結果

問題 No.2066 Simple Math !
ユーザー QCFiumQCFium
提出日時 2022-09-02 22:12:32
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 155 ms / 2,000 ms
コード長 2,559 bytes
コンパイル時間 1,494 ms
コンパイル使用メモリ 168,388 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-11-16 03:51:47
合計ジャッジ時間 5,995 ms
ジャッジサーバーID
(参考情報)
judge5 / judge2
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>
int ri() {
int n;
scanf("%d", &n);
return n;
}
// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
unsigned long long m,
unsigned long long a,
unsigned long long b) {
unsigned long long ans = 0;
while (true) {
if (a >= m) {
ans += n * (n - 1) / 2 * (a / m);
a %= m;
}
if (b >= m) {
ans += n * (b / m);
b %= m;
}
unsigned long long y_max = a * n + b;
if (y_max < m) break;
// y_max < m * (n + 1)
// floor(y_max / m) <= n
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
long long floor_sum(long long n, long long m, long long a, long long b) {
assert(0 <= n && n < (1LL << 32));
assert(1 <= m && m < (1LL << 32));
unsigned long long ans = 0;
if (a < 0) {
unsigned long long a2 = safe_mod(a, m);
ans -= 1ULL * n * (n - 1) / 2 * ((a2 - a) / m);
a = a2;
}
if (b < 0) {
unsigned long long b2 = safe_mod(b, m);
ans -= 1ULL * n * ((b2 - b) / m);
b = b2;
}
return ans + floor_sum_unsigned(n, m, a, b);
}
int gcd(int a, int b) {
while (a && b) {
if (a > b) a %= b;
else b %= a;
}
return a + b;
}
int64_t solve(int p, int q, int k) {
int g = gcd(p, q);
p /= g;
q /= g;
int64_t lcm = (int64_t) p * q;
int64_t lcm_cnt = floor_sum(p, p, q, p + q - 1);
// std::cerr << lcm_cnt << std::endl;
if (k <= lcm_cnt) {
int64_t l = -1;
int64_t r = lcm;
while (r - l > 1) {
int64_t m = l + ((r - l) >> 1);
uint64_t t0 = m / p;
uint64_t t1 = m / q;
if (t0 * t1 / t0 != t1 || t0 * t1 >= 1000000000000) {
r = m;
continue;
}
int64_t s = m / p;
int64_t cur = floor_sum(s + 1, q, p, m - s * p) + s;
// std::cerr << m << " " << cur << std::endl;
if (cur < k) l = m;
else r = m;
}
return r * g;
} else {
k -= lcm_cnt;
return (lcm + k) * g;
}
}
int main() {
int t = ri();
for (int i = 0; i < t; i++) {
int p = ri();
int q = ri();
int k = ri();
printf("%" PRId64 "\n", solve(p, q, k));
}
return 0;
}
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