結果
| 問題 |
No.2522 Fall in love, Girls!
|
| コンテスト | |
| ユーザー |
 dyktr_06
|
| 提出日時 | 2023-10-28 06:00:57 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 124 ms / 2,000 ms |
| コード長 | 12,497 bytes |
| コンパイル時間 | 4,375 ms |
| コンパイル使用メモリ | 270,856 KB |
| 最終ジャッジ日時 | 2025-02-17 16:34:52 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge4 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 30 |
ソースコード
#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();
}