結果
問題 | No.3106 Simple Math Problem 3 |
ユーザー |
👑 |
提出日時 | 2025-04-11 21:54:09 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 1,330 ms / 2,000 ms |
コード長 | 5,927 bytes |
コンパイル時間 | 1,146 ms |
コンパイル使用メモリ | 121,512 KB |
実行使用メモリ | 131,356 KB |
最終ジャッジ日時 | 2025-04-11 21:54:47 |
合計ジャッジ時間 | 34,455 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge4 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 42 |
ソースコード
#include <cassert> #include <cmath> #include <cstdint> #include <cstdio> #include <cstdlib> #include <cstring> #include <algorithm> #include <bitset> #include <chrono> #include <complex> #include <deque> #include <functional> #include <iostream> #include <limits> #include <map> #include <numeric> #include <queue> #include <random> #include <set> #include <sstream> #include <string> #include <unordered_map> #include <unordered_set> #include <utility> #include <vector> using namespace std; using Int = long long; template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; }; template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; } template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; } template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; } template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; } #define COLOR(s) ("\x1b[" s "m") //////////////////////////////////////////////////////////////////////////////// template <unsigned M_> struct ModInt { static constexpr unsigned M = M_; unsigned x; constexpr ModInt() : x(0U) {} constexpr ModInt(unsigned x_) : x(x_ % M) {} constexpr ModInt(unsigned long long x_) : x(x_ % M) {} constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {} constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {} ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; } ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; } ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; } ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); } ModInt pow(long long e) const { if (e < 0) return inv().pow(-e); ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b; } ModInt inv() const { unsigned a = M, b = x; int y = 0, z = 1; for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; } assert(a == 1U); return ModInt(y); } ModInt operator+() const { return *this; } ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; } ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); } ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); } ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); } ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); } template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); } template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); } template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); } template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); } explicit operator bool() const { return x; } bool operator==(const ModInt &a) const { return (x == a.x); } bool operator!=(const ModInt &a) const { return (x != a.x); } friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; } }; //////////////////////////////////////////////////////////////////////////////// constexpr unsigned MO = 998244353; using Mint = ModInt<MO>; constexpr int LIM = 1'000'010; Int N, sqrtN; int lpf[LIM]; int main() { for (; ~scanf("%lld", &N); ) { sqrtN = floor(sqrt((long double)N)); for (int p = 2; p <= sqrtN; ++p) lpf[p] = p; for (int p = 2; p <= sqrtN; ++p) if (lpf[p] == p) { for (int n = p; n <= sqrtN; n += p) chmin(lpf[n], p); } const Int off = N - sqrtN; vector<Int> sieve(sqrtN + 1); for (int i = 0; i <= sqrtN; ++i) sieve[i] = off + i; vector<vector<pair<Int, int>>> pess(sqrtN + 1); for (int p = 2; p <= sqrtN; ++p) if (lpf[p] == p) { for (Int n = max((off + p - 1) / p, 1LL) * p; n <= N; n += p) { const int i = n - off; int e = 0; do { ++e; sieve[i] /= p; } while (sieve[i] % p == 0); pess[i].emplace_back(p, e); } } for (int i = 0; i <= sqrtN; ++i) if (sieve[i] > 1) { pess[i].emplace_back(sieve[i], 1); } // if(N<=100)cerr<<off<<" "<<pess<<endl; Mint ans = 0; const Int lim = off - 1; if (lim >= 1) { // B > q >= r for (Int q = 1; q <= sqrtN; ++q) { const Int b = lim / q; ans += Mint(max(b - q, 0LL)) * (Mint(q) * Mint(q+1) / 2); } // r < B <= q for (Int b = 1; b <= sqrtN; ++b) { const Int q = lim / b; ans += Mint(max(q - b + 1, 0LL)) * (Mint(b-1) * Mint(b) / 2); } } cerr<<"lim = "<<lim<<": ans = "<<ans<<endl; for (int i = 0; i <= sqrtN; ++i) { vector<Int> ds{1}; for (const auto &pe : pess[i]) { const Int p = pe.first; const int e = pe.second; const int len = ds.size(); ds.resize(len * (e + 1)); for (int h = len; h < len * (e + 1); ++h) ds[h] = ds[h - len] * p; } const int len = ds.size(); __int128 sum = 0; for (int h = 0; h < len; ++h) { const Int b = ds[h]; const Int q = ds[len - 1 - h]; const Int r = min({b - 1, q, sqrtN - i}); // if(N<=100)cerr<<"b = "<<b<<", q = "<<q<<", r = "<<r<<endl; sum += r * (r + 1); } ans += (int)((sum / 2) % MO); } printf("%u\n", ans.x); } return 0; }