結果
| 問題 |
No.3225 2×2行列相似判定 〜easy〜
|
| ユーザー |
 hitonanode
|
| 提出日時 | 2025-08-08 22:11:02 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 14,246 bytes |
| コンパイル時間 | 3,205 ms |
| コンパイル使用メモリ | 242,996 KB |
| 実行使用メモリ | 7,716 KB |
| 最終ジャッジ日時 | 2025-08-08 22:11:08 |
| 合計ジャッジ時間 | 4,927 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 32 RE * 1 |
ソースコード
// https://judge.yosupo.jp/submission/183810
#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 <memory>
#include <numeric>
#include <optional>
#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> 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; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class 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 <class 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 <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::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) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif
// #include <bits/stdc++.h>
using u32 = unsigned int;
using u64 = unsigned long long;
constexpr unsigned int P = 67, P2 = P * 2;
struct Fp {
u32 v;
Fp() : v() {}
Fp(u32 v) : v(v) {}
Fp operator+(const Fp& rhs) const {
u32 a = v + rhs.v;
if (a >= P) a -= P;
return a;
}
Fp& operator+=(const Fp& rhs) { if ((v += rhs.v) >= P) v -= P; return *this; }
Fp operator-() const { return v ? P - v : v; }
Fp operator-(const Fp& rhs) const {
u32 a = v - rhs.v;
if (int(a) < 0) a += P;
return a;
}
Fp& operator-=(const Fp& rhs) { if (int(v -= rhs.v) < 0) v += P; return *this; }
Fp operator*(const Fp& rhs) const { return u32(u64(v) * rhs.v % P); }
Fp& operator*=(const Fp& rhs) { v = u64(v) * rhs.v % P; return *this; }
Fp inv() const;
Fp operator/(const Fp& rhs) const { return *this * rhs.inv(); }
Fp& operator/=(const Fp& rhs) { return *this *= rhs.inv(); }
operator u32() const { return v; }
Fp quo2() const { return (v & 1) ? ((v + P) >> 1) : (v >> 1); }
};
Fp mpow(const Fp& a, unsigned k) {
if (k == 0) return 1u;
Fp ret = mpow(a * a, k >> 1);
if (k & 1) ret *= a;
return ret;
}
Fp Fp::inv() const { return mpow(*this, P - 2); }
std::mt19937 rng(std::chrono::steady_clock::now().time_since_epoch().count());
std::uniform_int_distribution<int> uid(0, P - 1);
using Poly = std::vector<Fp>;
using Vec = std::vector<Fp>;
using Matrix = std::vector<Vec>;
const int _ = 505;
int N;
Matrix transpose(const Matrix& mat) {
Matrix ret(N, Vec(N));
for (int i = 0; i != N; ++i)
for (int j = 0; j != N; ++j)
ret[i][j] = mat[j][i];
return ret;
}
Matrix operator*(const Matrix& lhs, Matrix rhs) {
for (int i = 0; i != N; ++i)
for (int j = 0; j != i; ++j)
std::swap(rhs[i][j], rhs[j][i]);
Matrix ret(N, Vec(N));
for (int i = 0; i != N; ++i)
for (int j = 0; j != N; ++j)
for (int k = 0; k != N; ++k)
ret[i][j] += lhs[i][k] * rhs[j][k];
return ret;
}
Vec operator+(const Vec& lhs, const Vec& rhs) {
Vec ret(N);
for (int i = 0; i != N; ++i) ret[i] = lhs[i] + rhs[i];
return ret;
}
Vec operator-(const Vec& lhs, const Vec& rhs) {
Vec ret(N);
for (int i = 0; i != N; ++i) ret[i] = lhs[i] - rhs[i];
return ret;
}
Vec operator*(const Vec& lhs, const Fp& rhs) {
Vec ret(N);
for (int i = 0; i != N; ++i) ret[i] = lhs[i] * rhs;
return ret;
}
struct Basis {
std::vector<Vec> vectors;
Matrix reduced, coefficients;
Basis() : reduced(N), coefficients(N) {}
Basis(const Basis& basis) : vectors(basis.vectors), reduced(basis.reduced), coefficients(basis.coefficients) {}
Poly insert(Vec vec) {
int id = vectors.size();
Vec coefficient(N);
vectors.push_back(vec);
for (int i = 0; i != N; ++i) {
if (vec[i] == 0) continue;
if (!reduced[i].empty()) {
Fp c = vec[i];
vec = vec - reduced[i] * c;
coefficient = coefficient - coefficients[i] * c;
} else {
Fp nv = vec[i].inv();
coefficient[id] = 1;
reduced[i] = vec * nv;
coefficients[i] = coefficient * nv;
return Poly();
}
}
coefficient.resize(id + 1);
coefficient[id] = 1;
return coefficient;
}
Matrix inv() {
for (int i = N - 1; i; --i)
for (int j = 0; j != i; ++j) {
Fp c = reduced[j][i];
reduced[j] = reduced[j] - reduced[i] * c;
coefficients[j] = coefficients[j] - coefficients[i] * c;
}
return coefficients;
}
};
Vec operator*(const Matrix& mat, const Vec& vec) {
Vec ret(N);
for (int i = 0; i != N; ++i)
for (int j = 0; j != N; ++j)
ret[i] += mat[i][j] * vec[j];
return ret;
}
Poly div(Poly a, Poly b) {
int n = a.size() - 1, m = b.size() - 1;
Poly ret(n - m + 1);
for (int i = n; i >= m; --i) {
ret[i - m] = a[i];
Fp c = -a[i];
for (int j = 0; j <= m; ++j) {
a[i - m + j] += c * b[j];
}
}
for (int i = 0; i != m; ++i) assert(a[i] == 0);
return ret;
}
Poly mod(Poly a, Poly b) {
int n = b.size() - 1;
if (a.size() < n) a.resize(n);
int m = a.size() - 1;
for (int i = m; i >= n; --i)
for (int j = 1; j <= n; ++j)
a[i - j] -= a[i] * b[n - j];
a.resize(n);
return a;
}
Poly powmod(Poly modulo, u64 K) {
int n = modulo.size() - 1;
if (K == 0) {
Poly ret(n); ret[0] = 1;
return ret;
}
Poly half = powmod(modulo, K >> 1);
Poly ret(n * 2 - 1);
for (int i = 0; i != n; ++i)
for (int j = 0; j != n; ++j)
ret[i + j] += half[i] * half[j];
if (K & 1) ret.insert(ret.begin(), 0);
return mod(ret, modulo);
}
Matrix Calc(Matrix a, int N, u64 K) {
std::vector<Poly> elementaryDivisors;
Basis basis = Basis();
while (basis.vectors.size() < N) {
// std::cerr << basis.vectors.size() << '\n';
Vec initVector(N);
for (int i = 0; i != N; ++i) initVector[i].v = uid(rng);
Vec iterVector = initVector;
Basis test = basis;
Poly coefficient;
while (true) {
coefficient = test.insert(iterVector);
if (!coefficient.empty()) break;
iterVector = a * iterVector;
}
Poly minimalPolynomial(coefficient.begin() + basis.vectors.size(), coefficient.end());
int minPolyDegree = minimalPolynomial.size() - 1;
int pre = 0;
for (int i = 0; i != elementaryDivisors.size(); ++i) {
int degree = elementaryDivisors[i].size() - 1;
if (degree <= minPolyDegree) {
pre += degree;
continue;
}
// std::cerr << degree << ' ' << minPolyDegree << '\n';
// std::cerr << "COEFF ";
// for (int j = 0; j != degree; ++j)
// std::cerr << coefficient[pre + j].v << ' ';
Poly res = div(Poly(coefficient.begin() + pre, coefficient.begin() + pre + degree),
minimalPolynomial);
// std::cerr << "SIZ " << res.size() << '\n';
// std::cerr << "RES: " << res[0] << '\n';
for (int j = 0; j != degree - minPolyDegree; ++j)
initVector = initVector + basis.vectors[pre + j] * res[j];
pre += degree;
}
elementaryDivisors.push_back(minimalPolynomial);
for (int rep = 0; rep != minPolyDegree; ++rep) {
basis.insert(initVector);
initVector = a * initVector;
}
}
Matrix b = transpose(basis.vectors);
Matrix inv = transpose(basis.inv());
Matrix canonicalFormPower(N, Vec(N));
int pre = 0;
for (Poly poly : elementaryDivisors) {
int degree = poly.size() - 1;
Poly res = powmod(poly, K);
for (int i = 0; i != degree; ++i) {
for (int j = 0; j != degree; ++j) canonicalFormPower[pre + j][pre + i] = res[j];
res.insert(res.begin(), 0);
res = mod(res, poly);
}
pre += degree;
}
return canonicalFormPower;
}
int main() {
N = 2;
std::ios::sync_with_stdio(false); std::cin.tie(nullptr); std::cout.tie(nullptr);
Matrix A(2, Vec(2));
Matrix B(2, Vec(2));
REP(i, 2) REP(j, 2) { cin >> A[i][j].v; }
REP(i, 2) REP(j, 2) { cin >> B[i][j].v; }
dbg(A);
dbg(B);
auto ca = Calc(A, 2, 1);
dbg(ca);
auto cb = Calc(B, 2, 1);
dbg(cb);
if (ca == cb) {
puts("Yes");
} else {
puts("No");
}
// std::ios::sync_with_stdio(false); std::cin.tie(nullptr); std::cout.tie(nullptr);
// u64 K;
// std::cin >> N >> K;
// Matrix a(N, Vec(N));
// for (int i = 0; i != N; ++i)
// for (int j = 0; j != N; ++j)
// std::cin >> a[i][j].v;
// Matrix power = b * canonicalFormPower * inv;
// for (int i = 0; i != N; ++i) {
// for (int j = 0; j != N; ++j)
// std::cout << power[i][j].v << " \n"[j == N - 1];
// }
// return 0;
}