& head, Tail&&... tail) {
    cerr << head;
    if (sizeof...(Tail) > 0) cerr << ", ";
    debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...)                                                                   \
    cerr << " ";                                                                     \
    cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \
    cerr << " ";                                                                     \
    debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }

template <class T1, class T2> inline bool chmin(T1& a, T2 b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T1, class T2> inline bool chmax(T1& a, T2 b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
#pragma endregion

/**
 * @brief modint
 * @docs docs/modulo/modint.md
 */
template <uint32_t mod> class modint {
    using i64 = int64_t;
    using u32 = uint32_t;
    using u64 = uint64_t;

public:
    u32 v;
    constexpr modint(const i64 x = 0) noexcept : v(x < 0 ? mod - 1 - (-(x + 1) % mod) : x % mod) {}
    constexpr u32& value() noexcept { return v; }
    constexpr const u32& value() const noexcept { return v; }
    constexpr modint operator+(const modint& rhs) const noexcept { return modint(*this) += rhs; }
    constexpr modint operator-(const modint& rhs) const noexcept { return modint(*this) -= rhs; }
    constexpr modint operator*(const modint& rhs) const noexcept { return modint(*this) *= rhs; }
    constexpr modint operator/(const modint& rhs) const noexcept { return modint(*this) /= rhs; }
    constexpr modint& operator+=(const modint& rhs) noexcept {
        v += rhs.v;
        if (v >= mod) v -= mod;
        return *this;
    }
    constexpr modint& operator-=(const modint& rhs) noexcept {
        if (v < rhs.v) v += mod;
        v -= rhs.v;
        return *this;
    }
    constexpr modint& operator*=(const modint& rhs) noexcept {
        v = (u64)v * rhs.v % mod;
        return *this;
    }
    constexpr modint& operator/=(const modint& rhs) noexcept { return *this *= rhs.pow(mod - 2); }
    constexpr modint pow(u64 exp) const noexcept {
        modint self(*this), res(1);
        while (exp > 0) {
            if (exp & 1) res *= self;
            self *= self;
            exp >>= 1;
        }
        return res;
    }
    constexpr modint& operator++() noexcept {
        if (++v == mod) v = 0;
        return *this;
    }
    constexpr modint& operator--() noexcept {
        if (v == 0) v = mod;
        return --v, *this;
    }
    constexpr modint operator++(int) noexcept {
        modint t = *this;
        return ++*this, t;
    }
    constexpr modint operator--(int) noexcept {
        modint t = *this;
        return --*this, t;
    }
    constexpr modint operator-() const noexcept { return modint(mod - v); }
    template <class T> friend constexpr modint operator+(T x, modint y) noexcept { return modint(x) + y; }
    template <class T> friend constexpr modint operator-(T x, modint y) noexcept { return modint(x) - y; }
    template <class T> friend constexpr modint operator*(T x, modint y) noexcept { return modint(x) * y; }
    template <class T> friend constexpr modint operator/(T x, modint y) noexcept { return modint(x) / y; }
    constexpr bool operator==(const modint& rhs) const noexcept { return v == rhs.v; }
    constexpr bool operator!=(const modint& rhs) const noexcept { return v != rhs.v; }
    constexpr bool operator!() const noexcept { return !v; }
    friend istream& operator>>(istream& s, modint& rhs) noexcept {
        i64 v;
        rhs = modint{(s >> v, v)};
        return s;
    }
    friend ostream& operator<<(ostream& s, const modint& rhs) noexcept { return s << rhs.v; }
};

/**
 * @brief combination
 * @docs docs/combinatorics/combination.md
 */
template <class M> struct Combination {
    vector<M> _fac, _inv, _finv;
    Combination(int n) : _fac(n + 1), _inv(n + 1), _finv(n + 1) {
        _fac[0] = _finv[n] = _inv[0] = 1;
        for (int i = 1; i <= n; i++) _fac[i] = _fac[i - 1] * i;
        _finv[n] /= _fac[n];
        for (int i = n - 1; i >= 0; i--) _finv[i] = _finv[i + 1] * (i + 1);
        for (int i = 1; i <= n; i++) _inv[i] = _finv[i] * _fac[i - 1];
    }
    M fac(int k) const { return _fac[k]; }
    M finv(int k) const { return _finv[k]; }
    M inv(int k) const { return _inv[k]; }
    M P(int n, int r) const {
        if (n < 0 || r < 0 || n < r) return 0;
        return _fac[n] * _finv[n - r];
    }
    M C(int n, int r) const {
        if (n < 0 || r < 0 || n < r) return 0;
        return _fac[n] * _finv[r] * _finv[n - r];
    }
};

/**
 * @brief UnionFind
 * @docs docs/datastructure/UnionFind.md
 */
struct UnionFind {
    int num;
    vector<int> par, rank;
    UnionFind(int n) : num(n), par(n), rank(n, 1) { iota(par.begin(), par.end(), 0); }
    int root(int x) { return (par[x] == x ? x : par[x] = root(par[x])); }
    bool merge(int x, int y) {
        x = root(x);
        y = root(y);
        if (x == y) return false;
        if (rank[x] < rank[y]) swap(x, y);
        par[y] = x;
        rank[x] += rank[y];
        num--;
        return true;
    }
    bool same(int x, int y) { return root(x) == root(y); }
    int size(int x) { return rank[root(x)]; }
    int count() { return num; }
    int operator[](int x) { return root(x); }
};

const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
// const long long MOD = 1000000007;
const long long MOD = 998244353;

using mint = modint<MOD>;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    Combination<mint> COM(5010);
    int N, M;
    cin >> N >> M;
    UnionFind UF(N);
    for (int i = 0; i < N; i++) {
        int p;
        cin >> p;
        UF.merge(i, --p);
    }

    vector<int> v;
    for (int i = 0; i < N; i++) {
        if (UF[i] == i) {
            v.emplace_back(UF.size(i));
        }
    }

    // x箱以下に条件を満たすように入れる
    auto calc = [&](int x) {
        vector<vector<mint>> dp(N + 1, vector<mint>(2, 0));
        dp[1][0] = x;
        for (int i = 1; i < N; i++) {
            dp[i + 1][0] += dp[i][1] * (x - 1);
            dp[i + 1][1] += dp[i][0] + dp[i][1] * (x - 2);
        }
        mint res = 1;
        for (int a : v) res *= dp[a][1] * (x - 1);
        return res;
    };

    mint ans = 0;
    for (int i = 0; i <= M; i++) {
        mint add = calc(M - i) * COM.C(M, i);
        if (i & 1)
            ans -= add;
        else
            ans += add;
    }
    ans *= COM.finv(M);

    cout << ans << '\n';
    return 0;
}
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