結果
| 問題 | No.1931 Fraction 2 |
| ユーザー |
 hitonanode
|
| 提出日時 | 2022-05-06 23:20:07 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 18,283 bytes |
| コンパイル時間 | 5,396 ms |
| コンパイル使用メモリ | 408,472 KB |
| 実行使用メモリ | 28,500 KB |
| 最終ジャッジ日時 | 2024-07-06 17:25:48 |
| 合計ジャッジ時間 | 40,343 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge4 |
（要ログイン）
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 | 13 ms
18,052 KB |
| testcase_01 | AC | 13 ms
10,984 KB |
| testcase_02 | AC | 13 ms
10,980 KB |
| testcase_03 | AC | 15 ms
10,964 KB |
| testcase_04 | AC | 14 ms
10,976 KB |
| testcase_05 | AC | 15 ms
11,108 KB |
| testcase_06 | AC | 15 ms
10,980 KB |
| testcase_07 | AC | 15 ms
11,104 KB |
| testcase_08 | AC | 13 ms
10,976 KB |
| testcase_09 | AC | 14 ms
10,968 KB |
| testcase_10 | AC | 12 ms
10,980 KB |
| testcase_11 | AC | 14 ms
10,980 KB |
| testcase_12 | AC | 13 ms
10,980 KB |
| testcase_13 | AC | 391 ms
12,388 KB |
| testcase_14 | AC | 1,939 ms
16,452 KB |
| testcase_15 | AC | 658 ms
13,552 KB |
| testcase_16 | AC | 78 ms
11,240 KB |
| testcase_17 | AC | 117 ms
11,488 KB |
| testcase_18 | TLE | - |
| testcase_19 | TLE | - |
| testcase_20 | TLE | - |
| testcase_21 | TLE | - |
| testcase_22 | TLE | - |
| testcase_23 | TLE | - |
| testcase_24 | TLE | - |
| testcase_25 | TLE | - |
| testcase_26 | TLE | - |
| testcase_27 | TLE | - |
| testcase_28 | TLE | - |
| testcase_29 | -- | - |
| testcase_30 | -- | - |
| testcase_31 | -- | - |
| testcase_32 | -- | - |
| testcase_33 | -- | - |
| testcase_34 | -- | - |
| testcase_35 | -- | - |
| testcase_36 | -- | - |
| testcase_37 | -- | - |
| testcase_38 | -- | - |
ソースコード
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <typename T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl
#define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr)
#else
#define dbg(x) 0
#define dbgif(cond, x) 0
#endif
#include <cassert>
#include <map>
#include <vector>
// Linear sieve algorithm for fast prime factorization
// Complexity: O(N) time, O(N) space:
// - MAXN = 10^7: ~44 MB, 80~100 ms (Codeforces / AtCoder GCC, C++17)
// - MAXN = 10^8: ~435 MB, 810~980 ms (Codeforces / AtCoder GCC, C++17)
// Reference:
// [1] D. Gries, J. Misra, "A Linear Sieve Algorithm for Finding Prime Numbers,"
// Communications of the ACM, 21(12), 999-1003, 1978.
// - https://cp-algorithms.com/algebra/prime-sieve-linear.html
// - https://37zigen.com/linear-sieve/
struct Sieve {
std::vector<int> min_factor;
std::vector<int> primes;
Sieve(int MAXN) : min_factor(MAXN + 1) {
for (int d = 2; d <= MAXN; d++) {
if (!min_factor[d]) {
min_factor[d] = d;
primes.emplace_back(d);
}
for (const auto &p : primes) {
if (p > min_factor[d] or d * p > MAXN) break;
min_factor[d * p] = p;
}
}
}
// Prime factorization for 1 <= x <= MAXN^2
// Complexity: O(log x) (x <= MAXN)
// O(MAXN / log MAXN) (MAXN < x <= MAXN^2)
template <class T> std::map<T, int> factorize(T x) const {
std::map<T, int> ret;
assert(x > 0 and
x <= ((long long)min_factor.size() - 1) * ((long long)min_factor.size() - 1));
for (const auto &p : primes) {
if (x < T(min_factor.size())) break;
while (!(x % p)) x /= p, ret[p]++;
}
if (x >= T(min_factor.size())) ret[x]++, x = 1;
while (x > 1) ret[min_factor[x]]++, x /= min_factor[x];
return ret;
}
// Enumerate divisors of 1 <= x <= MAXN^2
// Be careful of highly composite numbers https://oeis.org/A002182/list
// https://gist.github.com/dario2994/fb4713f252ca86c1254d#file-list-txt (n, (# of div. of n)):
// 45360->100, 735134400(<1e9)->1344, 963761198400(<1e12)->6720
template <class T> std::vector<T> divisors(T x) const {
std::vector<T> ret{1};
for (const auto p : factorize(x)) {
int n = ret.size();
for (int i = 0; i < n; i++) {
for (T a = 1, d = 1; d <= p.second; d++) {
a *= p.first;
ret.push_back(ret[i] * a);
}
}
}
return ret; // NOT sorted
}
// Euler phi functions of divisors of given x
// Verified: ABC212 G https://atcoder.jp/contests/abc212/tasks/abc212_g
// Complexity: O(sqrt(x) + d(x))
template <class T> std::map<T, T> euler_of_divisors(T x) const {
assert(x >= 1);
std::map<T, T> ret;
ret[1] = 1;
std::vector<T> divs{1};
for (auto p : factorize(x)) {
int n = ret.size();
for (int i = 0; i < n; i++) {
ret[divs[i] * p.first] = ret[divs[i]] * (p.first - 1);
divs.push_back(divs[i] * p.first);
for (T a = divs[i] * p.first, d = 1; d < p.second; a *= p.first, d++) {
ret[a * p.first] = ret[a] * p.first;
divs.push_back(a * p.first);
}
}
}
return ret;
}
// Moebius function Table, (-1)^{# of different prime factors} for square-free x
// return: [0=>0, 1=>1, 2=>-1, 3=>-1, 4=>0, 5=>-1, 6=>1, 7=>-1, 8=>0, ...] https://oeis.org/A008683
std::vector<int> GenerateMoebiusFunctionTable() const {
std::vector<int> ret(min_factor.size());
for (unsigned i = 1; i < min_factor.size(); i++) {
if (i == 1) {
ret[i] = 1;
} else if ((i / min_factor[i]) % min_factor[i] == 0) {
ret[i] = 0;
} else {
ret[i] = -ret[i / min_factor[i]];
}
}
return ret;
}
// Calculate [0^K, 1^K, ..., nmax^K] in O(nmax)
// Note: **0^0 == 1**
template <class MODINT> std::vector<MODINT> enumerate_kth_pows(long long K, int nmax) const {
assert(nmax < int(min_factor.size()));
assert(K >= 0);
if (K == 0) return std::vector<MODINT>(nmax + 1, 1);
std::vector<MODINT> ret(nmax + 1);
ret[0] = 0, ret[1] = 1;
for (int n = 2; n <= nmax; n++) {
if (min_factor[n] == n) {
ret[n] = MODINT(n).pow(K);
} else {
ret[n] = ret[n / min_factor[n]] * ret[min_factor[n]];
}
}
return ret;
}
};
Sieve sieve((1 << 20));
#include <boost/multiprecision/cpp_int.hpp>
using mpint = boost::multiprecision::cpp_int;
#include <iostream>
#include <set>
#include <vector>
template <int md> struct ModInt {
#if __cplusplus >= 201402L
#define MDCONST constexpr
#else
#define MDCONST
#endif
using lint = long long;
MDCONST static int mod() { return md; }
static int get_primitive_root() {
static int primitive_root = 0;
if (!primitive_root) {
primitive_root = [&]() {
std::set<int> fac;
int v = md - 1;
for (lint i = 2; i * i <= v; i++)
while (v % i == 0) fac.insert(i), v /= i;
if (v > 1) fac.insert(v);
for (int g = 1; g < md; g++) {
bool ok = true;
for (auto i : fac)
if (ModInt(g).pow((md - 1) / i) == 1) {
ok = false;
break;
}
if (ok) return g;
}
return -1;
}();
}
return primitive_root;
}
int val_;
int val() const noexcept { return val_; }
MDCONST ModInt() : val_(0) {}
MDCONST ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; }
MDCONST ModInt(lint v) { _setval(v % md + md); }
MDCONST explicit operator bool() const { return val_ != 0; }
MDCONST ModInt operator+(const ModInt &x) const {
return ModInt()._setval((lint)val_ + x.val_);
}
MDCONST ModInt operator-(const ModInt &x) const {
return ModInt()._setval((lint)val_ - x.val_ + md);
}
MDCONST ModInt operator*(const ModInt &x) const {
return ModInt()._setval((lint)val_ * x.val_ % md);
}
MDCONST ModInt operator/(const ModInt &x) const {
return ModInt()._setval((lint)val_ * x.inv().val() % md);
}
MDCONST ModInt operator-() const { return ModInt()._setval(md - val_); }
MDCONST ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
MDCONST ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
MDCONST ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
MDCONST ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
friend MDCONST ModInt operator+(lint a, const ModInt &x) {
return ModInt()._setval(a % md + x.val_);
}
friend MDCONST ModInt operator-(lint a, const ModInt &x) {
return ModInt()._setval(a % md - x.val_ + md);
}
friend MDCONST ModInt operator*(lint a, const ModInt &x) {
return ModInt()._setval(a % md * x.val_ % md);
}
friend MDCONST ModInt operator/(lint a, const ModInt &x) {
return ModInt()._setval(a % md * x.inv().val() % md);
}
MDCONST bool operator==(const ModInt &x) const { return val_ == x.val_; }
MDCONST bool operator!=(const ModInt &x) const { return val_ != x.val_; }
MDCONST bool operator<(const ModInt &x) const {
return val_ < x.val_;
} // To use std::map<ModInt, T>
friend std::istream &operator>>(std::istream &is, ModInt &x) {
lint t;
return is >> t, x = ModInt(t), is;
}
MDCONST friend std::ostream &operator<<(std::ostream &os, const ModInt &x) {
return os << x.val_;
}
MDCONST ModInt pow(lint n) const {
ModInt ans = 1, tmp = *this;
while (n) {
if (n & 1) ans *= tmp;
tmp *= tmp, n >>= 1;
}
return ans;
}
static std::vector<ModInt> facs, facinvs, invs;
MDCONST static void _precalculation(int N) {
int l0 = facs.size();
if (N > md) N = md;
if (N <= l0) return;
facs.resize(N), facinvs.resize(N), invs.resize(N);
for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;
facinvs[N - 1] = facs.back().pow(md - 2);
for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);
for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];
}
MDCONST ModInt inv() const {
if (this->val_ < std::min(md >> 1, 1 << 21)) {
while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
return invs[this->val_];
} else {
return this->pow(md - 2);
}
}
MDCONST ModInt fac() const {
while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
return facs[this->val_];
}
MDCONST ModInt facinv() const {
while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
return facinvs[this->val_];
}
MDCONST ModInt doublefac() const {
lint k = (this->val_ + 1) / 2;
return (this->val_ & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac())
: ModInt(k).fac() * ModInt(2).pow(k);
}
MDCONST ModInt nCr(const ModInt &r) const {
return (this->val_ < r.val_) ? 0 : this->fac() * (*this - r).facinv() * r.facinv();
}
MDCONST ModInt nPr(const ModInt &r) const {
return (this->val_ < r.val_) ? 0 : this->fac() * (*this - r).facinv();
}
ModInt sqrt() const {
if (val_ == 0) return 0;
if (md == 2) return val_;
if (pow((md - 1) / 2) != 1) return 0;
ModInt b = 1;
while (b.pow((md - 1) / 2) == 1) b += 1;
int e = 0, m = md - 1;
while (m % 2 == 0) m >>= 1, e++;
ModInt x = pow((m - 1) / 2), y = (*this) * x * x;
x *= (*this);
ModInt z = b.pow(m);
while (y != 1) {
int j = 0;
ModInt t = y;
while (t != 1) j++, t *= t;
z = z.pow(1LL << (e - j - 1));
x *= z, z *= z, y *= z;
e = j;
}
return ModInt(std::min(x.val_, md - x.val_));
}
};
template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};
using mint = ModInt<998244353>;
// using mint = ModInt<1000000007>;
mpint mpgcd(mpint x, mpint y) {
while (x != y and x and y) {
if (x < y) swap(x, y);
auto d = x / y;
x -= d * y;
}
return max(x, y);
}
int main() {
int N;
cin >> N;
vector<pint> AB(N);
REP(i, N) cin >> AB[i].first >> AB[i].second;
vector<int> pcnt(201010);
vector<int> pcnthi(pcnt.size()), pcntex(pcnt.size()), pcnthi2(pcnt.size());
for (auto [a, b] : AB) {
for (auto [p, deg] : sieve.factorize(b)) {
pcnt[p] += deg;
pcntex[p]++;
if (deg >= pcnthi[p]) {
pcnthi2[p] = pcnthi[p];
pcnthi[p] = deg;
} else {
chmax(pcnthi2[p], deg);
}
// chmax(pcnthi[p], deg);
// chmin(pcntlo[p], deg);
}
}
using P = pair<mpint, mpint>;
auto rec = [&](auto &&self, int l, int r) -> P {
if (l + 1 == r) return make_pair(AB[l].first, AB[l].second);
const int c = (l + r) / 2;
auto [a1num, a1den] = self(self, l, c);
auto [a2num, a2den] = self(self, c, r);
auto den = a1den * a2den;
auto num = a1num * a2den + a1den * a2num;
// auto g = mpgcd(den, num);
return make_pair(num, den);
};
auto [num_, den_] = rec(rec, 0, N);
// auto g = mpgcd(num, den);
// mint num = lint(num_ % 998244353);
// mint den = lint(den_ % 998244353);
vector<int> gs;
REP(p, pcnt.size()) {
int deg = pcnt[p] - pcnthi[p];
// mint g = mint(p).pow(deg);
// num /= g;
// den /= g;
REP(_, deg) gs.push_back(p);
}
auto rec2 = [&](auto &&self, int l, int r) -> mpint {
if (l == r) return 1;
if (l + 1 == r) return gs[l];
int c = (l + r) / 2;
return self(self, l, c) * self(self, c, r);
};
auto gtmp = rec2(rec2, 0, gs.size());
num_ /= gtmp;
den_ /= gtmp;
mint num = lint(num_ % 998244353);
mint den = lint(den_ % 998244353);
REP(p, pcnt.size()) {
lint div = 1;
REP(t, pcnthi[p]) {
div *= p;
if (num_ % div == 0) {
continue;
} else {
div /= p;
break;
}
}
num /= div;
den /= div;
}
// auto g = mpgcd(num_, den_);
// cout << (num_ / g % 998244353) << ' ' << (den_ / g % 998244353) << '\n';
cout << num << ' ' << den << endl;
}