結果

問題 No.1116 Cycles of Dense Graph
ユーザー hitonanode
提出日時 2020-07-17 22:15:14
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
TLE  
(最新)
AC  
(最初)
実行時間 -
コード長 10,855 bytes
コンパイル時間 14,758 ms
コンパイル使用メモリ 283,724 KB
最終ジャッジ日時 2025-01-11 22:49:45
ジャッジサーバーID
(参考情報)
judge1 / judge2
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 33 TLE * 5
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 #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }
template <typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args
    ...); }
template <typename V, typename T> void ndfill(V &x, const T &val) { x = val; }
template <typename V, typename T> void ndfill(vector<V> &vec, const T &val) { for (auto &v : vec) ndfill(v, val); }
template <typename T> bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template <typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l
    .second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l
    .second - r.second); }
template <typename T> vector<T> srtunq(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return
    vec; }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os;
    }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec) { os << "{"; for (auto v : vec) os << v << ","; os << "}"; return
    os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os;
    }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << "{"; for (auto v : vec) os << v << ","; os << "}";
    return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << "(" << pa.first << "," << pa.second << ")";
    return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << "{"; for (auto v : mp) os << v.first << "=>" << v
    .second << ","; os << "}"; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp) { os << "{"; for (auto v : mp) os << v.first <<
    "=>" << v.second << ","; os << "}"; return os; }
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;
template <int mod>
struct ModInt
{
using lint = long long;
static int get_mod() { return mod; }
static int get_primitive_root() {
static int primitive_root = 0;
if (!primitive_root) {
primitive_root = [&](){
std::set<int> fac;
int v = mod - 1;
for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i;
if (v > 1) fac.insert(v);
for (int g = 1; g < mod; g++) {
bool ok = true;
for (auto i : fac) if (ModInt(g).power((mod - 1) / i) == 1) { ok = false; break; }
if (ok) return g;
}
return -1;
}();
}
return primitive_root;
}
int val;
constexpr ModInt() : val(0) {}
constexpr ModInt &_setval(lint v) { val = (v >= mod ? v - mod : v); return *this; }
constexpr ModInt(lint v) { _setval(v % mod + mod); }
explicit operator bool() const { return val != 0; }
constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }
constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); }
constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); }
constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); }
constexpr ModInt operator-() const { return ModInt()._setval(mod - val); }
constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); }
friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); }
friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); }
friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); }
constexpr bool operator==(const ModInt &x) const { return val == x.val; }
constexpr bool operator!=(const ModInt &x) const { return val != x.val; }
bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map<ModInt, T>
friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; is >> t; x = ModInt(t); return is; }
friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val; return os; }
constexpr lint power(lint n) const {
lint ans = 1, tmp = this->val;
while (n) {
if (n & 1) ans = ans * tmp % mod;
tmp = tmp * tmp % mod;
n /= 2;
}
return ans;
}
constexpr lint inv() const { return this->power(mod - 2); }
constexpr ModInt operator^(lint n) const { return ModInt(this->power(n)); }
constexpr ModInt &operator^=(lint n) { return *this = *this ^ n; }
inline ModInt fac() const {
static std::vector<ModInt> facs;
int l0 = facs.size();
if (l0 > this->val) return facs[this->val];
facs.resize(this->val + 1);
for (int i = l0; i <= this->val; i++) facs[i] = (i == 0 ? ModInt(1) : facs[i - 1] * ModInt(i));
return facs[this->val];
}
ModInt doublefac() const {
lint k = (this->val + 1) / 2;
if (this->val & 1) return ModInt(k * 2).fac() / ModInt(2).power(k) / ModInt(k).fac();
else return ModInt(k).fac() * ModInt(2).power(k);
}
ModInt nCr(const ModInt &r) const {
if (this->val < r.val) return ModInt(0);
return this->fac() / ((*this - r).fac() * r.fac());
}
ModInt sqrt() const {
if (val == 0) return 0;
if (mod == 2) return val;
if (power((mod - 1) / 2) != 1) return 0;
ModInt b = 1;
while (b.power((mod - 1) / 2) == 1) b += 1;
int e = 0, m = mod - 1;
while (m % 2 == 0) m >>= 1, e++;
ModInt x = power((m - 1) / 2), y = (*this) * x * x;
x *= (*this);
ModInt z = b.power(m);
while (y != 1) {
int j = 0;
ModInt t = y;
while (t != 1) j++, t *= t;
z = z.power(1LL << (e - j - 1));
x *= z, z *= z, y *= z;
e = j;
}
return ModInt(std::min(x.val, mod - x.val));
}
};
constexpr lint MOD = 998244353;
using mint = ModInt<MOD>;
vector<vector<mint>> dp;
// UnionFind, able to rewind to the previous state by undo()
// Written for Educational Codeforces 62 F, although not verified yet.
struct UndoSizeAwareUnionFind
{
using pint = std::pair<int, int>;
std::vector<int> par, cou;
std::stack<std::pair<int, pint>> history;
UndoSizeAwareUnionFind(int N) : par(N), cou(N, 1) {
std::iota(par.begin(), par.end(), 0);
}
int find(int x) { return (par[x] == x) ? x :find(par[x]); }
void unite(int x, int y) {
x = find(x), y = find(y);
if (cou[x] < cou[y]) std::swap(x, y);
history.emplace(y, pint(par[y], cou[x]));
if (x != y) par[y] = x, cou[x] += cou[y];
}
void undo() {
cou[par[history.top().first]] = history.top().second.second;
par[history.top().first] = history.top().second.first;
history.pop();
}
void reset() {
while (!history.empty()) undo();
}
int count(int x) { return cou[find(x)]; }
bool same(int x, int y) { return find(x) == find(y); }
};
int main()
{
int N, M;
cin >> N >> M;
vector<pint> p(M);
REP(i, M)
{
cin >> p[i].first >> p[i].second;
}
mint ret = 0;
FOR(i, 3, N + 1)
{
ret += mint(N).fac() / mint(N - i).fac() / i;
}
dbg(ret);
ndarray(dp, M + 1, 2 * M + 1);
ndfill(dp, 2);
FOR(e, 1, M + 1) FOR(v, 1, M * 2 + 1) if (N - v >= 0)
{
mint tmp = 0;
REP(nins, N - v + 1)
{
if (v + nins < 3) continue;
tmp += mint(N - v).nCr(nins) * mint(nins).fac() * mint(nins + e - 1).nCr(e - 1);
}
dp[e][v] = tmp * mint(e - 1).fac() * mint(2).power(e);
}
UndoSizeAwareUnionFind uf(N + 1);
REP(S, 1 << M) if (S)
{
unordered_map<int, int> cnt;
uf.reset();
int pc = __builtin_popcount(S);
int r = -1;
REP(i, M) if ((S >> i) & 1)
{
cnt[p[i].first]++;
cnt[p[i].second]++;
r = p[i].first;
uf.unite(p[i].first, p[i].second);
}
bool ok = true;
int nb1 = 0;
set<int> vd1;
for (auto pa : cnt)
{
if (pa.second > 2) ok = false;
nb1 += (pa.second == 1);
if (pa.second == 1) vd1.insert(pa.first);
}
int nok = 0, nbad = 0;
for (auto pa : cnt)
{
int v = pa.first;
bool flg = false;
for (auto x : vd1) if (uf.same(v, x)) flg = true;
if (flg) nok++;
else nbad++;
}
if (nok and nbad) ok = false;
if (!nok and uf.count(r) != pc) ok = false;
if (!ok) continue;
int e = nb1 / 2;
int v = e + pc;
ret += dp.at(e).at(v) * (pc % 2 ? -1 : 1);
}
cout << ret / 2 << '\n';
}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0