結果
問題 | No.1760 Setwise Coprime |
ユーザー |
|
提出日時 | 2021-10-13 22:29:18 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 31 ms / 2,000 ms |
コード長 | 7,095 bytes |
コンパイル時間 | 2,553 ms |
コンパイル使用メモリ | 202,456 KB |
最終ジャッジ日時 | 2025-01-25 00:21:45 |
ジャッジサーバーID (参考情報) |
judge2 / judge4 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 36 |
ソースコード
#include <bits/stdc++.h> using namespace std; #define rep(i, n) for (int i = 0; i < n; i++) #define rep2(i, x, n) for (int i = x; i <= n; i++) #define rep3(i, x, n) for (int i = x; i >= n; i--) #define each(e, v) for (auto &e : v) #define pb push_back #define eb emplace_back #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define sz(x) (int)x.size() using ll = long long; using pii = pair<int, int>; using pil = pair<int, ll>; using pli = pair<ll, int>; using pll = pair<ll, ll>; template <typename T> bool chmax(T &x, const T &y) { return (x < y) ? (x = y, true) : false; } template <typename T> bool chmin(T &x, const T &y) { return (x > y) ? (x = y, true) : false; } template <typename T> int flg(T x, int i) { return (x >> i) & 1; } template <typename T> void print(const vector<T> &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' '); } template <typename T> void printn(const vector<T> &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << '\n'; } template <typename T> int lb(const vector<T> &v, T x) { return lower_bound(begin(v), end(v), x) - begin(v); } template <typename T> int ub(const vector<T> &v, T x) { return upper_bound(begin(v), end(v), x) - begin(v); } template <typename T> void rearrange(vector<T> &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); } template <typename T> vector<int> id_sort(const vector<T> &v, bool greater = false) { int n = v.size(); vector<int> ret(n); iota(begin(ret), end(ret), 0); sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; }); return ret; } struct io_setup { io_setup() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout << fixed << setprecision(15); } } io_setup; const int inf = (1 << 30) - 1; const ll INF = (1LL << 60) - 1; // const int MOD = 1000000007; const int MOD = 998244353; template <int mod> struct Mod_Int { int x; Mod_Int() : x(0) {} Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} static int get_mod() { return mod; } Mod_Int &operator+=(const Mod_Int &p) { if ((x += p.x) >= mod) x -= mod; return *this; } Mod_Int &operator-=(const Mod_Int &p) { if ((x += mod - p.x) >= mod) x -= mod; return *this; } Mod_Int &operator*=(const Mod_Int &p) { x = (int)(1LL * x * p.x % mod); return *this; } Mod_Int &operator/=(const Mod_Int &p) { *this *= p.inverse(); return *this; } Mod_Int &operator++() { return *this += Mod_Int(1); } Mod_Int operator++(int) { Mod_Int tmp = *this; ++*this; return tmp; } Mod_Int &operator--() { return *this -= Mod_Int(1); } Mod_Int operator--(int) { Mod_Int tmp = *this; --*this; return tmp; } Mod_Int operator-() const { return Mod_Int(-x); } Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; } Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; } Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; } Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; } bool operator==(const Mod_Int &p) const { return x == p.x; } bool operator!=(const Mod_Int &p) const { return x != p.x; } Mod_Int inverse() const { assert(*this != Mod_Int(0)); return pow(mod - 2); } Mod_Int pow(long long k) const { Mod_Int now = *this, ret = 1; for (; k > 0; k >>= 1, now *= now) { if (k & 1) ret *= now; } return ret; } friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; } friend istream &operator>>(istream &is, Mod_Int &p) { long long a; is >> a; p = Mod_Int<mod>(a); return is; } }; using mint = Mod_Int<MOD>; template <typename T> void divisors_zeta_transform(vector<T> &a, bool upper) { int n = a.size(); vector<bool> is_prime(n, true); if (!upper) { for (int i = 1; i < n; i++) a[0] += a[i]; } for (int i = 2; i < n; i++) { if (!is_prime[i]) continue; if (upper) { for (int j = (n - 1) / i; j > 0; j--) { is_prime[j * i] = false; a[j] += a[j * i]; } } else { for (int j = 1; j * i < n; j++) { is_prime[j * i] = false; a[j * i] += a[j]; } } } if (upper) { for (int i = 1; i < n; i++) a[i] += a[0]; } } template <typename T> void divisors_mobius_transform(vector<T> &a, bool upper) { int n = a.size(); vector<bool> is_prime(n, true); if (upper) { for (int i = 1; i < n; i++) a[i] -= a[0]; } for (int i = 2; i < n; i++) { if (!is_prime[i]) continue; if (upper) { for (int j = 1; j * i < n; j++) { is_prime[j * i] = false; a[j] -= a[j * i]; } } else { for (int j = (n - 1) / i; j > 0; j--) { is_prime[j * i] = false; a[j * i] -= a[j]; } } } if (!upper) { for (int i = 1; i < n; i++) a[0] -= a[i]; } } template <typename T> vector<T> gcd_convolve(vector<T> a, vector<T> b) { int n = a.size(); assert((int)b.size() == n); divisors_zeta_transform(a, true), divisors_zeta_transform(b, true); for (int i = 0; i < n; i++) a[i] *= b[i]; divisors_mobius_transform(a, true); return a; } template <typename T> vector<T> lcm_convolve(vector<T> a, vector<T> b) { // lcm(i, j) >= n の場合はa[i]*b[j]はc[0]に足される int n = a.size(); assert((int)b.size() == n); divisors_zeta_transform(a, false), divisors_zeta_transform(b, false); for (int i = 0; i < n; i++) a[i] *= b[i]; divisors_mobius_transform(a, false); return a; } int main() { int N; cin >> N; vector<mint> p2(2 * N + 1, 1), ip2(2 * N + 1, 1), p3(2 * N + 1, 1); mint tw = mint(2).inverse(); rep(i, 2 * N) { p2[i + 1] = p2[i] * 2; ip2[i + 1] = ip2[i] * tw; p3[i + 1] = p3[i] * 3; } vector<mint> c(N + 1, 0); c[1] = 1; divisors_mobius_transform(c, false); // print(c); vector<mint> f(N + 1, 0); mint ans = 0; /* rep2(i, 1, N) { rep2(j, 1, N) { int k = lcm(i, j); mint x = c[i] * c[j]; mint tmp = p3[N / k] * p2[N / i + N / j - 2 * (N / k)]; tmp -= p2[N / i] + p2[N / j] - 1; ans += tmp * x; } } cout << ans << '\n'; */ rep2(i, 1, N) { f[i] += c[i] * p2[N / i]; ans -= -c[0] * c[i] * (p2[N / i] - 1) * 2; } ans -= c[0] * c[0]; f = lcm_convolve(f, f); ans += f[0]; rep2(i, 1, N) ans += f[i] * ip2[2 * (N / i)] * p3[N / i]; cout << ans << '\n'; }