結果
| 問題 | No.1116 Cycles of Dense Graph |
| ユーザー |
 jell
|
| 提出日時 | 2020-07-18 22:38:14 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
CE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 18,153 bytes |
| コンパイル時間 | 2,840 ms |
| コンパイル使用メモリ | 221,272 KB |
| 最終ジャッジ日時 | 2024-05-08 08:17:40 |
| 合計ジャッジ時間 | 3,353 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
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ただし、clay言語の場合は開発者のデバッグのため、公開されます。
ただし、clay言語の場合は開発者のデバッグのため、公開されます。
コンパイルメッセージ
main.cpp:104:8: error: 'template<class T> struct read' redeclared as different kind of entity
104 | struct read
| ^~~~
In file included from /usr/include/x86_64-linux-gnu/bits/sigstksz.h:24,
from /usr/include/signal.h:328,
from /home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.3.0/include/c++/12/csignal:42,
from /home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.3.0/include/c++/12/x86_64-pc-linux-gnu/bits/stdc++.h:43,
from main.cpp:15:
/usr/include/unistd.h:371:16: note: previous declaration 'ssize_t read(int, void*, size_t)'
371 | extern ssize_t read (int __fd, void *__buf, size_t __nbytes) __wur
| ^~~~
main.cpp:112:8: error: 'read' is not a class template
112 | struct read<void>
| ^~~~
main.cpp:113:1: error: explicit specialization of non-template 'read'
113 | {
| ^
ソースコード
#pragma region preprocessor
#ifdef LOCAL
//*
#define _GLIBCXX_DEBUG // gcc
/*/
#define _LIBCPP_DEBUG 0 // clang
//*/
// #define __buffer_check__
#else
#pragma GCC optimize("Ofast")
// #define NDEBUG
#endif
#define __precision__ 15
#define __iostream_untie__ true
#include <bits/stdc++.h>
#include <ext/rope>
#ifdef LOCAL
#include "dump.hpp"
#define mesg(str) std::cerr << "[ " << __LINE__ << " : " << __FUNCTION__ << " ] " << str << "\n"
#else
#define dump(...) ((void)0)
#define mesg(str) ((void)0)
#endif
#pragma endregion
#pragma region std-overload
namespace std
{
// hash
template <class T> size_t hash_combine(size_t seed, T const &key) { return seed ^ (hash<T>()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2)); }
template <class T, class U> struct hash<pair<T, U>> { size_t operator()(pair<T, U> const &pr) const { return hash_combine(hash_combine(0, pr.first), pr.second); } };
template <class tuple_t, size_t index = tuple_size<tuple_t>::value - 1> struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(tuple_hash_calc<tuple_t, index - 1>::apply(seed, t), get<index>(t)); } };
template <class tuple_t> struct tuple_hash_calc<tuple_t, 0> { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(seed, get<0>(t)); } };
template <class... T> struct hash<tuple<T...>> { size_t operator()(tuple<T...> const &t) const { return tuple_hash_calc<tuple<T...>>::apply(0, t); } };
// iostream
template <class T, class U> istream &operator>>(istream &is, pair<T, U> &p) { return is >> p.first >> p.second; }
template <class T, class U> ostream &operator<<(ostream &os, const pair<T, U> &p) { return os << p.first << ' ' << p.second; }
template <class tuple_t, size_t index> struct tupleis { static istream &apply(istream &is, tuple_t &t) { tupleis<tuple_t, index - 1>::apply(is, t); return is >> get<index>(t); } };
template <class tuple_t> struct tupleis<tuple_t, SIZE_MAX> { static istream &apply(istream &is, tuple_t &t) { return is; } };
template <class... T> istream &operator>>(istream &is, tuple<T...> &t) { return tupleis<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(is, t); }
template <> istream &operator>>(istream &is, tuple<> &t) { return is; }
template <class tuple_t, size_t index> struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { tupleos<tuple_t, index - 1>::apply(os, t); return os << ' ' << get<index>(t); } };
template <class tuple_t> struct tupleos<tuple_t, 0> { static ostream &apply(ostream &os, const tuple_t &t) { return os << get<0>(t); } };
template <class... T> ostream &operator<<(ostream &os, const tuple<T...> &t) { return tupleos<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(os, t); }
template <> ostream &operator<<(ostream &os, const tuple<> &t) { return os; }
template <class Container, typename Value = typename Container::value_type, enable_if_t<!is_same<decay_t<Container>, string>::value, nullptr_t> = nullptr>
istream& operator>>(istream& is, Container &cont) { for(auto&& e : cont) is >> e; return is; }
template <class Container, typename Value = typename Container::value_type, enable_if_t<!is_same<decay_t<Container>, string>::value, nullptr_t> = nullptr>
ostream& operator<<(ostream& os, const Container &cont) { bool flag = 1; for(auto&& e : cont) flag ? flag = 0 : (os << ' ', 0), os << e; return os; }
} // namespace std
#pragma endregion
#pragma region config
namespace config
{
const auto start_time{std::chrono::system_clock::now()};
int64_t elapsed()
{
using namespace std::chrono;
const auto end_time{std::chrono::system_clock::now()};
return duration_cast<milliseconds>(end_time - start_time).count();
}
__attribute__((constructor)) void setup()
{
using namespace std;
if(__iostream_untie__) ios::sync_with_stdio(false), cin.tie(nullptr);
cout << fixed << setprecision(__precision__);
#ifdef DEBUG
freopen("debug.out","w",stdout);
freopen("debug.err","w",stderr);
if(!freopen("debug.in","r",stdin))
{
cerr << "error: \"./debug.in\" not found.\n";
exit(EXIT_FAILURE);
}
#endif
#ifdef stderr_path
freopen(stderr_path, "a", stderr);
#endif
#ifdef LOCAL
cerr << fixed << setprecision(__precision__) << boolalpha << "\n----- stderr at LOCAL -----\n\n";
atexit([]{ cerr << "\n----- Exec time : " << elapsed() << " ms -----\n\n"; });
#endif
#ifdef __buffer_check__
atexit([]{ ofstream cnsl("CON"); char bufc; if(cin >> bufc) cnsl << "\n\033[1;35mwarning\033[0m: buffer not empty.\n\n"; });
#endif
}
} // namespace config
#pragma endregion
#pragma region utility
// lambda wrapper for recursive method.
template <class lambda_type>
class fixed_point
{
lambda_type func;
public:
fixed_point(lambda_type &&f) : func(std::move(f)) {}
template <class... Args> auto operator()(Args &&... args) const { return func(*this, std::forward<Args>(args)...); }
};
// read with std::cin.
template <class T = void>
struct read
{
typename std::remove_const<T>::type value;
template <class... types>
read(types... args) : value(args...) { std::cin >> value; }
operator T() const { return value; }
};
template <>
struct read<void>
{
template <class T>
operator T() const { T value; std::cin >> value; return value; }
};
// substitute y for x if x > y.
template <class T> inline bool chmin(T &x, const T &y) { return x > y ? x = y, true : false; }
// substitute y for x if x < y.
template <class T> inline bool chmax(T &x, const T &y) { return x < y ? x = y, true : false; }
// binary search on discrete range.
template <class iter_type, class pred_type>
iter_type binary(iter_type __ok, iter_type __ng, pred_type pred)
{
assert(__ok != __ng);
std::ptrdiff_t dist(__ng - __ok);
while(std::abs(dist) > 1)
{
iter_type mid(__ok + dist / 2);
if(pred(mid)) __ok = mid, dist -= dist / 2;
else __ng = mid, dist /= 2;
}
return __ok;
}
// binary search on real numbers.
template <class pred_type>
long double binary(long double __ok, long double __ng, const long double eps, pred_type pred)
{
assert(__ok != __ng);
while(std::abs(__ok - __ng) > eps)
{
long double mid{(__ok + __ng) / 2};
(pred(mid) ? __ok : __ng) = mid;
}
return __ok;
}
// trinary search on discrete range.
template <class iter_type, class comp_type>
iter_type trinary(iter_type __first, iter_type __last, comp_type comp)
{
assert(__first < __last);
std::ptrdiff_t dist(__last - __first);
while(dist > 2)
{
iter_type __left(__first + dist / 3), __right(__first + dist * 2 / 3);
if(comp(__left, __right)) __last = __right, dist = dist * 2 / 3;
else __first = __left, dist -= dist / 3;
}
if(dist > 1 && comp(next(__first), __first)) ++__first;
return __first;
}
// trinary search on real numbers.
template <class comp_type>
long double trinary(long double __first, long double __last, const long double eps, comp_type comp)
{
assert(__first < __last);
while(__last - __first > eps)
{
long double __left{(__first * 2 + __last) / 3}, __right{(__first + __last * 2) / 3};
if(comp(__left, __right)) __last = __right;
else __first = __left;
}
return __first;
}
// size of array.
template <class A, size_t N> size_t size(A (&array)[N]) { return N; }
// be careful that val is type-sensitive.
template <class T, class A, size_t N> void init(A (&array)[N], const T &val) { std::fill((T*)array, (T*)(array + N), val); }
#pragma endregion
#pragma region alias
using namespace std;
using i32 = int_least32_t; using i64 = int_least64_t; using u32 = uint_least32_t; using u64 = uint_least64_t;
using p32 = pair<i32, i32>; using p64 = pair<i64, i64>;
template <class T, class Comp = less<T>> using heap = priority_queue<T, vector<T>, Comp>;
template <class T> using hashset = unordered_set<T>;
template <class Key, class Value> using hashmap = unordered_map<Key, Value>;
using namespace __gnu_cxx;
#pragma endregion
#pragma region library
// verified at https://judge.yosupo.jp/submission/3400
#ifndef union_find_hpp
#define union_find_hpp
#include <cassert>
#include <vector>
class union_find
{
std::vector<int> link;
public:
explicit union_find(const unsigned n = 0) : link(n, -1) {}
unsigned find(unsigned x)
{
assert(x < size());
return link[x] < 0 ? x : (link[x] = find(link[x]));
}
unsigned size() const { return link.size(); }
unsigned size(const unsigned x)
{
assert(x < size());
return -link[find(x)];
}
bool same(const unsigned x, const unsigned y)
{
assert(x < size() && y < size());
return find(x) == find(y);
}
bool unite(unsigned x, unsigned y)
{
assert(x < size() && y < size());
x = find(x), y = find(y);
if(x == y) return false;
if(link[x] > link[y]) std::swap(x, y);
link[x] += link[y];
link[y] = x;
return true;
}
}; // class union_find
#endif // union_find_hpp
#ifndef number_theoretic_transform_hpp
#define number_theoretic_transform_hpp
#include <algorithm>
#include <cassert>
#include <iostream>
#include <vector>
namespace number_theoretic_transform
{
constexpr int mod = 998244353;
constexpr int primitive = 3;
class modint
{
int val;
public:
constexpr modint() noexcept : val{0} {}
constexpr modint(long long x) noexcept : val((x %= mod) < 0 ? mod + x : x) {}
constexpr long long value() const noexcept { return val; }
constexpr modint operator++(int) noexcept { modint t = *this; return ++val, t; }
constexpr modint operator--(int) noexcept { modint t = *this; return --val, t; }
constexpr modint &operator++() noexcept { return ++val, *this; }
constexpr modint &operator--() noexcept { return --val, *this; }
constexpr modint operator-() const noexcept { return modint(-val); }
constexpr modint &operator+=(const modint &other) noexcept { return (val += other.val) < mod ? 0 : val -= mod, *this; }
constexpr modint &operator-=(const modint &other) noexcept { return (val += mod - other.val) < mod ? 0 : val -= mod, *this; }
constexpr modint &operator*=(const modint &other) noexcept { return val = (long long)val * other.val % mod, *this; }
constexpr modint &operator/=(const modint &other) noexcept { return *this *= inverse(other); }
constexpr modint operator+(const modint &other) const noexcept { return modint(*this) += other; }
constexpr modint operator-(const modint &other) const noexcept { return modint(*this) -= other; }
constexpr modint operator*(const modint &other) const noexcept { return modint(*this) *= other; }
constexpr modint operator/(const modint &other) const noexcept { return modint(*this) /= other; }
constexpr bool operator==(const modint &other) const noexcept { return val == other.val; }
constexpr bool operator!=(const modint &other) const noexcept { return val != other.val; }
constexpr bool operator!() const noexcept { return !val; }
friend constexpr modint operator+(long long x, modint y) noexcept { return modint(x) + y; }
friend constexpr modint operator-(long long x, modint y) noexcept { return modint(x) - y; }
friend constexpr modint operator*(long long x, modint y) noexcept { return modint(x) * y; }
friend constexpr modint operator/(long long x, modint y) noexcept { return modint(x) / y; }
static constexpr modint inverse(const modint &other) noexcept
{
assert(other != 0);
int a{mod}, b{other.val}, u{}, v{1}, t{};
while(b) t = a / b, a ^= b ^= (a -= t * b) ^= b, u ^= v ^= (u -= t * v) ^= v;
return {u};
}
static constexpr modint pow(modint other, long long e) noexcept
{
if(e < 0) e = e % (mod - 1) + mod - 1;
modint res{1};
while(e) { if(e & 1) res *= other; other *= other, e >>= 1; }
return res;
}
friend std::ostream &operator<<(std::ostream &os, const modint &other) noexcept { return os << other.val; }
friend std::istream &operator>>(std::istream &is, modint &other) noexcept { long long val; other = {(is >> val, val)}; return is; }
}; // class modint
class zeta_calc
{
static constexpr size_t n = __builtin_ctz(mod - 1);
modint _zeta[n + 1];
public:
constexpr zeta_calc() : _zeta{}
{
_zeta[n] = modint::pow(modint(primitive), (mod - 1) / (1 << n));
for(size_t i{n}; i; --i) _zeta[i - 1] = _zeta[i] * _zeta[i];
}
constexpr modint operator[](size_t k) const { return _zeta[k]; }
}; // class zeta_calc
constexpr zeta_calc zeta;
class inv_calc
{
static constexpr size_t n = __builtin_ctz(mod - 1);
modint _inv[n + 1];
public:
constexpr inv_calc() : _inv{1, (mod + 1) / 2} { for(size_t i{1}; i < n; ++i) _inv[i + 1] = _inv[i] * _inv[1]; }
constexpr modint operator[](size_t k) const { return _inv[k]; }
}; // class inv_calc
constexpr inv_calc inv;
using poly_t = std::vector<modint>;
void discrete_Fourier_transform(poly_t &f)
{
const size_t n{f.size()}, mask{n - 1};
assert(__builtin_popcount(n) == 1); // degree of f must be a power of two.
static poly_t g; g.resize(n);
for(size_t i{n >> 1}, ii{1}; i; i >>= 1, ++ii, swap(f, g))
{
modint powzeta{1};
for(size_t j{}; j < n; powzeta *= zeta[ii])
{
for(size_t k{}, x{mask & j << 1}, y{mask & (i + (j << 1))}; k < i; ++k, ++j, ++x, ++y)
{
g[j] = f[x] + powzeta * f[y];
}
}
}
}
void inverse_discrete_Fourier_transform(poly_t &f)
{
discrete_Fourier_transform(f), reverse(next(f.begin()), f.end());
const size_t k = __builtin_ctz(f.size()); for(modint &e : f) e *= inv[k];
}
poly_t convolute(poly_t f, poly_t g)
{
if(f.empty() || g.empty()) return poly_t();
const size_t deg_f{f.size() - 1}, deg_g{g.size() - 1}, deg_h{deg_f + deg_g}, n(1u << (32 - __builtin_clz(deg_h)));
static poly_t h;
f.resize(n, 0), g.resize(n, 0), h.resize(n);
discrete_Fourier_transform(f), discrete_Fourier_transform(g);
for(size_t i{}; i < n; ++i) h[i] = f[i] * g[i];
inverse_discrete_Fourier_transform(h); h.resize(deg_h + 1);
return h;
}
} // namespace Number_theoretic_transform
#endif // number_theoretic_transform_hpp
#pragma endregion
struct solver; template <class> void main_(); int main() { main_<solver>(); }
template <class solver> void main_()
{
unsigned t = 1;
#ifdef LOCAL
t = 1;
#endif
// t = -1; // infinite loop
// cin >> t; // case number given
while(t--) solver();
}
struct solver
{
solver()
{
using namespace number_theoretic_transform;
using mint=modint;
int n,m; cin>>n>>m;
vector<p32> ed(m); cin>>ed;
int spv=0;
{
vector<int> sv;
for(auto [a,b]: ed)
{
sv.emplace_back(a);
sv.emplace_back(b);
}
sort(begin(sv), end(sv));
sv.erase(unique(begin(sv), end(sv)), end(sv));
for(auto &[a,b]: ed)
{
a=lower_bound(begin(sv), end(sv), a)-begin(sv);
b=lower_bound(begin(sv), end(sv), b)-begin(sv);
}
spv=sv.size();
}
mint ans=0;
{
mint y=1;
for(int x=n,u=1; x>0; u++,x--)
{
y*=x;
if(u>=3) ans+=y/u;
}
}
ans/=2;
poly_t pex(n+1);
pex[0]=1;
for(int i=1; i<=n; i++)
{
pex[i]=pex[i-1]/i;
}
vector<poly_t> q(m+1);
for(int c=0; c<=m; c++)
{
q[c].resize(n+1);
q[c][0]=1;
for(int i=1; i<=c; i++) q[c][0]*=i;
for(int i=1; i<=n; i++)
{
q[c][i]=q[c][i-1]/i*(i+c);
}
q[c]=convolute(q[c],pex);
mint fa=1;
for(int i=1; i<=n; i++)
{
fa*=i;
q[c][i]*=fa;
}
}
for(int s=1; s<1<<m; s++)
{
union_find uf(spv);
vector<int> cnt(spv);
bool fail=0;
int con=0;
int sz=0;
bool cycl=false;
int cmp=spv;
for(int i=0; i<m; i++)
{
if(s>>i&1)
{
sz++;
auto [a,b]=ed[i];
if(!uf.unite(a,b)) cycl=1;
else cmp--;
if(cnt[a]>1 || cnt[b]>1) fail=1;
cnt[a]++;
cnt[b]++;
}
}
if(cycl)
{
int no=0;
for(int x: cnt) no+=x>0;
if(cmp>spv-no+1) fail=1;
}
if(fail) continue;
for(int x: cnt) if(x>1) con++;
if(sz>con)
{
mint tmp=q[sz-con-1][n-sz*2+con];
if(sz==1)
{
tmp-=1;
}
for(int x=1; x<sz-con; x++) tmp*=2;
if(sz&1) ans-=tmp;
else ans+=tmp;
}
else
{
if(sz&1) ans-=1;
else ans+=1;
}
}
cout << ans << "\n";
}
};