結果

問題 No.2066 Simple Math !
ユーザー drken1215
提出日時 2022-12-26 18:41:30
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 477 ms / 2,000 ms
コード長 2,778 bytes
コンパイル時間 2,100 ms
コンパイル使用メモリ 195,136 KB
最終ジャッジ日時 2025-02-09 21:03:22
ジャッジサーバーID
（参考情報） 		judge1 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 1
other AC * 31
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 #
プレゼンテーションモードにする

#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;
}
using pint = pair<int, int>;
using pll = pair<long long, long long>;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
#define REP(i, n) for (long long i = 0; i < (long long)(n); ++i)
#define REP2(i, a, b) for (long long i = a; i < (long long)(b); ++i)
#define COUT(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << endl
template<class T1, class T2> ostream& operator << (ostream &s, pair<T1,T2> P)
{ return s << '<' << P.first << ", " << P.second << '>'; }
template<class T> ostream& operator << (ostream &s, vector<T> P)
{ for (int i = 0; i < P.size(); ++i) { if (i > 0) { s << " "; } s << P[i]; } return s; }
template<class T> ostream& operator << (ostream &s, deque<T> P)
{ for (int i = 0; i < P.size(); ++i) { if (i > 0) { s << " "; } s << P[i]; } return s; }
template<class T> ostream& operator << (ostream &s, vector<vector<T> > P)
{ for (int i = 0; i < P.size(); ++i) { s << endl << P[i]; } return s << endl; }
template<class T> ostream& operator << (ostream &s, set<T> P)
{ for(auto it : P) { s << "<" << it << "> "; } return s; }
template<class T1, class T2> ostream& operator << (ostream &s, map<T1,T2> P)
{ for(auto it : P) { s << "<" << it.first << "->" << it.second << "> "; } return s; }
// 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;
}
int main() {
    /*
    COUT(calc_num(3, 4, 3));
    COUT(calc_num(3, 4, 4));
    COUT(calc_num(3, 4, 5));
    */
    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;
    }
}
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