結果
問題 | No.2066 Simple Math ! |
ユーザー | drken1215 |
提出日時 | 2022-12-26 18:47:36 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
WA
|
実行時間 | - |
コード長 | 5,314 bytes |
コンパイル時間 | 2,216 ms |
コンパイル使用メモリ | 211,084 KB |
実行使用メモリ | 6,824 KB |
最終ジャッジ日時 | 2024-11-21 04:34:38 |
合計ジャッジ時間 | 4,254 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge2 |
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テストケース
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testcase_00 | WA | - |
testcase_01 | WA | - |
testcase_02 | WA | - |
testcase_03 | WA | - |
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testcase_18 | WA | - |
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testcase_27 | WA | - |
testcase_28 | WA | - |
testcase_29 | WA | - |
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testcase_31 | WA | - |
ソースコード
// // floor sum // // verified // AtCoder ABC 283 Ex - Popcount Sum // https://atcoder.jp/contests/abc283/tasks/abc283_h // // OUPC 2020 I - Cafe au lait // https://onlinejudge.u-aizu.ac.jp/beta/room.html#OUPC2020/problems/I // // yukicoder 2066 No.2066 Simple Math ! // https://yukicoder.me/problems/no/2066 // #include <bits/stdc++.h> using namespace std; // sum_{i=0}^{n-1} floor((a * i + b) / m) // O(log(n + m + a + b)) // __int128 can be used for T template<class T> T floor_sum(T n, T a, T b, T m) { if (n == 0) return 0; T res = 0; if (a >= m) { res += n * (n - 1) * (a / m) / 2; a %= m; } if (b >= m) { res += n * (b / m); b %= m; } if (a == 0) return res; T ymax = (a * n + b) / m, xmax = ymax * m - b; if (ymax == 0) return res; res += (n - (xmax + a - 1) / a) * ymax; res += floor_sum(ymax, m, (a - xmax % a) % a, a); return res; } // #lp under (and on) the segment (x1, y1)-(x2, y2) // not including y = 0, x = x2 template<class T> T num_lattice_points(T x1, T y1, T x2, T y2) { T dx = x2 - x1; return floor_sum(dx, y2 - y1, dx * y1, dx); } ///////////////////////////////////////// // Solvers ///////////////////////////////////////// // calc #n that can be expressed n = Px + Qy (P, Q is coprime) // 0 <= n <= M long long calc_num(__int128 P, __int128 Q, __int128 M) { __int128 mp = M / P; __int128 N = min(mp + 1, Q); __int128 a = P, b = M + Q - a * (N - 1); return floor_sum(N, a, b, Q) - 1; } void solveYukicoder2066() { int CASE; cin >> CASE; while (CASE--) { long long P, Q, K; cin >> P >> Q >> K; long long G = gcd(P, Q); P /= G, Q /= G; long long low = -1, high = 1LL<<50; while (high - low > 1) { long long M = (low + high) / 2; if (calc_num(P, Q, M) >= K) high = M; else low = M; } cout << high * G << endl; } } // modint template<int MOD> struct Fp { long long val; constexpr Fp(long long v = 0) noexcept : val(v % MOD) { if (val < 0) val += MOD; } constexpr int getmod() const { return MOD; } constexpr Fp operator - () const noexcept { return val ? MOD - val : 0; } constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; } constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; } constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; } constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; } constexpr Fp& operator += (const Fp& r) noexcept { val += r.val; if (val >= MOD) val -= MOD; return *this; } constexpr Fp& operator -= (const Fp& r) noexcept { val -= r.val; if (val < 0) val += MOD; return *this; } constexpr Fp& operator *= (const Fp& r) noexcept { val = val * r.val % MOD; return *this; } constexpr Fp& operator /= (const Fp& r) noexcept { long long a = r.val, b = MOD, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b, swap(a, b); u -= t * v, swap(u, v); } val = val * u % MOD; if (val < 0) val += MOD; return *this; } constexpr bool operator == (const Fp& r) const noexcept { return this->val == r.val; } constexpr bool operator != (const Fp& r) const noexcept { return this->val != r.val; } friend constexpr istream& operator >> (istream& is, Fp<MOD>& x) noexcept { is >> x.val; x.val %= MOD; if (x.val < 0) x.val += MOD; return is; } friend constexpr ostream& operator << (ostream& os, const Fp<MOD>& x) noexcept { return os << x.val; } friend constexpr Fp<MOD> modpow(const Fp<MOD>& r, long long n) noexcept { if (n == 0) return 1; if (n < 0) return modpow(modinv(r), -n); auto t = modpow(r, n / 2); t = t * t; if (n & 1) t = t * r; return t; } friend constexpr Fp<MOD> modinv(const Fp<MOD>& r) noexcept { long long a = r.val, b = MOD, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b, swap(a, b); u -= t * v, swap(u, v); } return Fp<MOD>(u); } }; const int MOD = 1000000007; using mint = Fp<MOD>; long long GCD(long long x, long long y) { return y ? GCD(y, x % y) : x; } int main() { int N; cin >> N; vector<long long> X(N), Y(N); for (int i = 0; i < N; ++i) cin >> X[i] >> Y[i]; vector<int> ids(N); iota(ids.begin(), ids.end(), 0); sort(ids.begin(), ids.end(), [&](int i, int j) { return Y[i]*X[j] < Y[j]*X[i]; }); mint res = 0; long long sy = 0; for (auto i : ids) { res -= mint(X[i]) * mint(sy); res -= num_lattice_points(0LL, 0LL, X[i], Y[i]); res += GCD(X[i], Y[i]); sy += Y[i]; } reverse(ids.begin(), ids.end()); sy = 0; for (auto i : ids) { res += mint(X[i]) * mint(sy); res += num_lattice_points(0LL, 0LL, X[i], Y[i]); sy += Y[i]; } cout << res << endl; } /* int main() { solveYukicoder2066(); } */