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number_theory/test/frac_binsearch_stress.test.cpp
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- Last update: 2025-06-28 10:05:47+09:00
- Problem: https://onlinejudge.u-aizu.ac.jp/courses/lesson/2/ITP1/1/ITP1_1_A
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Code
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/lesson/2/ITP1/1/ITP1_1_A"
#define FAST_IO
#define FIX_SEED
#include "../../template/template.hpp"
#include "../../template/random.hpp"
#include "../../number_theory/frac_binsearch.hpp"
struct Rational {
i64 num, den;
Rational() : num(0), den(1) {}
Rational(i64 n, i64 d) : num(n), den(d) {
assert(den != 0);
i64 g = gcd(num, den);
num /= g;
den /= g;
if (den < 0) {
num = -num;
den = -den;
}
}
friend i64 comp(Rational lhs, Rational rhs) {
return lhs.num * rhs.den - rhs.num * lhs.den;
}
friend bool operator<(Rational lhs, Rational rhs) {
return comp(lhs, rhs) < 0;
}
friend bool operator>(Rational lhs, Rational rhs) {
return comp(lhs, rhs) > 0;
}
friend bool operator<=(Rational lhs, Rational rhs) {
return comp(lhs, rhs) <= 0;
}
friend bool operator>=(Rational lhs, Rational rhs) {
return comp(lhs, rhs) >= 0;
}
friend bool operator==(Rational lhs, Rational rhs) {
return comp(lhs, rhs) == 0;
}
friend bool operator!=(Rational lhs, Rational rhs) {
return comp(lhs, rhs) != 0;
}
};
void test() {
constexpr i32 B = 1000;
V<Rational> rats;
REP(num, 1, B + 1) {
REP(den, num + 1, B + 1) {
if (gcd(num, den) == 1) {
rats.push_back(Rational(num, den));
}
}
}
rats.push_back(Rational(0, 1));
rats.push_back(Rational(1, 1));
sort(ALL(rats));
constexpr i64 C = 1'000'000'000'000'000;
REP(i, 100000) {
i64 c = (uniform(2) ? B + 1 : C + 1);
i64 num = uniform(1LL, c + 1);
i64 den = uniform(1LL, c + 1);
while (num == den) {
num = uniform(1LL, c + 1);
den = uniform(1LL, c + 1);
}
if (num > den) {
swap(num, den);
}
Rational r(num, den);
// >=r
{
auto [a, b] = get_lim_true(B, [&](i32 x, i32 y) -> bool {
return Rational(x, y) >= r;
});
auto it = lower_bound(ALL(rats), r);
assert(Rational(a, b) == *it);
}
// <=r
{
auto [a, b] = get_lim_true(B, [&](i32 x, i32 y) -> bool {
return Rational(x, y) <= r;
});
auto it = upper_bound(ALL(rats), r) - 1;
assert(Rational(a, b) == *it);
}
// >r
{
auto [a, b] = get_lim_true(B, [&](i32 x, i32 y) -> bool {
return Rational(x, y) > r;
});
auto it = upper_bound(ALL(rats), r);
assert(Rational(a, b) == *it);
}
// <r
{
auto [a, b] = get_lim_true(B, [&](i32 x, i32 y) -> bool {
return Rational(x, y) < r;
});
auto it = lower_bound(ALL(rats), r) - 1;
assert(Rational(a, b) == *it);
}
}
}
int main() {
test();
cout << "Hello World\n";
}#line 1 "number_theory/test/frac_binsearch_stress.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/lesson/2/ITP1/1/ITP1_1_A"
#define FAST_IO
#define FIX_SEED
#line 2 "template/template.hpp"
#include <bits/stdc++.h>
#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER2(i, n) for (i32 i = (i32)(n)-1; i >= 0; --i)
#define PER3(i, m, n) for (i32 i = (i32)(n)-1; i >= (i32)(m); --i)
#define PER(...) OVERRIDE(__VA_ARGS__, PER3, PER2)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
#define LEN(x) (i32)(x.size())
using namespace std;
using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;
using pi = pair<i32, i32>;
using pl = pair<i64, i64>;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = V<V<T>>;
template <typename T>
using VVV = V<V<V<T>>>;
template <typename T>
using VVVV = V<V<V<V<T>>>>;
template <typename T>
using PQR = priority_queue<T, V<T>, greater<T>>;
template <typename T>
bool chmin(T &x, const T &y) {
if (x > y) {
x = y;
return true;
}
return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
if (x < y) {
x = y;
return true;
}
return false;
}
template <typename T>
i32 lob(const V<T> &arr, const T &v) {
return (i32)(lower_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
i32 upb(const V<T> &arr, const T &v) {
return (i32)(upper_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
V<i32> argsort(const V<T> &arr) {
V<i32> ret(arr.size());
iota(ALL(ret), 0);
sort(ALL(ret), [&](i32 i, i32 j) -> bool {
if (arr[i] == arr[j]) {
return i < j;
} else {
return arr[i] < arr[j];
}
});
return ret;
}
#ifdef INT128
using u128 = __uint128_t;
using i128 = __int128_t;
#endif
[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
SetUpIO() {
#ifdef FAST_IO
ios::sync_with_stdio(false);
cin.tie(nullptr);
#endif
cout << fixed << setprecision(15);
}
} set_up_io;
void scan(char &x) { cin >> x; }
void scan(u32 &x) { cin >> x; }
void scan(u64 &x) { cin >> x; }
void scan(i32 &x) { cin >> x; }
void scan(i64 &x) { cin >> x; }
void scan(f64 &x) { cin >> x; }
void scan(string &x) { cin >> x; }
template <typename T>
void scan(V<T> &x) {
for (T &ele : x) {
scan(ele);
}
}
void read() {}
template <typename Head, typename... Tail>
void read(Head &head, Tail &...tail) {
scan(head);
read(tail...);
}
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__);
#define U32(...) \
u32 __VA_ARGS__; \
read(__VA_ARGS__);
#define U64(...) \
u64 __VA_ARGS__; \
read(__VA_ARGS__);
#define I32(...) \
i32 __VA_ARGS__; \
read(__VA_ARGS__);
#define I64(...) \
i64 __VA_ARGS__; \
read(__VA_ARGS__);
#define F64(...) \
f64 __VA_ARGS__; \
read(__VA_ARGS__);
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__);
#define VEC(type, name, size) \
V<type> name(size); \
read(name);
#define VVEC(type, name, size1, size2) \
VV<type> name(size1, V<type>(size2)); \
read(name);
#line 4 "template/random.hpp"
#if defined(LOCAL) || defined(FIX_SEED)
std::mt19937_64 mt(123456789);
#else
std::mt19937_64 mt(std::chrono::steady_clock::now().time_since_epoch().count());
#endif
template <typename T>
T uniform(T l, T r) {
return std::uniform_int_distribution<T>(l, r - 1)(mt);
}
template <typename T>
T uniform(T n) {
return std::uniform_int_distribution<T>(0, n - 1)(mt);
}
#line 2 "number_theory/frac_binsearch.hpp"
#line 6 "number_theory/frac_binsearch.hpp"
// f :: I -> I -> bool
template <typename I, typename F>
std::pair<I, I> get_lim_true(I bound, F f) {
assert(bound >= 1);
std::pair<I, I> ok(0, 1), ng(1, 0);
if (!f(0, 1)) {
std::swap(ok, ng);
}
while (true) {
std::pair<I, I> now(ok.first + ng.first, ok.second + ng.second);
bool rt = f(now.first, now.second);
std::pair<I, I> &from = (rt ? ok : ng), &to = (rt ? ng : ok);
I l = 1, r = 2;
while (f(from.first + to.first * r, from.second + to.second * r) == rt) {
l *= 2;
r *= 2;
if (std::max(from.first + to.first * l, from.second + to.second * l) > bound) {
if (rt) {
I t = l;
if (to.first != 0) {
t = std::min(t, (bound - from.first) / to.first);
}
if (to.second != 0) {
t = std::min(t, (bound - from.second) / to.second);
}
return std::pair<I, I>(from.first + to.first * t, from.second + to.second * t);
} else {
return ok;
}
}
}
while (r - l > 1) {
I mid = (l + r) / 2;
std::pair<I, I> nxt(from.first + to.first * mid, from.second + to.second * mid);
if (std::max(nxt.first, nxt.second) <= bound && f(nxt.first, nxt.second) == rt) {
l = mid;
} else {
r = mid;
}
}
if (std::max(from.first + to.first * r, from.second + to.second * r) > bound) {
if (rt) {
return std::pair<I, I>(from.first + to.first * l, from.second + to.second * l);
} else {
return to;
}
}
from.first += to.first * l;
from.second += to.second * l;
}
assert(false);
}
#line 8 "number_theory/test/frac_binsearch_stress.test.cpp"
struct Rational {
i64 num, den;
Rational() : num(0), den(1) {}
Rational(i64 n, i64 d) : num(n), den(d) {
assert(den != 0);
i64 g = gcd(num, den);
num /= g;
den /= g;
if (den < 0) {
num = -num;
den = -den;
}
}
friend i64 comp(Rational lhs, Rational rhs) {
return lhs.num * rhs.den - rhs.num * lhs.den;
}
friend bool operator<(Rational lhs, Rational rhs) {
return comp(lhs, rhs) < 0;
}
friend bool operator>(Rational lhs, Rational rhs) {
return comp(lhs, rhs) > 0;
}
friend bool operator<=(Rational lhs, Rational rhs) {
return comp(lhs, rhs) <= 0;
}
friend bool operator>=(Rational lhs, Rational rhs) {
return comp(lhs, rhs) >= 0;
}
friend bool operator==(Rational lhs, Rational rhs) {
return comp(lhs, rhs) == 0;
}
friend bool operator!=(Rational lhs, Rational rhs) {
return comp(lhs, rhs) != 0;
}
};
void test() {
constexpr i32 B = 1000;
V<Rational> rats;
REP(num, 1, B + 1) {
REP(den, num + 1, B + 1) {
if (gcd(num, den) == 1) {
rats.push_back(Rational(num, den));
}
}
}
rats.push_back(Rational(0, 1));
rats.push_back(Rational(1, 1));
sort(ALL(rats));
constexpr i64 C = 1'000'000'000'000'000;
REP(i, 100000) {
i64 c = (uniform(2) ? B + 1 : C + 1);
i64 num = uniform(1LL, c + 1);
i64 den = uniform(1LL, c + 1);
while (num == den) {
num = uniform(1LL, c + 1);
den = uniform(1LL, c + 1);
}
if (num > den) {
swap(num, den);
}
Rational r(num, den);
// >=r
{
auto [a, b] = get_lim_true(B, [&](i32 x, i32 y) -> bool {
return Rational(x, y) >= r;
});
auto it = lower_bound(ALL(rats), r);
assert(Rational(a, b) == *it);
}
// <=r
{
auto [a, b] = get_lim_true(B, [&](i32 x, i32 y) -> bool {
return Rational(x, y) <= r;
});
auto it = upper_bound(ALL(rats), r) - 1;
assert(Rational(a, b) == *it);
}
// >r
{
auto [a, b] = get_lim_true(B, [&](i32 x, i32 y) -> bool {
return Rational(x, y) > r;
});
auto it = upper_bound(ALL(rats), r);
assert(Rational(a, b) == *it);
}
// <r
{
auto [a, b] = get_lim_true(B, [&](i32 x, i32 y) -> bool {
return Rational(x, y) < r;
});
auto it = lower_bound(ALL(rats), r) - 1;
assert(Rational(a, b) == *it);
}
}
}
int main() {
test();
cout << "Hello World\n";
}