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number_theory/test/ax_by_c_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/ax_by_c.hpp"
void test() {
constexpr int ITER = 1'000'000;
for (int t = 0; t < ITER; ++t) {
i64 a = uniform(-1'000'000, 1'000'000);
i64 b = uniform(-1'000'000, 1'000'000);
i64 c = uniform(-1'000'000, 1'000'000);
optional<pair<i64, i64>> ret = ax_by_c(a, b, c);
if (ret.has_value()) {
auto [x, y] = *ret;
assert(a * x + b * y == c);
if (a && b && c) {
assert(abs(x) <= abs(b * c));
assert(abs(y) <= abs(a * c));
}
}
}
for (int a = -50; a <= 50; ++a) {
for (int b = -50; b <= 50; ++b) {
for (int c = -50; c <= 50; ++c) {
optional<pair<i32, i32>> ret = ax_by_c(a, b, c);
if (ret.has_value()) {
auto [x, y] = *ret;
assert(a * x + b * y == c);
if (a && b && c) {
assert(abs(x) <= abs(b * c));
assert(abs(y) <= abs(a * c));
}
}
}
}
}
}
int main() {
test();
cout << "Hello World\n";
}#line 1 "number_theory/test/ax_by_c_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/ax_by_c.hpp"
#line 2 "number_theory/utils.hpp"
#line 4 "number_theory/utils.hpp"
constexpr bool is_prime(unsigned n) {
if (n == 0 || n == 1) {
return false;
}
for (unsigned i = 2; i * i <= n; ++i) {
if (n % i == 0) {
return false;
}
}
return true;
}
constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
unsigned ret = 1, self = x;
while (y != 0) {
if (y & 1) {
ret = (unsigned)((unsigned long long)ret * self % mod);
}
self = (unsigned)((unsigned long long)self * self % mod);
y /= 2;
}
return ret;
}
template <unsigned mod>
constexpr unsigned primitive_root() {
static_assert(is_prime(mod), "`mod` must be a prime number.");
if (mod == 2) {
return 1;
}
unsigned primes[32] = {};
int it = 0;
{
unsigned m = mod - 1;
for (unsigned i = 2; i * i <= m; ++i) {
if (m % i == 0) {
primes[it++] = i;
while (m % i == 0) {
m /= i;
}
}
}
if (m != 1) {
primes[it++] = m;
}
}
for (unsigned i = 2; i < mod; ++i) {
bool ok = true;
for (int j = 0; j < it; ++j) {
if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
ok = false;
break;
}
}
if (ok) return i;
}
return 0;
}
// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
x %= y;
if (x < 0) {
x += y;
}
return x;
}
// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
if (y < 0) {
x *= -1;
y *= -1;
}
if (x >= 0) {
return x / y;
} else {
return -((-x + y - 1) / y);
}
}
// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
if (y < 0) {
x *= -1;
y *= -1;
}
if (x >= 0) {
return (x + y - 1) / y;
} else {
return -(-x / y);
}
}
// b >= 1
// returns (g, x) s.t. g = gcd(a, b), a * x = g (mod b), 0 <= x < b / g
// from ACL
template <typename T>
std::pair<T, T> extgcd(T a, T b) {
a = safe_mod(a, b);
T s = b, t = a, m0 = 0, m1 = 1;
while (t) {
T u = s / t;
s -= t * u;
m0 -= m1 * u;
std::swap(s, t);
std::swap(m0, m1);
}
if (m0 < 0) {
m0 += b / s;
}
return std::pair<T, T>(s, m0);
}
// b >= 1
// returns (g, x, y) s.t. g = gcd(a, b), a * x + b * y = g, 0 <= x < b / g, |y| < max(2, |a| / g)
template <typename T>
std::tuple<T, T, T> extgcd2(T a, T b) {
T _a = safe_mod(a, b);
T quot = (a - _a) / b;
T x00 = 0, x01 = 1, y0 = b;
T x10 = 1, x11 = -quot, y1 = _a;
while (y1) {
T u = y0 / y1;
x00 -= u * x10;
x01 -= u * x11;
y0 -= u * y1;
std::swap(x00, x10);
std::swap(x01, x11);
std::swap(y0, y1);
}
if (x00 < 0) {
x00 += b / y0;
x01 -= a / y0;
}
return std::tuple<T, T, T>(y0, x00, x01);
}
// gcd(x, m) == 1
template <typename T>
T inv_mod(T x, T m) {
return extgcd(x, m).second;
}
#line 4 "number_theory/ax_by_c.hpp"
#include <optional>
// solve a * x + b * y = c
// |x| <= |b * c|, |y| <= |a * c| (|a|, |b|, |c| > 0)
template <typename T>
std::optional<std::pair<T, T>> ax_by_c(T a, T b, T c) {
if (c == 0) {
return std::pair<T, T>(0, 0);
}
if (a == 0 && b == 0) {
return std::nullopt;
}
if (a == 0) {
if (c % b) {
return std::nullopt;
}
return std::pair<T, T>(0, c / b);
}
if (b == 0) {
if (c % a) {
return std::nullopt;
}
return std::pair<T, T>(c / a, 0);
}
if (b < 0) {
a = -a;
b = -b;
c = -c;
}
auto [g, x, y] = extgcd2(a, b);
if (c % g) {
return std::nullopt;
}
T mult = c / g;
x *= mult;
y *= mult;
return std::pair<T, T>(x, y);
}
#line 8 "number_theory/test/ax_by_c_stress.test.cpp"
void test() {
constexpr int ITER = 1'000'000;
for (int t = 0; t < ITER; ++t) {
i64 a = uniform(-1'000'000, 1'000'000);
i64 b = uniform(-1'000'000, 1'000'000);
i64 c = uniform(-1'000'000, 1'000'000);
optional<pair<i64, i64>> ret = ax_by_c(a, b, c);
if (ret.has_value()) {
auto [x, y] = *ret;
assert(a * x + b * y == c);
if (a && b && c) {
assert(abs(x) <= abs(b * c));
assert(abs(y) <= abs(a * c));
}
}
}
for (int a = -50; a <= 50; ++a) {
for (int b = -50; b <= 50; ++b) {
for (int c = -50; c <= 50; ++c) {
optional<pair<i32, i32>> ret = ax_by_c(a, b, c);
if (ret.has_value()) {
auto [x, y] = *ret;
assert(a * x + b * y == c);
if (a && b && c) {
assert(abs(x) <= abs(b * c));
assert(abs(y) <= abs(a * c));
}
}
}
}
}
}
int main() {
test();
cout << "Hello World\n";
}