結果

問題 No.2522 Fall in love, Girls!
ユーザー dyktr_06dyktr_06
提出日時 2023-10-28 06:00:57
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 154 ms / 2,000 ms
コード長 12,497 bytes
コンパイル時間 5,573 ms
コンパイル使用メモリ 283,328 KB
実行使用メモリ 42,856 KB
最終ジャッジ日時 2024-09-25 16:05:50
合計ジャッジ時間 8,120 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge4
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 5 ms
11,704 KB
testcase_01 AC 5 ms
11,816 KB
testcase_02 AC 5 ms
11,728 KB
testcase_03 AC 100 ms
11,756 KB
testcase_04 AC 5 ms
11,708 KB
testcase_05 AC 5 ms
11,692 KB
testcase_06 AC 10 ms
14,536 KB
testcase_07 AC 18 ms
19,352 KB
testcase_08 AC 20 ms
20,152 KB
testcase_09 AC 58 ms
42,712 KB
testcase_10 AC 143 ms
42,748 KB
testcase_11 AC 5 ms
11,624 KB
testcase_12 AC 58 ms
42,648 KB
testcase_13 AC 150 ms
42,788 KB
testcase_14 AC 154 ms
42,804 KB
testcase_15 AC 152 ms
42,660 KB
testcase_16 AC 151 ms
42,856 KB
testcase_17 AC 56 ms
42,164 KB
testcase_18 AC 72 ms
42,496 KB
testcase_19 AC 70 ms
42,396 KB
testcase_20 AC 67 ms
41,344 KB
testcase_21 AC 64 ms
39,796 KB
testcase_22 AC 67 ms
40,888 KB
testcase_23 AC 73 ms
41,216 KB
testcase_24 AC 54 ms
34,304 KB
testcase_25 AC 6 ms
11,684 KB
testcase_26 AC 6 ms
11,648 KB
testcase_27 AC 28 ms
24,832 KB
testcase_28 AC 6 ms
11,644 KB
testcase_29 AC 43 ms
32,496 KB
testcase_30 AC 69 ms
40,960 KB
testcase_31 AC 49 ms
32,768 KB
testcase_32 AC 6 ms
11,732 KB
testcase_33 AC 60 ms
38,144 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>
#include <atcoder/all>

using namespace std;
using namespace atcoder;

#define overload4(_1, _2, _3, _4, name, ...) name
#define rep1(n) for(int i = 0; i < (int)(n); ++i)
#define rep2(i, n) for(int i = 0; i < (int)(n); ++i)
#define rep3(i, a, b) for(int i = (a); i < (int)(b); ++i)
#define rep4(i, a, b, c) for(int i = (a); i < (int)(b); i += (c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)

#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; --i)
#define ALL(a) (a).begin(), (a).end()
#define Sort(a) (sort((a).begin(), (a).end()))
#define RSort(a) (sort((a).rbegin(), (a).rend()))
#define UNIQUE(a) (a.erase(unique((a).begin(), (a).end()), (a).end()))

typedef long long int ll;
typedef unsigned long long ul;
typedef long double ld;
typedef vector<int> vi;
typedef vector<long long> vll;
typedef vector<char> vc;
typedef vector<string> vst;
typedef vector<double> vd;
typedef vector<long double> vld;
typedef pair<long long, long long> P;

template<class T> long long sum(const T& a){ return accumulate(a.begin(), a.end(), 0LL); }
template<class T> auto min(const T& a){ return *min_element(a.begin(), a.end()); }
template<class T> auto max(const T& a){ return *max_element(a.begin(), a.end()); }

const long long MINF = 0x7fffffffffff;
const long long INF = 0x1fffffffffffffff;
const long long MOD = 998244353;
const long double EPS = 1e-9;
const long double PI = acos(-1);
 
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; }

template<typename T1, typename T2> istream &operator>>(istream &is, pair<T1, T2> &p){ is >> p.first >> p.second; return is; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){ os << "(" << p.first << ", " << p.second << ")"; return os; }
template<typename T> istream &operator>>(istream &is, vector<T> &v){ for(T &in : v) is >> in; 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 S> ostream &operator<<(ostream &os, const map<T, S> &mp){ for(auto &[key, val] : mp){ os << key << ":" << val << " "; } return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int)st.size(); ++i){ os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int)st.size(); ++i){ os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, queue<T> q){ while(q.size()){ os << q.front() << " "; q.pop(); } return os; }
template <typename T> ostream &operator<<(ostream &os, deque<T> q){ while(q.size()){ os << q.front() << " "; q.pop_front(); } return os; }
template <typename T> ostream &operator<<(ostream &os, stack<T> st){ while(st.size()){ os << st.top() << " "; st.pop(); } return os; }
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq){ while(pq.size()){ os << pq.top() << " "; pq.pop(); } return os; }

template<class T, class U> inline T vin(T& vec, U n) { vec.resize(n); for(int i = 0; i < (int) n; ++i) cin >> vec[i]; return vec; }
template<class T> inline void vout(T vec, string s = "\n"){ for(auto x : vec) cout << x << s; }
template<class... T> void in(T&... a){ (cin >> ... >> a); }
void out(){ cout << '\n'; }
template<class T, class... Ts> void out(const T& a, const Ts&... b){ cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; }
template<class T, class U> void inGraph(vector<vector<T>>& G, U n, U m, bool directed = false){ G.resize(n); for(int i = 0; i < m; ++i){ int a, b; cin >> a >> b; a--, b--; G[a].push_back(b); if(!directed) G[b].push_back(a); } }

template <long long Modulus>
struct ModInt{
    long long val;
    constexpr ModInt(const long long &_val = 0) noexcept : val(_val) {
        normalize();
    }
    void normalize(){
        val = (val % Modulus + Modulus) % Modulus;
    }
    inline ModInt& operator+=(const ModInt& rhs) noexcept {
        if(val += rhs.val, val >= Modulus) val -= Modulus;
        return *this;
    }
    inline ModInt& operator-=(const ModInt& rhs) noexcept {
        if(val -= rhs.val, val < 0) val += Modulus;
        return *this;
    }
    inline ModInt& operator*=(const ModInt& rhs) noexcept {
        val = val * rhs.val % Modulus;
        return *this;
    }
    inline ModInt& operator/=(const ModInt& rhs) noexcept {
        val = val * inv(rhs.val).val % Modulus;
        return *this;
    }
    inline ModInt& operator++() noexcept {
        if(++val >= Modulus) val -= Modulus;
        return *this;
    }
    inline ModInt operator++(int) noexcept {
        ModInt t = val;
        if(++val >= Modulus) val -= Modulus;
        return t;
    }
    inline ModInt& operator--() noexcept {
        if(--val < 0) val += Modulus;
        return *this;
    }
    inline ModInt operator--(int) noexcept {
        ModInt t = val;
        if(--val < 0) val += Modulus;
        return t;
    }
    inline ModInt operator-() const noexcept { return (Modulus - val) % Modulus; }
    inline ModInt inv(void) const { return inv(val); }
    ModInt inv(const long long& n) const {
        long long a = n, b = Modulus, u = 1, v = 0;
        while(b){
            long long t = a / b;
            a -= t * b; swap(a, b);
            u -= t * v; swap(u, v);
        }
        u %= Modulus;
        if(u < 0) u += Modulus;
        return u;
    }
    friend inline ModInt operator+(const ModInt& lhs, const ModInt& rhs) noexcept { return ModInt(lhs) += rhs; }
    friend inline ModInt operator-(const ModInt& lhs, const ModInt& rhs) noexcept { return ModInt(lhs) -= rhs; }
    friend inline ModInt operator*(const ModInt& lhs, const ModInt& rhs) noexcept { return ModInt(lhs) *= rhs; }
    friend inline ModInt operator/(const ModInt& lhs, const ModInt& rhs) noexcept { return ModInt(lhs) /= rhs; }
    friend inline bool operator==(const ModInt& lhs, const ModInt& rhs) noexcept { return lhs.val == rhs.val; }
    friend inline bool operator!=(const ModInt& lhs, const ModInt& rhs) noexcept { return lhs.val != rhs.val; }
    friend inline istream& operator>>(istream& is, ModInt& x) noexcept {
        is >> x.val;
        x.normalize();
        return is;
    }
    friend inline ostream& operator<<(ostream& os, const ModInt& x) noexcept { return os << x.val; }
};

struct Combination{
    vector<long long> memo, memoinv, inv;
    const long long mod;
    Combination(const int &N, const long long &m) : memo(N + 1), memoinv(N + 1), inv(N + 1), mod(m){
        memo[0] = memo[1] = 1;
        memoinv[0] = memoinv[1] = 1;
        inv[1] = 1;
        for(int i = 2; i <= N; ++i){
            memo[i] = memo[i - 1] * i % mod;
            inv[i] = mod - inv[mod % i] * (m / i) % mod;
            memoinv[i] = memoinv[i - 1] * inv[i] % mod;
        }
    }
    inline long long fact(const long long &n) const {
        return memo[n];
    }
    inline long long factinv(const long long &n) const {
        return memoinv[n];
    }
    inline long long ncr(const long long &n, const long long &r) const {
        if(n < r || r < 0) return 0;
        return (memo[n] * memoinv[r] % mod) * memoinv[n - r] % mod;
    }
    inline long long npr(const long long &n, const long long &r) const {
        if(n < r || r < 0) return 0;
        return (memo[n] % mod) * memoinv[n - r] % mod;
    }
    inline long long nhr(const long long &n, const long long &r) const {
        if(n == 0 && r == 0) return 1;
        return ncr(n + r - 1, r);
    }
};

using mint = ModInt<998244353>;

template <typename T>
struct compress{
    vector<T> sorted, compressed;

    compress(const vector<T>& vec){
        int n = vec.size();
        compressed.resize(n);
        for(T x : vec){
            sorted.emplace_back(x);
        }
        sort(sorted.begin(), sorted.end());
        sorted.erase(unique(sorted.begin(), sorted.end()), sorted.end());
        for(int i = 0; i < n; ++i){
            compressed[i] = lower_bound(sorted.begin(), sorted.end(), vec[i]) - sorted.begin();
        }
    }

    int get(const T& x) const{
        return lower_bound(sorted.begin(), sorted.end(), x) - sorted.begin();
    }

    T inv(const T& x) const{
        return sorted[x];
    }

    size_t size() const{
        return sorted.size();
    }

    vector<T> getCompressed() const{
        return compressed;
    }
};

template <typename T>
struct SCC{
    int siz;
    vector<vector<T>> G_reverse;
    vector<bool> check;
    vector<int> memo;
    vector<T> s;
    vector<vector<T>> result;
 
    SCC(const vector<vector<T>> &G) : G_reverse((int) G.size()), check((int) G.size()){
        siz = (int) G.size();
        for(int i = 0; i < siz; ++i){
            for(const auto &x : G[i]){
                G_reverse[x].emplace_back(i);
            }
        }
 
        for(int i = 0; i < siz; ++i){
            if(!check[i]){
                dfs(G, i);
            }
        }
        reverse(memo.begin(), memo.end());
 
        for(int i = 0; i < siz; ++i) check[i] = false;
        for(const auto &x : memo){
            if(!check[x]){
                s = {};
                dfs2(G_reverse, x);
                result.emplace_back(s);
            }
        }
    }
 
    void dfs(const vector<vector<T>> &G, int curr){
        check[curr] = true;
        for(const auto &x : G[curr]){
            if(check[x]){
                continue;
            }
            dfs(G, x);
        }
        memo.emplace_back(curr);
    }
 
    void dfs2(const vector<vector<T>> &G, int curr){
        s.emplace_back(curr);
        check[curr] = true;
        for(const auto &x : G[curr]){
            if(check[x]){
                continue;
            }
            dfs2(G, x);
        }
    }
 
    vector<vector<T>> get() const {
        return result;
    }
};

template <typename T>
vector<T> topological_sort(const vector<vector<T>> &G){
    int siz = (int) G.size();
    vector<int> indegree(siz);
    for(int i = 0; i < siz; i++){
        for(auto x : G[i]){
            indegree[x]++;
        }
    }

    priority_queue<int, vector<int>, greater<int>> heap;
    for(int i = 0; i < siz; i++){
        if(indegree[i] == 0){
            heap.push(i);
        }
    }

    vector<T> res;
    while(!heap.empty()){
        int node = heap.top();
        heap.pop();
        res.push_back(node);
        for(auto x : G[node]){
            indegree[x]--;
            if(indegree[x] == 0){
                heap.push(x);
            }
        }
    }
    return res;
}

ll n, m, k;
vll x, y;

void input(){
    in(n, m, k);
    x.resize(k);
    y.resize(k);
    rep(i, k) in(x[i], y[i]);
}

mint dp[1 << 20];
vector<vll> G;

void solve(){
    vll a;
    rep(i, k){
        a.push_back(x[i]);
        a.push_back(y[i]);
    }

    compress<ll> comp(a);
    ll siz = comp.size();
    G.resize(siz);
    vll deg(siz);
    rep(i, k){
        G[comp.get(y[i])].push_back(comp.get(x[i]));
        deg[comp.get(y[i])]++;
    }
    SCC<ll> scc(G);
    for(auto s : scc.get()){
        if((int) s.size() >= 2){
            out(0);
            return;
        }
    }

    vll check(n);
    vll ts = topological_sort(G);
    rep(i, siz){
        for(auto x : G[ts[i]]){
            check[x] |= 1 << ts[i];
            check[x] |= check[ts[i]];
        }
    }

    dp[0] = 1;
    rep(bit, 1 << siz){
        rep(i, siz){
            if(bit & (1 << i)) continue;
            if((check[i] & bit) == check[i]){
                dp[bit | (1 << i)] += dp[bit];
            }
        }
    }

    mint d = n - m;

    mint ans = 0;
    Combination comb(n, MOD);
    rep(i, siz){
        if(comp.inv(i) > m) d--;
        if(deg[i] == 0 && comp.inv(i) > m){
            mint mul = dp[((1 << siz) - 1) ^ (1 << i)];
            mul *= comb.fact(n - 1);
            mul *= comb.factinv(siz - 1);
            ans += mul;
        }
    }

    mint mul = d * dp[(1 << siz) - 1];
    mul *= comb.fact(n - 1);
    mul *= comb.factinv(siz);
    ans += mul;
    out(ans);
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(20);
    
    input();
    solve();
}
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