結果

問題 No.1760 Setwise Coprime
ユーザー satashun
提出日時 2021-11-20 14:23:37
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 46 ms / 2,000 ms
コード長 7,985 bytes
コンパイル時間 2,156 ms
コンパイル使用メモリ 201,028 KB
最終ジャッジ日時 2025-01-25 21:42:56
ジャッジサーバーID
（参考情報） 		judge2 / judge5
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ファイルパターン 結果
sample AC * 3
other AC * 36
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 # 

//#pragma GCC optimize("Ofast")
//#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using ull = unsigned long long;
using pii = pair<int, int>;
template <class T>
using V = vector<T>;
template <class T>
using VV = V<V<T>>;

template <class T>
V<T> make_vec(size_t a) {
    return V<T>(a);
}

template <class T, class... Ts>
auto make_vec(size_t a, Ts... ts) {
    return V<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...));
}

#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define rep(i, n) rep2(i, 0, n)
#define rep2(i, m, n) for (int i = m; i < (n); i++)
#define per(i, b) per2(i, 0, b)
#define per2(i, a, b) for (int i = int(b) - 1; i >= int(a); i--)
#define ALL(c) (c).begin(), (c).end()
#define SZ(x) ((int)(x).size())

constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }

template <class T, class U>
void chmin(T& t, const U& u) {
    if (t > u) t = u;
}
template <class T, class U>
void chmax(T& t, const U& u) {
    if (t < u) t = u;
}

template <class T>
void mkuni(vector<T>& v) {
    sort(ALL(v));
    v.erase(unique(ALL(v)), end(v));
}

template <class T>
vector<int> sort_by(const vector<T>& v) {
    vector<int> res(v.size());
    iota(res.begin(), res.end(), 0);
    sort(res.begin(), res.end(), [&](int i, int j) { return v[i] < v[j]; });
    return res;
}

template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << "(" << p.first << "," << p.second << ")";
    return os;
}

template <class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
    os << "{";
    rep(i, v.size()) {
        if (i) os << ",";
        os << v[i];
    }
    os << "}";
    return os;
}

#ifdef LOCAL
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << " " << H;
    debug_out(T...);
}
#define debug(...) \
    cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif

template <class T>
void scan(vector<T>& v, T offset = T(0)) {
    for (auto& x : v) {
        cin >> x;
        x += offset;
    }
}

template <class T>
void print(T x, int suc = 1) {
    cout << x;
    if (suc == 1)
        cout << "\n";
    else if (suc == 2)
        cout << " ";
}

template <class T>
void print(const vector<T>& v, int suc = 1) {
    for (int i = 0; i < v.size(); ++i)
        print(v[i], i == int(v.size()) - 1 ? suc : 2);
}

struct prepare_io {
    prepare_io() {
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(10);
    }
} prep_io;

template <unsigned int MOD>
struct ModInt {
    using uint = unsigned int;
    using ull = unsigned long long;
    using M = ModInt;

    uint v;

    ModInt(ll _v = 0) { set_norm(_v % MOD + MOD); }
    M& set_norm(uint _v) {  //[0, MOD * 2)->[0, MOD)
        v = (_v < MOD) ? _v : _v - MOD;
        return *this;
    }

    explicit operator bool() const { return v != 0; }
    explicit operator int() const { return v; }
    M operator+(const M& a) const { return M().set_norm(v + a.v); }
    M operator-(const M& a) const { return M().set_norm(v + MOD - a.v); }
    M operator*(const M& a) const { return M().set_norm(ull(v) * a.v % MOD); }
    M operator/(const M& a) const { return *this * a.inv(); }
    M& operator+=(const M& a) { return *this = *this + a; }
    M& operator-=(const M& a) { return *this = *this - a; }
    M& operator*=(const M& a) { return *this = *this * a; }
    M& operator/=(const M& a) { return *this = *this / a; }
    M operator-() const { return M() - *this; }
    M& operator++(int) { return *this = *this + 1; }
    M& operator--(int) { return *this = *this - 1; }

    M pow(ll n) const {
        if (n < 0) return inv().pow(-n);
        M x = *this, res = 1;
        while (n) {
            if (n & 1) res *= x;
            x *= x;
            n >>= 1;
        }
        return res;
    }

    M inv() const {
        ll a = v, b = MOD, p = 1, q = 0, t;
        while (b != 0) {
            t = a / b;
            swap(a -= t * b, b);
            swap(p -= t * q, q);
        }
        return M(p);
    }

    friend ostream& operator<<(ostream& os, const M& a) { return os << a.v; }
    friend istream& operator>>(istream& in, M& x) {
        ll v_;
        in >> v_;
        x = M(v_);
        return in;
    }

    bool operator<(const M& r) const { return v < r.v; }
    bool operator>(const M& r) const { return v < *this; }
    bool operator<=(const M& r) const { return !(r < *this); }
    bool operator>=(const M& r) const { return !(*this < r); }
    bool operator==(const M& a) const { return v == a.v; }
    bool operator!=(const M& a) const { return v != a.v; }

    static uint get_mod() { return MOD; }
};

// using Mint = ModInt<1000000007>;
using Mint = ModInt<998244353>;

const int X = 1e6;

bitset<X> is_prime;
vector<int> pr;

int mu[X];

void init() {
    is_prime.flip();
    is_prime[0] = is_prime[1] = false;
    mu[1] = 1;
    for (int i = 2; i < X; i++) {
        if (is_prime[i]) {
            pr.push_back(i);
            mu[i] = -1;
        }
        for (int p : pr) {
            if (ll(i) * p >= X) break;
            is_prime[i * p] = false;
            mu[i * p] = -mu[i];
            if (i % p == 0) {
                mu[i * p] = 0;
                break;
            }
        }
    }
}

int main() {
    init();

    int N;
    cin >> N;

    Mint mu_sum;
    for (int i = 1; i <= N; ++i) mu_sum += mu[i];
    Mint ans = mu_sum * mu_sum;

    for (int i = 1; i <= N; ++i) {
        Mint x = Mint(2).pow(N / i) * mu_sum * 2;
        ans -= x * mu[i];
    }

    V<Mint> sub(N + 1);
    Mint all_sum;

    for (int i = 1; i <= N; ++i) {
        Mint x = Mint(2).pow(N / i) * mu[i];
        all_sum += x;
        for (int j = i; j <= N; j += i) {
            sub[j] += x;
        }
    }

    V<Mint> dp(N + 1), way(N + 1);
    ans += all_sum * all_sum;

    for (int lc = 1; lc <= N; ++lc) {
        int c = N / lc;
        dp[lc] += sub[lc] * sub[lc];
        ans -= dp[lc];
        ans += dp[lc] / Mint(2).pow(c * 2) * Mint(3).pow(c);

        for (int j = lc * 2; j <= N; j += lc) {
            dp[j] -= dp[lc];
        }
    }
    /*
        for (int i = N; i >= 1; --i) {
            for (int j = N; j >= 1; --j) {
                if (lcm(i, j) > N) {
                    //  ans += Mint(2).pow(N / i) * Mint(2).pow(N / j) * mu[i] *
                    //  mu[j];
                }
            }
        }*/
    /*
        for (int i = N; i >= 1; --i) {
            for (int j = N; j >= 1; --j) {
                int c = N / lcm(i, j);
                ans += Mint(2).pow(N / i) * Mint(2).pow(N / j) * Mint(3).pow(c)
       / Mint(2).pow(c * 2) * mu[i] * mu[j];
            }
        }*/

    /*
      auto dp = make_vec<Mint>(N + 1, N + 1);

        for (int i = N; i >= 1; --i) {
            for (int j = N; j >= 1; --j) {
                int c = N / lcm(i, j);
                int a = N / i - c, b = N / j - c;
                ans += Mint(2).pow(a + b) * Mint(3).pow(c) * mu[i] * mu[j];

                // dp[i][j] = Mint(2).pow(a + b) * Mint(3).pow(c);
                // dp[i][j] -= Mint(2).pow(N / j);
                // dp[i][j] -= Mint(2).pow(N / i);
                // dp[i][j]++;
                // debug(i, j, dp[i][j]);
                // ans += dp[i][j] * mu[i] * mu[j];
                    for (int k = i; k <= N; k += i) {
                        for (int l = j; l <= N; l += j) {
                            if (k != i || l != j) {
                                dp[i][j] -= dp[k][l];
                            }
                        }
                    }
            }
        }

    // rep(i, N + 1) { debug(dp[i]); }
    // cout << dp[1][1] << endl;
    */
    // debug(dp);
    print(ans);

    return 0;
}
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