結果

問題 No.2442 線形写像
ユーザー Focus_SashFocus_Sash
提出日時 2023-08-25 22:00:03
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 272 ms / 2,000 ms
コード長 8,885 bytes
コンパイル時間 3,534 ms
コンパイル使用メモリ 234,148 KB
実行使用メモリ 42,240 KB
最終ジャッジ日時 2023-08-26 12:18:10
合計ジャッジ時間 6,325 ms
ジャッジサーバーID
（参考情報） 		judge15 / judge12
このコードへのチャレンジ
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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 1 ms
4,380 KB
testcase_01 AC 2 ms
4,380 KB
testcase_02 AC 1 ms
4,380 KB
testcase_03 AC 1 ms
4,380 KB
testcase_04 AC 2 ms
4,380 KB
testcase_05 AC 1 ms
4,380 KB
testcase_06 AC 1 ms
4,376 KB
testcase_07 AC 1 ms
4,376 KB
testcase_08 AC 1 ms
4,376 KB
testcase_09 AC 2 ms
4,384 KB
testcase_10 AC 2 ms
4,376 KB
testcase_11 AC 3 ms
4,380 KB
testcase_12 AC 3 ms
4,380 KB
testcase_13 AC 3 ms
4,380 KB
testcase_14 AC 2 ms
4,376 KB
testcase_15 AC 138 ms
22,536 KB
testcase_16 AC 147 ms
22,596 KB
testcase_17 AC 261 ms
42,048 KB
testcase_18 AC 270 ms
42,176 KB
testcase_19 AC 272 ms
42,136 KB
testcase_20 AC 268 ms
41,796 KB
testcase_21 AC 272 ms
42,240 KB
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ソースコード

diff # 

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")

#include "bits/stdc++.h"
using namespace std;

#define rep(i, n) for (ll(i) = 0; (i) < (n); ++(i))
#define reps(i, k, n) for (ll(i) = (k); (i) < (n); ++(i))
#define repsi(i, k, n) for (ll(i) = (k); (i) <= (n); ++(i))
#define dreps(i, k, n) for (ll(i) = (k); (i) >= (n); --(i))

namespace util {
using ll = long long;
using vl = std::vector<long long>;
using pl = std::pair<long long, long long>;

constexpr long long kInf = std::numeric_limits<long long>::max() / 8;
constexpr long long kMax = std::numeric_limits<long long>::max();

template <typename T, typename U>
inline bool UpdateMax(T &x, const U &y) {
  if (x < y) {
    x = y;
    return true;
  }
  return false;
}

template <typename T, typename U>
inline bool UpdateMin(T &x, const U &y) {
  if (x > y) {
    x = y;
    return true;
  }
  return false;
}

// verified
inline long long Pow(long long x, long long n) {
  assert(n >= 0);
  if (x == 0) return 0;
  long long res = 1LL;
  while (n > 0) {
    if (n & 1) {
      assert(x != 0 && std::abs(res) <= kMax / std::abs(x));
      res = res * x;
    }
    if (n >>= 1) {
      assert(x != 0 && std::abs(x) <= kMax / std::abs(x));
      x = x * x;
    }
  }
  return res;
}

// verified
inline long long Mod(long long n, const long long m) {
  // returns the "arithmetic modulo"
  // for a pair of integers (n, m) with m != 0, there exists a unique pair of
  // integer (q, r) s.t. n = qm + r and 0 <= r < |m| returns this r
  assert(m != 0);
  if (m < 0) return Mod(n, -m);
  if (n >= 0)
    return n % m;
  else
    return (m + n % m) % m;
}

inline long long Quotient(long long n, long long m) {
  // returns the "arithmetic quotient"
  assert((n - Mod(n, m)) % m == 0);
  return (n - Mod(n, m)) / m;
}

inline long long DivFloor(long long n, long long m) {
  // returns floor(n / m)
  assert(m != 0);
  if (m < 0) {
    n = -n;
    m = -m;
  }
  if (n >= 0)
    return n / m;
  else if (n % m == 0)
    return -(abs(n) / m);
  else
    return -(abs(n) / m) - 1;
}

inline long long DivCeil(long long n, long long m) {
  // returns ceil(n / m)
  assert(m != 0);
  if (n % m == 0)
    return DivFloor(n, m);
  else
    return DivFloor(n, m) + 1;
}

template <typename T>
inline T Sum(const std::vector<T> &vec) {
  return std::accumulate(vec.begin(), vec.end(), T(0));
}
inline long long Max(const std::vector<long long> &v) {
  return *std::max_element(v.begin(), v.end());
}
inline long long Min(const std::vector<long long> &v) {
  return *std::min_element(v.begin(), v.end());
}
template <typename T, typename F>
bool Exists(const std::vector<T> &v, F &&f) {
  return std::any_of(v.begin(), v.end(), f);
}
template <typename T, typename F>
bool ForAll(const std::vector<T> &v, F &&f) {
  return std::all_of(v.begin(), v.end(), f);
}
class Sorted {
 private:
  const std::vector<long long> &vec_;

 public:
  Sorted(const std::vector<long long> &vec) : vec_(vec) {}

  long long CountInRange(long long begin, long long end) {
    return std::lower_bound(vec_.begin(), vec_.end(), end) -
           std::lower_bound(vec_.begin(), vec_.end(), begin);
  }

  long long CountSmaller(long long x) {
    return std::lower_bound(vec_.begin(), vec_.end(), x) - vec_.begin();
  }

  long long CountLarger(long long x) {
    return vec_.end() - std::upper_bound(vec_.begin(), vec_.end(), x);
  }

  long long CountFrom(long long x) {
    return vec_.end() - std::lower_bound(vec_.begin(), vec_.end(), x);
  }

  long long CountTo(long long x) {
    return std::upper_bound(vec_.begin(), vec_.end(), x) - vec_.begin();
  }
};
inline long long PowMod(long long x, long long n, const long long m) {
  assert(n >= 0);
  assert(m != 0);
  if (x == 0) return 0;
  long long res = 1;
  x = Mod(x, m);
  while (n > 0) {
    if (n & 1) {
      assert(x == 0 || std::abs(res) <= kMax / std::abs(x));
      res = Mod(res * x, m);
    }
    if (n >>= 1) {
      assert(x == 0 || std::abs(x) <= kMax / std::abs(x));
      x = Mod(x * x, m);
    }
  }
  return res;
}
void Print(std::string s) { cout << s << '\n'; }
void Print(long long x) { cout << x << '\n'; }
template <typename T>
void Print(std::vector<T> v) {
  for (int i = 0; i < v.size(); ++i) {
    cout << v[i] << " \n"[i == v.size() - 1];
  }
}
}  // namespace util
using namespace util;

#include <algorithm>
#include <cassert>
#include <vector>

template <typename T>
class Matrix {
 private:
  int row_, col_;

 public:
  std::vector<std::vector<T>> m_;

  Matrix(int row, int col) : row_(row), col_(col), m_() {}

  Matrix(int row, int col, T x)
      : row_(row), col_(col), m_(row, std::vector<T>(col)) {
    for (int i = 0; i < row_; i++) {
      for (int j = 0; j < col_; j++) m_[i][j] = x;
    }
  }

  Matrix(std::vector<std::vector<T>> &m)
      : row_((int)m.size()), col_((int)m[0].size()), m_(m) {}

  Matrix(std::initializer_list<std::vector<T>> init) : m_(init) {
    row_ = (int)m_.size();
    col_ = (int)m_[0].size();
  }

  bool operator==(const Matrix &x) {
    if (row_ != x.n || col_ != x.m) return false;
    for (int i = 0; i < row_; i++) {
      for (int j = 0; j < col_; j++) {
        if (m_[i][j] != x[i][j]) return false;
      }
    }
    return true;
  }

  Matrix &operator=(const Matrix &x) = default;

  Matrix operator+(const Matrix &x) {
    assert(row_ == x.row_ && col_ == x.col_);
    Matrix res(m_);
    for (int i = 0; i < row_; i++) {
      for (int j = 0; j < col_; j++) {
        res.m_[i][j] += x.m_[i][j];
      }
    }
    return res;
  }

  Matrix operator-(const Matrix &x) {
    assert(row_ == x.row_ && col_ == x.col_);
    Matrix res(m_);
    for (int i = 0; i < row_; i++) {
      for (int j = 0; j < col_; j++) {
        res.m_[i][j] -= x.m_[i][j];
      }
    }
    return res;
  }

  Matrix operator*(const Matrix &x) {
    assert(col_ == x.row_);
    Matrix res(row_, x.col_, T());
    for (int i = 0; i < row_; i++) {
      for (int k = 0; k < col_; k++) {
        for (int j = 0; j < x.col_; j++) {
          res.m_[i][j] += m_[i][k] * x.m_[k][j];
        }
      }
    }
    return res;
  }

  std::vector<T> operator*(const std::vector<T> &v) {
    assert(col_ == (int)v.size());
    std::vector<T> res(row_, 0);
    for (int i = 0; i < row_; i++) {
      for (int j = 0; j < col_; j++) {
        res[i] += m_[i][j] * v[j];
      }
    }
    return res;
  }

  Matrix &operator+=(const Matrix &x) {
    *this = *this + x;
    return *this;
  }

  Matrix &operator-=(const Matrix &x) {
    *this = *this - x;
    return *this;
  }

  Matrix &operator*=(const Matrix &x) {
    *this = *this * x;
    return *this;
  }

  T &operator()(long long i, long long j) { return m_[i][j]; }

  std::vector<T> &operator[](long long i) { return m_[i]; }

  Matrix pow(long long k) {
    assert(k >= 0);
    assert(row_ == col_);
    std::vector<std::vector<T>> x(row_, std::vector<T>(row_));
    for (int i = 0; i < row_; i++) x[i][i] = 1;
    Matrix res(x), tmp = *this;
    while (k) {
      if (k & 1) res *= tmp;
      k >>= 1;
      tmp *= tmp;
    }
    return res;
  }

  Matrix transpose() {
    Matrix<T> ret(col_, row_, 0);
    for (int i = 0; i < col_; i++) {
      for (int j = 0; j < row_; j++) {
        ret[i][j] = (*this)[j][i];
      }
    }
    return ret;
  }
};

template <typename T>
Matrix<T> DiagonalMatrix(const int n, const T d) {
  Matrix<T> res(n, n);
  for (int i = 0; i < n; i++) res.m_[i][i] = d;
  return res;
}

template <typename T>
Matrix<T> IdentityMatrix(const int n) {
  return diag(n, T(1));
}

std::vector<long long> GaussianElimination(
    const std::vector<long long> &binary_vectors) {
  std::vector<long long> basis;
  for (auto v : binary_vectors) {
    for (long long e : basis) {
      v = std::min(v, v ^ e);
    }
    if (v > 0) basis.emplace_back(v);
  }
  std::sort(basis.begin(), basis.end());
  int k = (int)basis.size();
  for (int i = 0; i < k; ++i) {
    int msb = __builtin_clzll(basis[i]);
    long long e = (1LL << (63 - msb));
    for (int j = i + 1; j < k; ++j) {
      if (basis[j] & e) basis[j] ^= basis[i];
    }
  }
  return basis;
}

#include <atcoder/modint>
using namespace atcoder;
using F2 = static_modint<2>;


void solve() {
  ll n;
  cin >> n;
  vector<unsigned long long> a(1 << n);
  vector<vector<F2>> a_bit(1 << n, vector<F2>(64));
  rep(i, 1 << n) {
    cin >> a[i];
    rep(j, 64) { a_bit[i][j] = ((a[i] & (1ul << j)) != 0); }
  }
  Matrix<F2> M(64, n, 0);
  rep(i, n) {
    rep(j, 64) { M[j][i] = ((a[1 << i] & (1ul << j)) != 0); }
  }
  rep(bits, 1 << n) {
    vector<F2> bit_v(n);
    rep(i, n) { bit_v[i] = ((bits & (1ll << i)) != 0); }
    auto v = M * bit_v;
    if (v != a_bit[bits]) {
      Print("No");
      return;
    }
  }
  Print("Yes");
}

int main() {
  std::cin.tie(nullptr);
  std::ios::sync_with_stdio(false);
  std::cout << std::fixed << std::setprecision(15);

  solve();

  return 0;
}
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