結果

問題 No.1392 Don't be together
ユーザー minatominato
提出日時 2021-02-12 23:17:30
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 534 ms / 2,000 ms
コード長 12,663 bytes
コンパイル時間 2,727 ms
コンパイル使用メモリ 227,856 KB
実行使用メモリ 102,744 KB
最終ジャッジ日時 2024-07-20 00:52:19
合計ジャッジ時間 6,752 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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 3 ms
5,248 KB
testcase_01 AC 3 ms
5,376 KB
testcase_02 AC 3 ms
5,376 KB
testcase_03 AC 3 ms
5,376 KB
testcase_04 AC 3 ms
5,376 KB
testcase_05 AC 3 ms
5,376 KB
testcase_06 AC 534 ms
44,980 KB
testcase_07 AC 143 ms
83,200 KB
testcase_08 AC 250 ms
73,728 KB
testcase_09 AC 477 ms
102,744 KB
testcase_10 AC 129 ms
51,840 KB
testcase_11 AC 179 ms
79,104 KB
testcase_12 AC 131 ms
48,768 KB
testcase_13 AC 160 ms
66,560 KB
testcase_14 AC 153 ms
73,856 KB
testcase_15 AC 105 ms
51,072 KB
testcase_16 AC 191 ms
80,000 KB
testcase_17 AC 132 ms
54,400 KB
testcase_18 AC 169 ms
71,936 KB
testcase_19 AC 147 ms
64,384 KB
testcase_20 AC 55 ms
30,336 KB
testcase_21 AC 22 ms
13,696 KB
testcase_22 AC 106 ms
45,312 KB
testcase_23 AC 69 ms
32,000 KB
testcase_24 AC 36 ms
20,224 KB
testcase_25 AC 85 ms
34,560 KB
testcase_26 AC 21 ms
11,776 KB
testcase_27 AC 41 ms
15,872 KB
testcase_28 AC 79 ms
38,016 KB
testcase_29 AC 42 ms
21,248 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>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
template <class T> using vec = vector<T>;
template <class T> using vvec = vector<vector<T>>;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define rrep(i, n) for (int i = int(n) - 1; i >= 0; i--)
#define all(x) begin(x), end(x)
constexpr char ln = '\n';
template <class Container> inline int SZ(const Container& v) { return int(v.size()); }
template <class T> inline void UNIQUE(vector<T>& v) { v.erase(unique(v.begin(), v.end()), v.end()); }
template <class T1, class T2> inline bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; }
template <class T1, class T2> inline bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; }
inline int topbit(ull x) { return x == 0 ? -1 : 63 - __builtin_clzll(x); }
inline int botbit(ull x) { return x == 0 ? 64 : __builtin_ctzll(x); }
inline int popcount(ull x) { return __builtin_popcountll(x); }
inline int kthbit(ull x, int k) { return (x >> k) & 1; }
inline constexpr long long TEN(int x) { return x == 0 ? 1 : TEN(x - 1) * 10; }
const string YESNO[2] = {"NO", "YES"};
const string YesNo[2] = {"No", "Yes"};
inline void YES(bool t = true) { cout << YESNO[t] << "\n"; }
inline void Yes(bool t = true) { cout << YesNo[t] << "\n"; }
template <class T> inline void drop(T x) { cout << x << "\n"; exit(0); }
inline void print() { cout << "\n"; }
template <class T> inline void print(const vector<T>& v) { for (auto it = v.begin(); it != v.end(); ++it) { if (it != v.begin()) { cout << " "; } cout << *it; } print(); }
template <class T, class... Args> inline void print(const T& x, const Args& ... args) { cout << x << " "; print(args...); }
#ifdef MINATO_LOCAL
template <class T1, class T2> ostream& operator<<(ostream& os, pair<T1, T2> p) { return os << "(" << p.first << ", " << p.second << ")"; }
template <size_t N, class TUPLE> void debug_tuple(ostream& os, TUPLE _) { (void)os; (void)_; }
template <size_t N, class TUPLE, class T, class ...Args> void debug_tuple(ostream &os, TUPLE t) { os << (N == 0 ? "" : ", ") << get<N>(t); debug_tuple<N + 1, TUPLE, Args...>(os, t); }
template <class ...Args> ostream& operator<<(ostream& os, tuple<Args...> t) { os << "("; debug_tuple<0, tuple<Args...>, Args...>(os, t); return os << ")"; }
string debug_delim(int& i) { return i++ == 0 ? "" : ", "; }
#define debug_embrace(x) { int i = 0; os << "{";  { x } return os << "}"; }
template <class T> ostream& operator<<(ostream& os, vector<T> v) { debug_embrace( for (T e : v) { os << debug_delim(i) << e; } ) }
template <class T, size_t N> ostream& operator<<(ostream& os, array<T, N> a) { debug_embrace( for (T e : a) { os << debug_delim(i) << e; } ) }
template <class T, size_t N> enable_if_t<!is_same_v<char, remove_cv_t<T>>, ostream>& operator<<(ostream& os, T(&a)[N]) { debug_embrace( for (T e : a) { os << debug_delim(i) << e; } ) }
template <class Key> ostream& operator<<(ostream& os, set<Key> s) { debug_embrace( for (Key e : s) { os << debug_delim(i) << e; }) }
template <class Key, class T> ostream& operator<<(ostream& os, map<Key, T> mp) { debug_embrace( for (auto e : mp) { os << debug_delim(i) << e; }) }
template <class Key> ostream& operator<<(ostream& os, multiset<Key> s) { debug_embrace( for (Key e : s) { os << debug_delim(i) << e; }) }
template <class T> ostream& operator<<(ostream& os, queue<T> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.front(); } ) }
template <class T> ostream& operator<<(ostream& os, deque<T> q) { debug_embrace( for (T e : q) { os << debug_delim(i) << e; } ) }
template <class T> ostream& operator<<(ostream& os, priority_queue<T> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.top(); } ) }
template <class T> ostream& operator<<(ostream& os, priority_queue<T, vector<T>, greater<T>> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.top(); } ) }
void debug_out() { cerr << endl; }
template <class T, class... Args> void debug_out(const T& x, const Args& ... args) { cerr << " " << x; debug_out(args...); }
#define debug(...) cerr << __LINE__ << " : [" << #__VA_ARGS__ << "] =", debug_out(__VA_ARGS__)
#else
#define debug(...) (void(0))
#endif
struct fast_ios { fast_ios() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); cerr << fixed << setprecision(7); }; } fast_ios_;
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

template <int m> 
struct ModInt {
  public:
    static constexpr int mod() { return m; }
    static ModInt raw(int v) {
        ModInt x;
        x._v = v;
        return x;
    }

    ModInt() : _v(0) {}
    ModInt(long long v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }

    unsigned int val() const { return _v; }

    explicit operator bool() const { return _v != 0; }
    ModInt& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    ModInt& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    ModInt operator++(int) {
        ModInt result = *this;
        ++*this;
        return result;
    }
    ModInt operator--(int) {
        ModInt result = *this;
        --*this;
        return result;
    }

    ModInt& operator+=(const ModInt& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    ModInt& operator-=(const ModInt& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    ModInt& operator*=(const ModInt& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    ModInt& operator^=(long long n) {
        ModInt x = *this;
        *this = 1;
        if (n < 0) x = x.inv(), n = -n;
        while (n) {
            if (n & 1) *this *= x;
            x *= x;
            n >>= 1;
        }
        return *this;
    }
    ModInt& operator/=(const ModInt& rhs) { return *this = *this * rhs.inv(); }

    ModInt operator+() const { return *this; }
    ModInt operator-() const { return ModInt() - *this; }

    ModInt pow(long long n) const {
        ModInt r = *this;
        r ^= n;
        return r;
    }
    ModInt inv() const {
        int a = _v, b = umod(), y = 1, z = 0, t;
        for (; ; ) {
            t = a / b; a -= t * b;
            if (a == 0) {
                assert(b == 1 || b == -1);
                return ModInt(b * z);
            }
            y -= t * z;
            t = b / a; b -= t * a;
            if (b == 0) {
                assert(a == 1 || a == -1);
                return ModInt(a * y);
            }
            z -= t * y;
        }
    }

    friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) += rhs; }
    friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) -= rhs; }
    friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) *= rhs; }
    friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) /= rhs; }
    friend ModInt operator^(const ModInt& lhs, long long rhs) { return ModInt(lhs) ^= rhs; }
    friend bool operator==(const ModInt& lhs, const ModInt& rhs) { return lhs._v == rhs._v; }
    friend bool operator!=(const ModInt& lhs, const ModInt& rhs) { return lhs._v != rhs._v; }
    friend ModInt operator+(long long lhs, const ModInt& rhs) { return (ModInt(lhs) += rhs); }
    friend ModInt operator-(long long lhs, const ModInt& rhs) { return (ModInt(lhs) -= rhs); }
    friend ModInt operator*(long long lhs, const ModInt& rhs) { return (ModInt(lhs) *= rhs); }
    friend ostream& operator<<(ostream& os, const ModInt& M) { return os << M._v; }
    friend istream& operator>>(istream& is, ModInt& M) { long long x; is >> x; M = x; return is; }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
};

//constexpr int MOD = 1000000007;
constexpr int MOD = 998244353;

using mint = ModInt<MOD>;

template <class M>
struct ModCombination {
  public:
    ModCombination() {}
    ModCombination(int n) : n_(n), fac_(n + 1), facinv_(n + 1) {
        assert(1 <= n);
        fac_[0] = 1;
        for (int i = 1; i <= n; i++) fac_[i] = fac_[i - 1] * i;
        facinv_[n] = M(1) / fac_[n];
        for (int i = n; i >= 1; i--) facinv_[i - 1] = facinv_[i] * i;
    }

    M fac(int k) const { 
        assert(0 <= k and k <= n_);
        return fac_[k]; 
    }
    M facinv(int k) const {
        assert(0 <= k and k <= n_); 
        return facinv_[k]; 
    }
    M inv(int k) const { 
        assert(1 <= k and k <= n_);
        return facinv_[k] * fac_[k - 1]; 
    }

    M P(int n, int k) const {
        if (k < 0 or k > n) return M(0);
        assert(n <= n_);
        return fac_[n] * facinv_[n - k];
    }
    M C(int n, int k) const {
        if (k < 0 or k > n) return M(0);
        assert(n <= n_);
        return fac_[n] * facinv_[n - k] * facinv_[k];
    }
    M H(int n, int k) const {
        if (n == 0 and k == 0) return M(1);
        return C(n + k - 1, n);
    }
    M catalan(int n) const {
        if (n == 0) return M(1);
        return C(2 * n, n) - C(2 * n, n - 1);
    }

  private:
    int n_;
    vector<M> fac_, facinv_;
};

struct UnionFind {
  public:
    UnionFind() : n_(0) {}
    UnionFind(int n) : n_(n), group_num(n), node(n, -1) {}

    int size() const { return n_; }

    int count() const { return group_num; }

    bool merge(int x, int y) {
        assert(0 <= x and x < n_);
        assert(0 <= y and y < n_);
        x = root_(x); y = root_(y);
        if (x == y) return false;
        if (node[x] > node[y]) swap(x,y);
        node[x] += node[y];
        node[y] = x;
        group_num--;
        return true; 
    }

    bool same(int x, int y) {
        assert(0 <= x and x < n_);
        assert(0 <= y and y < n_);
        return root_(x) == root_(y); 
    }

    int root(int x) {
        assert(0 <= x and x < n_);
        return root_(x);
    }

    int size(int x) { 
        assert(0 <= x and x < n_);
        return -node[root_(x)]; 
    }

    int operator[](int x) {
        assert(0 <= x and x < n_);
        return root_(x);
    }

    vector<vector<int>> groups() {
        vector<int> leader_buf(n_), group_size(n_);
        for (int i = 0; i < n_; i++) {
            leader_buf[i] = root_(i);
            group_size[leader_buf[i]]++;
        }
        vector<vector<int>> result(n_);
        for (int i = 0; i < n_; i++) {
            result[i].reserve(group_size[i]);
        }
        for (int i = 0; i < n_; i++) {
            result[leader_buf[i]].push_back(i);
        }
        result.erase(
            remove_if(result.begin(), result.end(),
                      [&](const vector<int>& v) { return v.empty(); }),
            result.end());
        return result;
    }

  private:
    int n_, group_num;
    vector<int> node;

    int root_(int x) {
        if (node[x] < 0) return x;
        return node[x] = root_(node[x]);
    }
};

int main() {
    ModCombination<mint> MC(100000);
    int N,M; cin >> N >> M;
    vvec<mint> table(N+1, vec<mint>(M+1));
    table[0][0] = 1;
    rep(i,N) {
        rep(j,M+1) {
            if (!table[i][j]) continue;
            table[i+1][j] += table[i][j]*j;
            if (j < M) table[i+1][j+1] += table[i][j]*(M-j);
        }
    }

    UnionFind uf(N);
    rep(i,N) {
        int p; cin >> p;
        p--;
        uf.merge(i,p);
    }
    vec<int> num;
    {
        set<int> dic;
        rep(i,N) {
            if (dic.count(uf[i])) continue;
            dic.emplace(uf[i]);
            num.push_back(uf.size(i));
        }
    }

    vvec<mint> dp(1,vec<mint>(2));
    dp[0][0] = 1;
    for (auto e : num) {
        vvec<mint> nex(SZ(dp)+e,vec<mint>(2));
        vec<tuple<mint, int, int>> seni;
        for (int i = 0; i <= e; i++) {
            seni.emplace_back(MC.C(e,i),max(1,e-i),i&1);
        }
        rep(i,SZ(dp)) {
            rep(k,2) {
                for (auto[val,cnt,odd] : seni) {
                    nex[i+cnt][k^odd] += val*dp[i][k];
                }
            }
        }
        swap(dp,nex);
    }

    mint ans = 0;
    rep(i,SZ(dp)) {
        ans += dp[i][0]*table[i][M];
        ans -= dp[i][1]*table[i][M];
    }
    ans *= MC.facinv(M);
    cout << ans << ln;
}
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