#513173 (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	hitonanode
提出日時	2020-07-17 22:03:42
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	WA
実行時間	-
コード長	10,224 bytes
コンパイル時間	2,671 ms
コンパイル使用メモリ	220,584 KB
実行使用メモリ	6,948 KB
最終ジャッジ日時	2024-05-07 08:43:42
合計ジャッジ時間	14,092 ms
ジャッジサーバーID （参考情報）	judge3 / judge2

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	3 ms 6,816 KB
testcase_01	AC	46 ms 6,944 KB
testcase_02	AC	11 ms 6,940 KB
testcase_03	AC	6 ms 6,940 KB
testcase_04	AC	8 ms 6,944 KB
testcase_05	AC	70 ms 6,940 KB
testcase_06	AC	70 ms 6,940 KB
testcase_07	AC	24 ms 6,944 KB
testcase_08	AC	8 ms 6,940 KB
testcase_09	AC	21 ms 6,940 KB
testcase_10	AC	17 ms 6,944 KB
testcase_11	AC	84 ms 6,940 KB
testcase_12	AC	54 ms 6,940 KB
testcase_13	AC	4 ms 6,944 KB
testcase_14	AC	11 ms 6,944 KB
testcase_15	AC	17 ms 6,940 KB
testcase_16	AC	52 ms 6,944 KB
testcase_17	AC	7 ms 6,940 KB
testcase_18	AC	29 ms 6,944 KB
testcase_19	AC	26 ms 6,940 KB
testcase_20	AC	225 ms 6,940 KB
testcase_21	AC	96 ms 6,944 KB
testcase_22	AC	683 ms 6,940 KB
testcase_23	AC	4 ms 6,940 KB
testcase_24	AC	1,368 ms 6,940 KB
testcase_25	AC	2 ms 6,944 KB
testcase_26	AC	1,546 ms 6,940 KB
testcase_27	AC	8 ms 6,944 KB
testcase_28	AC	194 ms 6,940 KB
testcase_29	AC	4 ms 6,940 KB
testcase_30	AC	2 ms 6,940 KB
testcase_31	AC	2 ms 6,940 KB
testcase_32	AC	2 ms 6,940 KB
testcase_33	AC	1 ms 6,940 KB
testcase_34	AC	2 ms 6,944 KB
testcase_35	AC	2 ms 6,944 KB
testcase_36	AC	1,693 ms 6,940 KB
testcase_37	WA	-
testcase_38	WA	-
testcase_39	AC	204 ms 6,940 KB
testcase_40	AC	203 ms 6,940 KB

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ソースコード

raw source code

#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 Tree (0-indexed), based on size of each disjoint set
struct UnionFind
{
    std::vector<int> par, cou;
    UnionFind(int N = 0) : par(N), cou(N, 1) {
        iota(par.begin(), par.end(), 0);
    }
    int find(int x) { return (par[x] == x) ? x : (par[x] = find(par[x])); }
    bool unite(int x, int y) {
        x = find(x), y = find(y);
        if (x == y) return false;
        if (cou[x] < cou[y]) std::swap(x, y);
        par[y] = x, cou[x] += cou[y];
        return true;
    }
    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);
    }

    REP(S, 1 << M) if (S)
    {
        unordered_map<int, int> cnt;
        REP(i, M) if ((S >> i) & 1)
        {
            cnt[p[i].first]++;
            cnt[p[i].second]++;
        }

        bool ok = true;
        int nb1 = 0;
        for (auto pa : cnt)
        {
            if (pa.second > 2) ok = false;
            nb1 += (pa.second == 1);
        }
        if (!ok) continue;

        // if (nb1 == 0)
        // {
        //     UnionFind uf(N + 1);
        //     int r = 0, sz = 0;
        //     REP(i, M) if ((S >> i) & 1)
        //     {
        //         uf.unite(p[i].first, p[i].second);
        //         r = p[i].first;
        //         sz++;
        //     }
        //     if (uf.count(r) != sz) continue;
        // }

        int e = nb1 / 2;
        int pc = __builtin_popcount(S);
        int v = e + pc;
        ret += dp.at(e).at(v) * (pc % 2 ? -1 : 1);
    }
    cout << ret / 2 << '\n';
}

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結果

テストケース

ソースコード