結果
問題 | No.1760 Setwise Coprime |
ユーザー |
![]() |
提出日時 | 2021-11-20 14:23:37 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 40 ms / 2,000 ms |
コード長 | 7,985 bytes |
コンパイル時間 | 2,147 ms |
コンパイル使用メモリ | 208,420 KB |
実行使用メモリ | 10,016 KB |
最終ジャッジ日時 | 2024-06-11 15:26:21 |
合計ジャッジ時間 | 3,722 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge5 |
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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 | 12 ms
7,732 KB |
testcase_01 | AC | 12 ms
7,712 KB |
testcase_02 | AC | 13 ms
7,708 KB |
testcase_03 | AC | 13 ms
7,760 KB |
testcase_04 | AC | 12 ms
7,708 KB |
testcase_05 | AC | 12 ms
7,752 KB |
testcase_06 | AC | 12 ms
7,804 KB |
testcase_07 | AC | 13 ms
7,808 KB |
testcase_08 | AC | 13 ms
7,708 KB |
testcase_09 | AC | 13 ms
7,784 KB |
testcase_10 | AC | 13 ms
7,772 KB |
testcase_11 | AC | 12 ms
7,796 KB |
testcase_12 | AC | 13 ms
7,724 KB |
testcase_13 | AC | 12 ms
7,592 KB |
testcase_14 | AC | 13 ms
7,820 KB |
testcase_15 | AC | 13 ms
7,680 KB |
testcase_16 | AC | 13 ms
7,936 KB |
testcase_17 | AC | 12 ms
7,836 KB |
testcase_18 | AC | 13 ms
7,808 KB |
testcase_19 | AC | 13 ms
7,756 KB |
testcase_20 | AC | 12 ms
7,756 KB |
testcase_21 | AC | 32 ms
9,500 KB |
testcase_22 | AC | 30 ms
9,372 KB |
testcase_23 | AC | 36 ms
9,624 KB |
testcase_24 | AC | 23 ms
8,476 KB |
testcase_25 | AC | 34 ms
9,500 KB |
testcase_26 | AC | 28 ms
8,988 KB |
testcase_27 | AC | 19 ms
8,216 KB |
testcase_28 | AC | 16 ms
7,836 KB |
testcase_29 | AC | 38 ms
9,756 KB |
testcase_30 | AC | 37 ms
9,760 KB |
testcase_31 | AC | 21 ms
8,344 KB |
testcase_32 | AC | 35 ms
9,628 KB |
testcase_33 | AC | 27 ms
8,984 KB |
testcase_34 | AC | 37 ms
9,880 KB |
testcase_35 | AC | 33 ms
9,372 KB |
testcase_36 | AC | 40 ms
10,008 KB |
testcase_37 | AC | 39 ms
10,016 KB |
testcase_38 | AC | 40 ms
9,884 KB |
ソースコード
//#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; }