結果

問題 No.2985 May Count Induced C4 Subgraphs
ユーザー hirayuu_yc
提出日時 2024-12-10 01:05:11
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
RE  
実行時間 -
コード長 18,459 bytes
コンパイル時間 4,239 ms
コンパイル使用メモリ 297,832 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-12-10 01:05:19
合計ジャッジ時間 7,152 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
other AC * 6 RE * 16
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ソースコード

diff #
プレゼンテーションモードにする

#line 2 "/root/AtCoder/Halc-Library/Template/Template.hpp"
#include <bits/stdc++.h>
using namespace std;
#line 8 "/root/AtCoder/Halc-Library/Template/InOut.hpp"
inline void scan() {}
inline void scan(int32_t &a) { std::cin >> a; }
inline void scan(uint32_t &a) { std::cin >> a; }
inline void scan(int64_t &a) { std::cin >> a; }
inline void scan(uint64_t &a) { std::cin >> a; }
inline void scan(char &a) { std::cin >> a; }
inline void scan(float &a) { std::cin >> a; }
inline void scan(double &a) { std::cin >> a; }
inline void scan(long double &a) { std::cin >> a; }
inline void scan(std::vector<bool> &vec) {
    for (int32_t i = 0; i < vec.size(); i++) {
        int a;
        scan(a);
        vec[i] = a;
    }
}
inline void scan(std::string &a) { std::cin >> a; }
template <class T>
inline void scan(std::vector<T> &vec);
template <class T, size_t size>
inline void scan(std::array<T, size> &vec);
template <class T, class L>
inline void scan(std::pair<T, L> &p);
template <class T, size_t size>
inline void scan(T (&vec)[size]);
template <class T>
inline void scan(std::vector<T> &vec) {
    for (auto &i : vec) scan(i);
}
template <class T>
inline void scan(std::deque<T> &vec) {
    for (auto &i : vec) scan(i);
}
template <class T, size_t size>
inline void scan(std::array<T, size> &vec) {
    for (auto &i : vec) scan(i);
}
template <class T, class L>
inline void scan(std::pair<T, L> &p) {
    scan(p.first);
    scan(p.second);
}
template <class T, size_t size>
inline void scan(T (&vec)[size]) {
    for (auto &i : vec) scan(i);
}
template <class T>
inline void scan(T &a) {
    std::cin >> a;
}
inline void in() {}
template <class Head, class... Tail>
inline void in(Head &head, Tail &...tail) {
    scan(head);
    in(tail...);
}
inline void print() { std::cout << ' '; }
inline void print(const bool &a) { std::cout << a; }
inline void print(const int32_t &a) { std::cout << a; }
inline void print(const uint32_t &a) { std::cout << a; }
inline void print(const int64_t &a) { std::cout << a; }
inline void print(const uint64_t &a) { std::cout << a; }
inline void print(const char &a) { std::cout << a; }
inline void print(const char a[]) { std::cout << a; }
inline void print(const float &a) { std::cout << a; }
inline void print(const double &a) { std::cout << a; }
inline void print(const long double &a) { std::cout << a; }
inline void print(const std::string &a) {
    for (auto &&i : a) print(i);
}
template <class T>
inline void print(const std::vector<T> &vec);
template <class T, size_t size>
inline void print(const std::array<T, size> &vec);
template <class T, class L>
inline void print(const std::pair<T, L> &p);
template <class T, size_t size>
inline void print(const T (&vec)[size]);
template <class T>
inline void print(const std::vector<T> &vec) {
    if (vec.empty()) return;
    print(vec[0]);
    for (auto i = vec.begin(); ++i != vec.end();) {
        std::cout << ' ';
        print(*i);
    }
}
template <class T>
inline void print(const std::deque<T> &vec) {
    if (vec.empty()) return;
    print(vec[0]);
    for (auto i = vec.begin(); ++i != vec.end();) {
        std::cout << ' ';
        print(*i);
    }
}
template <class T, size_t size>
inline void print(const std::array<T, size> &vec) {
    print(vec[0]);
    for (auto i = vec.begin(); ++i != vec.end();) {
        std::cout << ' ';
        print(*i);
    }
}
template <class T, class L>
inline void print(const std::pair<T, L> &p) {
    print(p.first);
    std::cout << ' ';
    print(p.second);
}
template <class T, size_t size>
inline void print(const T (&vec)[size]) {
    print(vec[0]);
    for (auto i = vec; ++i != end(vec);) {
        std::cout << ' ';
        print(*i);
    }
}
template <class T>
inline void print(const T &a) {
    std::cout << a;
}
inline void out() { std::cout << '\n'; }
template <class T>
inline void out(const T &t) {
    print(t);
    std::cout << '\n';
}
template <class Head, class... Tail>
inline void out(const Head &head, const Tail &...tail) {
    print(head);
    std::cout << ' ';
    out(tail...);
}
inline void Yes(bool i = true) { out(i ? "Yes" : "No"); }
inline void No(bool i = true) { out(i ? "No" : "Yes"); }
inline void Takahashi(bool i = true) { out(i ? "Takahashi" : "Aoki"); }
inline void Aoki(bool i = true) { out(i ? "Aoki" : "Takahashi"); }
inline void Alice(bool i = true) { out(i ? "Alice" : "Bob"); }
inline void Bob(bool i = true) { out(i ? "Bob" : "Alice"); }
inline void First(bool i = true) { out(i ? "First" : "Second"); }
inline void Second(bool i = true) { out(i ? "Second" : "First"); }
inline void Possible(bool i = true) { out(i ? "Possible" : "Impossible"); }
inline void Impossible(bool i = true) { out(i ? "Impossible" : "Possible"); }
inline void fls() { std::flush(std::cout); }
struct IOsetup {
    IOsetup() {
        std::ios::sync_with_stdio(false);
        std::cin.tie(nullptr);
        std::cout << std::fixed << std::setprecision(16);
    }
} iosetup;
#line 9 "/root/AtCoder/Halc-Library/Template/Util.hpp"
using ll = int64_t;
using ld = long double;
using ull = uint64_t;
using uint = uint32_t;
using pll = std::pair<ll, ll>;
using pii = std::pair<int32_t, int32_t>;
using vl = std::vector<ll>;
using vvl = std::vector<std::vector<ll>>;
using pdd = std::pair<ld, ld>;
using tuplis = std::array<ll, 3>;
template <class T>
using pq = std::priority_queue<T, std::vector<T>, std::greater<T>>;
constexpr ll LINF = (1LL << 62) - (1LL << 31);
constexpr int32_t INF = INT_MAX >> 1;
constexpr ll MINF = 1LL << 40;
constexpr ld DINF = std::numeric_limits<ld>::infinity();
constexpr int32_t MODD = 1000000007;
constexpr int32_t MOD = 998244353;
constexpr ld EPS = 1e-9;
constexpr ld PI = 3.1415926535897932;
const ll four[] = {0, 1, 0, -1, 0};
const ll eight[] = {0, 1, 1, 0, -1, -1, 1, -1, 0};
template <class T>
bool chmin(T &a, const T &b) {
    if (a > b) {
        a = b;
        return true;
    } else
        return false;
}
template <class T>
bool chmax(T &a, const T &b) {
    if (a < b) {
        a = b;
        return true;
    } else
        return false;
}
template <class T>
ll sum(const T &a) {
    return accumulate(std::begin(a), std::end(a), 0LL);
}
template <class T>
ld dsum(const T &a) {
    return accumulate(std::begin(a), std::end(a), 0.0L);
}
template <class T>
auto min(const T &a) {
    return *min_element(std::begin(a), std::end(a));
}
template <class T>
auto max(const T &a) {
    return *max_element(std::begin(a), std::end(a));
}
#line 1 "/root/AtCoder/Halc-Library/Template/Macro.hpp"
#define _overload3(_1, _2, _3, name, ...) name
#define _overload4(_1, _2, _3, _4, name, ...) name
#define _rep1(i, n) for (int64_t i = 0; i < (n); i++)
#define _rep2(i, a, b) for (int64_t i = (a); i < (b); i++)
#define _rep3(i, a, b, c) for (int64_t i = (a); i < (b); i += (c))
#define rep(...) _overload4(__VA_ARGS__, _rep3, _rep2, _rep1)(__VA_ARGS__)
#define _rrep1(i, n) for (int64_t i = (n) - 1; i >= 0; i--)
#define _rrep2(i, a, b) for (int64_t i = (b) - 1; i >= (a); i--)
#define rrep(...) _overload3(__VA_ARGS__, _rrep2, _rrep1)(__VA_ARGS__)
#define each(i, ...) for (auto&& i : __VA_ARGS__)
#define all(i) std::begin(i), std::end(i)
#define rall(i) std::rbegin(i), std::rend(i)
#define len(x) ((int64_t)(x).size())
#define fi first
#define se second
#define uniq(x) x.erase(unique(all(x)), std::end(x))
#define vec(type, name, ...) vector<type> name(__VA_ARGS__);
#define vv(type, name, h, ...) std::vector<std::vector<type>> name(h, std::vector<type>(__VA_ARGS__));
#define INT(...) int32_t __VA_ARGS__; in(__VA_ARGS__)
#define LL(...) int64_t __VA_ARGS__; in(__VA_ARGS__)
#define ULL(...) uint64_t __VA_ARGS__; in(__VA_ARGS__)
#define STR(...) std::string __VA_ARGS__; in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__; in(__VA_ARGS__)
#define LD(...) long double __VA_ARGS__; in(__VA_ARGS__)
#define VEC(type, name, size) std::vector<type> name(size); in(name)
#define VV(type, name, h, w) std::vector<std::vector<type>> name(h, std::vector<type>(w)); in(name)
#line 3 "/root/AtCoder/Halc-Library/Modint/Modint.hpp"
#line 6 "/root/AtCoder/Halc-Library/Modint/Modint.hpp"
template <uint64_t Mod>
struct Modint {
    uint64_t x;
    constexpr Modint() noexcept { x = 0; }
    constexpr Modint(int64_t val) noexcept {
        x = (val < 0 ? val % (int64_t)(Mod) + Mod : val % Mod);
    }
    inline uint64_t _get_mod(uint64_t val) noexcept {
        const static uint64_t m_inv = (-1ULL) / Mod + 1;
        uint64_t ret = ((unsigned __int128)(val)*m_inv) >> 64;
        uint64_t pro = ret * Mod;
        return (val - pro + (val < pro ? Mod : 0));
    }
    friend std::ostream &operator<<(std::ostream &os, Modint &b) noexcept {
        return os << b.x;
    }
    friend std::istream &operator>>(std::istream &is, Modint &b) noexcept {
        return is >> b.x;
    }
    constexpr uint64_t val() noexcept { return x; }
    constexpr Modint operator+() noexcept { return (*this); }
    constexpr Modint operator-() noexcept { return Modint() - (*this); }
    friend Modint operator+(const Modint lhs, const Modint rhs) noexcept {
        return Modint(lhs) += rhs;
    }
    friend Modint operator-(const Modint lhs, const Modint rhs) noexcept {
        return Modint(lhs) -= rhs;
    }
    friend Modint operator*(const Modint lhs, const Modint rhs) noexcept {
        return Modint(lhs) *= rhs;
    }
    friend Modint operator/(const Modint lhs, const Modint rhs) {
        return Modint(lhs) /= rhs;
    }
    constexpr Modint &operator+=(const Modint rhs) noexcept {
        x += rhs.x;
        if (x >= Mod) x -= Mod;
        return *this;
    }
    constexpr Modint &operator-=(const Modint rhs) noexcept {
        if (x < rhs.x) x += Mod;
        x -= rhs.x;
        return *this;
    }
    constexpr Modint &operator*=(const Modint rhs) noexcept {
        x = _get_mod(x * rhs.x);
        return *this;
    }
    friend bool operator==(const Modint lhs, const Modint rhs) noexcept {
        return lhs.x == rhs.x;
    }
    friend bool operator!=(const Modint lhs, const Modint rhs) noexcept {
        return rhs.x != rhs.x;
    }
    constexpr Modint &operator/=(Modint rhs) { return (*this) *= rhs.inv(); }
    constexpr Modint inv() {
        int64_t a = (*this).x, b = get_mod();
        assert(a != 0);
        int64_t s = b, t = a;
        int64_t m0 = 0, m1 = 1;
        while (t) {
            int64_t u = s / t;
            s -= t * u;
            m0 -= m1 * u;
            int64_t tmp = s;
            s = t;
            t = tmp;
            tmp = m0;
            m0 = m1;
            m1 = tmp;
        }
        assert(s == 1);
        if (m0 < 0) m0 += b;
        return Modint(m0);
    }
    constexpr Modint pow(uint64_t x) noexcept {
        Modint ret = 1;
        Modint bin = (*this);
        while (x) {
            if (x & 1) ret *= bin;
            bin *= bin;
            x >>= 1;
        }
        return ret;
    }
    static uint64_t get_mod() noexcept { return Mod; }
};
template <int64_t id>
struct ArbitraryModint {
    uint64_t x;
    static uint64_t &mod() noexcept {
        static uint64_t Mod = 0;
        return Mod;
    }
    constexpr ArbitraryModint() noexcept { x = 0; }
    constexpr ArbitraryModint(int64_t val) noexcept {
        x = (val < 0 ? val % (int64_t)(get_mod()) + get_mod()
                     : val % get_mod());
    }
    inline uint64_t _get_mod(uint64_t val) noexcept {
        const static uint64_t m_inv = (-1ULL) / get_mod() + 1;
        uint64_t ret = ((unsigned __int128)(val)*m_inv) >> 64;
        uint64_t pro = ret * get_mod();
        return (val - pro + (val < pro ? get_mod() : 0));
    }
    friend std::ostream &operator<<(std::ostream &os,
                                    ArbitraryModint &b) noexcept {
        return os << b.x;
    }
    friend std::istream &operator>>(std::istream &is,
                                    ArbitraryModint &b) noexcept {
        return is >> b.x;
    }
    constexpr uint64_t val() noexcept { return x; }
    constexpr ArbitraryModint operator+() noexcept { return (*this); }
    constexpr ArbitraryModint operator-() noexcept {
        return ArbitraryModint() - (*this);
    }
    friend ArbitraryModint operator+(const ArbitraryModint lhs,
                                     const ArbitraryModint rhs) noexcept {
        return ArbitraryModint(lhs) += rhs;
    }
    friend ArbitraryModint operator-(const ArbitraryModint lhs,
                                     const ArbitraryModint rhs) noexcept {
        return ArbitraryModint(lhs) -= rhs;
    }
    friend ArbitraryModint operator*(const ArbitraryModint lhs,
                                     const ArbitraryModint rhs) noexcept {
        return ArbitraryModint(lhs) *= rhs;
    }
    friend ArbitraryModint operator/(const ArbitraryModint lhs,
                                     const ArbitraryModint rhs) {
        return ArbitraryModint(lhs) /= rhs;
    }
    constexpr ArbitraryModint &operator+=(const ArbitraryModint rhs) noexcept {
        x += rhs.x;
        if (x >= mod()) x -= mod();
        return *this;
    }
    constexpr ArbitraryModint &operator-=(const ArbitraryModint rhs) noexcept {
        if (x < rhs.x) x += mod();
        x -= rhs.x;
        return *this;
    }
    constexpr ArbitraryModint &operator*=(const ArbitraryModint rhs) noexcept {
        x = _get_mod(x * rhs.x);
        return *this;
    }
    friend bool operator==(const ArbitraryModint lhs,
                           const ArbitraryModint rhs) noexcept {
        return lhs.x == rhs.x;
    }
    friend bool operator!=(const ArbitraryModint lhs,
                           const ArbitraryModint rhs) noexcept {
        return rhs.x != rhs.x;
    }
    constexpr ArbitraryModint &operator/=(ArbitraryModint rhs) {
        return (*this) *= rhs.inv();
    }
    constexpr ArbitraryModint inv() {
        int64_t a = (*this).x, b = get_mod();
        assert(a != 0);
        int64_t s = b, t = a;
        int64_t m0 = 0, m1 = 1;
        while (t) {
            int64_t u = s / t;
            s -= t * u;
            m0 -= m1 * u;
            int64_t tmp = s;
            s = t;
            t = tmp;
            tmp = m0;
            m0 = m1;
            m1 = tmp;
        }
        assert(s == 1);
        if (m0 < 0) m0 += b;
        return ArbitraryModint(m0);
    }
    constexpr ArbitraryModint pow(uint64_t x) noexcept {
        ArbitraryModint ret = 1;
        ArbitraryModint bin = (*this);
        while (x) {
            if (x & 1) ret *= bin;
            bin *= bin;
            x >>= 1;
        }
        return ret;
    }
    static void set_mod(const uint64_t x) noexcept { mod() = x; }
    static uint64_t get_mod() noexcept { return mod(); }
};
template <uint64_t N>
inline void scan(Modint<N> &a) {
    std::cin >> a.x;
}
template <int64_t id>
inline void scan(ArbitraryModint<id> &a) {
    std::cin >> a.x;
}
template <uint64_t N>
inline void print(Modint<N> a) {
    std::cout << a.x;
}
template <int64_t id>
inline void print(ArbitraryModint<id> a) {
    std::cout << a.x;
}
#line 3 "main.cpp"
using mint=Modint<MOD>;
class CountingC4 {
private:
    int V, threshold;
    vector<vector<int> > G;
    vector<vector<array<int, 2> > > memo;
    vector<int> flag1, flag2;
    void process_high_degree(long long& ans){
        for(int i = 0; i < V; ++i){
            if((int)G[i].size() <= threshold) continue;
            for(const int u : G[i]){
                if(u > i) flag1[u] = 1;
                flag2[u] = 1;
            }
            for(int j = 0; j < i; ++j){
                if((int)G[j].size() > threshold) continue;
                long long cnt1 = 0, cnt2 = 0;
                for(const int u : G[j]){
                    if(u < j || !flag2[u]) continue;
                    if((int)G[u].size() > threshold) ++cnt1;
                    else ++cnt2; 
                }
                ans += (cnt1 + cnt2) * (cnt1 + cnt2 - 1) / 2;
            }
            for(int j = i + 1; j < V; ++j){
                long long cnt = 0;
                for(const int u : G[j]){
                    if(flag1[u]) ++cnt;
                }
                ans += cnt * (cnt - 1) / 2;
            }
            for(const int u : G[i]) flag1[u] = flag2[u] = 0;
        }
    }
    void process_low_degree(long long& ans){
        for(int i = 0; i < V; ++i){
            if((int)G[i].size() > threshold) continue;
            for(const int u : G[i]){
                for(const int v : G[i]){
                    if(v > u) memo[u].push_back({i, v});
                }
            }
        }
        for(int i = 0; i < V; ++i){
            for(const auto& e : memo[i]){
                if(e[0] < i) ++flag1[e[1]];
                else ++flag2[e[1]];
            }
            for(const auto& e : memo[i]){
                ans += (long long)(flag1[e[1]] + 2 * flag2[e[1]] - 1) * flag1[e[1]] / 2;
                flag1[e[1]] = flag2[e[1]] = 0;
            }
        }
    }
public:
    CountingC4(const int node_size)
         : V(node_size), threshold(0), G(V), memo(V), flag1(V, 0), flag2(V, 0){}
    void add_edge(const int u, const int v){
        G[u].push_back(v), G[v].push_back(u);
        ++threshold;
    }
    long long solve(){
        threshold = floor(sqrt(2 * threshold)) / 2;
        long long ans = 0;
        process_high_degree(ans);
        process_low_degree(ans);
        return ans;
    }
};
void solve() {
    LL(N,M);
    if(N<=3){
        out(0,0);
        return;
    }
    vec(bitset<200000>,gr,N);
    CountingC4 gr2(N);
    vec(pll,edge,M);
    vec(ll,cnt,N,0);
    rep(i,M){
        LL(U,V);
        edge[i]={U-1,V-1};
        gr2.add_edge(U-1,V-1);
        cnt[U-1]++;cnt[V-1]++;
        gr[U-1][V-1]=1;
        gr[V-1][U-1]=1;
    }
    mint ans=0;
    ans=mint(N)*(N-1)*(N-2)*(N-3)/24;
    ans-=mint(M)*(N-2)*(N-3)/2;
    mint adj=0;
    rep(i,N){
        adj+=cnt[i]*(cnt[i]-1)/2;
    }
    ans+=adj*(N-3);
    ans+=(mint(M)*(M-1)/2-adj);
    vec(ll,common,M);
    rep(i,M){
        common[i]=(gr[edge[i].fi]&gr[edge[i].se]).count();
    }
    mint tri=0;
    mint nt=0;
    mint four=0;
    mint five=0;
    rep(i,M){
        tri+=common[i];
        nt+=(cnt[edge[i].fi]-1)*(cnt[edge[i].se]-1)-common[i];
        four+=common[i]*(cnt[edge[i].fi]+cnt[edge[i].se]-4);
        five+=common[i]*(common[i]-1)/2;
    }
    ans-=tri/3*(N-3);
    ans-=nt;
    rep(i,N){
        ans-=cnt[i]*(cnt[i]-1)*(cnt[i]-2)/6;
    }
    ans+=four/2;
    ans+=gr2.solve()*mint(2)/3;
    ans-=five*mint(2)/3;
    out(mint(-1)/3,ans);
}
int main() { solve(); }
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