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algebra/test/division_free_determinant.test.cpp
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- Last update: 2026-06-19 12:45:09+09:00
- Problem: https://onlinejudge.u-aizu.ac.jp/courses/lesson/2/ITP1/1/ITP1_1_A
Depends on
- algebra/determinant.hpp
- algebra/division_free_determinant.hpp
- algebra/matrix.hpp
- number_theory/mod_int.hpp
- number_theory/utils.hpp
- template/random.hpp
- template/template.hpp
Code
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/lesson/2/ITP1/1/ITP1_1_A"
#include "../../template/template.hpp"
#include "../../template/random.hpp"
#include "../../algebra/determinant.hpp"
#include "../../algebra/division_free_determinant.hpp"
#include "../../number_theory/mod_int.hpp"
int main() {
using M = ModInt<998244353>;
REP(n, 50) {
Matrix<M> mat(n);
REP(i, n) REP(j, n) {
mat(i, j) = M(uniform(M::get_mod()));
}
M det = determinant(mat);
M div_free = division_free_determinant(mat);
assert(det == div_free);
}
cout << "Hello World\n";
}#line 1 "algebra/test/division_free_determinant.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/lesson/2/ITP1/1/ITP1_1_A"
#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 5 "algebra/matrix.hpp"
template <typename T>
class Matrix {
int _h, _w;
std::vector<std::vector<T>> dat;
public:
Matrix() : dat() {}
Matrix(int n) : _h(n), _w(n), dat(n, std::vector<T>(n, T())) {
assert(0 <= n);
}
Matrix(int _h, int _w) : _h(_h), _w(_w), dat(_h, std::vector<T>(_w, T())) {
assert(0 <= _h && 0 <= _w);
}
static Matrix<T> ident(int n) {
assert(0 <= n);
Matrix<T> ret(n);
for (int i = 0; i < n; ++i) {
ret.dat[i][i] = T(1);
}
return ret;
}
int h() const { return _h; }
int w() const { return _w; }
std::pair<int, int> shape() const { return std::pair<int, int>(_h, _w); }
const T &operator()(int i, int j) const {
assert(0 <= i && i < _h && 0 <= j && j < _w);
return dat[i][j];
}
T &operator()(int i, int j) {
assert(0 <= i && i < _h && 0 <= j && j < _w);
return dat[i][j];
}
void swap_row(int i, int j) {
assert(0 <= i && i < _h && 0 <= j && j < _h);
std::swap(dat[i], dat[j]);
}
void swap_column(int i, int j) {
assert(0 <= i && i < _w && 0 <= j && j < _w);
for (int k = 0; k < _h; ++k) {
std::swap(dat[k][i], dat[k][j]);
}
}
Matrix<T> trans() const {
Matrix<T> ret(_w, _h);
for (int i = 0; i < _h; ++i) {
for (int j = 0; j < _w; ++j) {
ret.dat[j][i] = dat[i][j];
}
}
return ret;
}
Matrix<T> &operator+=(const Matrix<T> &rhs) {
assert(shape() == rhs.shape());
for (int i = 0; i < _h; ++i) {
for (int j = 0; j < _w; ++j) {
dat[i][j] += rhs.dat[i][j];
}
}
return *this;
}
Matrix<T> &operator-=(const Matrix<T> &rhs) {
assert(shape() == rhs.shape());
for (int i = 0; i < _h; ++i) {
for (int j = 0; j < _w; ++j) {
dat[i][j] -= rhs.dat[i][j];
}
}
return *this;
}
Matrix<T> &operator*=(const Matrix<T> &rhs) { return *this = *this * rhs; }
friend Matrix<T> operator+(Matrix<T> lhs, const Matrix<T> &rhs) {
return lhs += rhs;
}
friend Matrix<T> operator-(Matrix<T> lhs, const Matrix<T> &rhs) {
return lhs -= rhs;
}
friend Matrix<T> operator*(const Matrix<T> &lhs, const Matrix<T> &rhs) {
assert(lhs._w == rhs._h);
std::vector<std::vector<T>> dat(lhs._h, std::vector<T>(rhs._w, T()));
for (int i = 0; i < lhs._h; ++i) {
for (int j = 0; j < rhs._w; ++j) {
for (int k = 0; k < lhs._w; ++k) {
dat[i][j] += lhs.dat[i][k] * rhs.dat[k][j];
}
}
}
Matrix<T> ret;
ret._h = lhs._h;
ret._w = rhs._w;
ret.dat = dat;
return ret;
}
Matrix<T> pow(unsigned long long t) const {
assert(_h == _w);
Matrix<T> ret = Matrix<T>::ident(_h);
Matrix<T> self = *this;
while (t > 0) {
if (t & 1) {
ret *= self;
}
self *= self;
t >>= 1;
}
return ret;
}
};
#line 3 "algebra/determinant.hpp"
template <typename T>
T determinant(Matrix<T> a) {
assert(a.h() == a.w());
int n = a.h();
T det(1);
for (int i = 0; i < n; ++i) {
int row = -1;
for (int j = i; j < n; ++j) {
if (a(j, i) != T()) {
row = j;
break;
}
}
if (row == -1) {
det = T(0);
break;
}
if (row != i) {
a.swap_row(i, row);
det = -det;
}
det *= a(i, i);
T inv = T(1) / a(i, i);
for (int j = i; j < n; ++j) {
a(i, j) *= inv;
}
for (int j = i + 1; j < n; ++j) {
T cf = a(j, i);
for (int k = i + 1; k < n; ++k) {
a(j, k) -= cf * a(i, k);
}
}
}
return det;
}
#line 4 "algebra/division_free_determinant.hpp"
template <typename T>
T division_free_determinant(Matrix<T> a) {
int n = a.h();
assert(a.w() == n);
if (n == 0) {
return T(1);
}
Matrix<T> t(n);
Matrix<T> x = a;
for (int i = 0; i < n; ++i) {
for (int j = i + 1; j < n; ++j) {
swap(a(i, j), a(j, i));
}
}
for (int i = 0; i < n - 1; ++i) {
T sum(0);
for (int j = n - i - 1; j >= 0; --j) {
sum += std::exchange(x(j, j), -sum);
}
for (int j = 0; j < n - i - 1; ++j) {
for (int k = 0; k < n; ++k) {
t(j, k) = T();
}
}
for (int j = 0; j < n - i - 1; ++j) {
for (int k = 0; k < n; ++k) {
T sum(0);
for (int l = j; l < n; ++l) {
sum += x(j, l) * a(k, l);
}
t(j, k) = sum;
}
}
x = t;
}
T ans = x(0, 0);
if (n % 2 == 0) {
ans = -ans;
}
return ans;
}
#line 2 "number_theory/mod_int.hpp"
#line 5 "number_theory/mod_int.hpp"
#include <type_traits>
#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 7 "number_theory/mod_int.hpp"
template <unsigned mod>
struct ModInt {
static_assert(mod != 0, "`mod` must not be equal to 0.");
static_assert(mod < (1u << 31),
"`mod` must be less than (1u << 31) = 2147483648.");
unsigned val;
static constexpr unsigned get_mod() { return mod; }
constexpr ModInt() : val(0) {}
template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>
constexpr ModInt(T x)
: val((unsigned)((long long)x % (long long)mod + (x < 0 ? mod : 0))) {}
template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>
constexpr ModInt(T x) : val((unsigned)(x % mod)) {}
static constexpr ModInt raw(unsigned x) {
ModInt<mod> ret;
ret.val = x;
return ret;
}
constexpr unsigned get_val() const { return val; }
constexpr ModInt operator+() const { return *this; }
constexpr ModInt operator-() const { return ModInt<mod>(0u) - *this; }
constexpr ModInt &operator+=(const ModInt &rhs) {
val += rhs.val;
if (val >= mod) val -= mod;
return *this;
}
constexpr ModInt &operator-=(const ModInt &rhs) {
val -= rhs.val;
if (val >= mod) val += mod;
return *this;
}
constexpr ModInt &operator*=(const ModInt &rhs) {
val = (unsigned long long)val * rhs.val % mod;
return *this;
}
constexpr ModInt &operator/=(const ModInt &rhs) {
val = (unsigned long long)val * rhs.inv().val % mod;
return *this;
}
friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) += rhs;
}
friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) -= rhs;
}
friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) *= rhs;
}
friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) /= rhs;
}
constexpr ModInt pow(unsigned long long x) const {
ModInt<mod> ret = ModInt<mod>::raw(1);
ModInt<mod> self = *this;
while (x != 0) {
if (x & 1) ret *= self;
self *= self;
x >>= 1;
}
return ret;
}
constexpr ModInt inv() const {
static_assert(is_prime(mod), "`mod` must be a prime number.");
assert(val != 0);
return this->pow(mod - 2);
}
friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {
long long val;
is >> val;
x.val = val % mod + (val < 0 ? mod : 0);
return is;
}
friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {
os << x.val;
return os;
}
friend bool operator==(const ModInt &lhs, const ModInt &rhs) {
return lhs.val == rhs.val;
}
friend bool operator!=(const ModInt &lhs, const ModInt &rhs) {
return lhs.val != rhs.val;
}
};
template <unsigned mod>
void debug(ModInt<mod> x) {
std::cerr << x.val;
}
#line 7 "algebra/test/division_free_determinant.test.cpp"
int main() {
using M = ModInt<998244353>;
REP(n, 50) {
Matrix<M> mat(n);
REP(i, n) REP(j, n) {
mat(i, j) = M(uniform(M::get_mod()));
}
M det = determinant(mat);
M div_free = division_free_determinant(mat);
assert(det == div_free);
}
cout << "Hello World\n";
}