#514259 (C++17) No.1116 Cycles of Dense Graph

提出ソース
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 13.2.0 + boost 1.83.0)
結果	AC
実行時間	94 ms / 2,000 ms
コード長	18,153 bytes
コンパイル時間	6,558 ms
コンパイル使用メモリ	244,212 KB
実行使用メモリ	5,052 KB
最終ジャッジ日時	2023-08-21 02:47:03
合計ジャッジ時間	6,376 ms
ジャッジサーバーID （参考情報）	judge14 / judge13
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	1 ms 4,384 KB
testcase_01	AC	8 ms 4,384 KB
testcase_02	AC	2 ms 4,380 KB
testcase_03	AC	2 ms 4,384 KB
testcase_04	AC	2 ms 4,380 KB
testcase_05	AC	5 ms 4,380 KB
testcase_06	AC	5 ms 4,380 KB
testcase_07	AC	3 ms 4,384 KB
testcase_08	AC	3 ms 4,384 KB
testcase_09	AC	4 ms 4,380 KB
testcase_10	AC	2 ms 4,384 KB
testcase_11	AC	6 ms 4,384 KB
testcase_12	AC	5 ms 4,380 KB
testcase_13	AC	2 ms 4,380 KB
testcase_14	AC	3 ms 4,384 KB
testcase_15	AC	3 ms 4,380 KB
testcase_16	AC	5 ms 4,380 KB
testcase_17	AC	3 ms 4,380 KB
testcase_18	AC	4 ms 4,384 KB
testcase_19	AC	4 ms 4,380 KB
testcase_20	AC	25 ms 4,380 KB
testcase_21	AC	17 ms 4,384 KB
testcase_22	AC	38 ms 4,380 KB
testcase_23	AC	4 ms 4,380 KB
testcase_24	AC	55 ms 4,580 KB
testcase_25	AC	2 ms 4,380 KB
testcase_26	AC	91 ms 5,052 KB
testcase_27	AC	3 ms 4,380 KB
testcase_28	AC	22 ms 4,380 KB
testcase_29	AC	2 ms 4,380 KB
testcase_30	AC	1 ms 4,504 KB
testcase_31	AC	1 ms 4,384 KB
testcase_32	AC	2 ms 4,384 KB
testcase_33	AC	2 ms 4,384 KB
testcase_34	AC	1 ms 4,384 KB
testcase_35	AC	1 ms 4,380 KB
testcase_36	AC	93 ms 5,044 KB
testcase_37	AC	93 ms 4,864 KB
testcase_38	AC	94 ms 4,852 KB
testcase_39	AC	13 ms 4,380 KB
testcase_40	AC	13 ms 4,384 KB
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ソースコード

raw source code
#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";
    }
};
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結果

テストケース

ソースコード
