#407983 (C++17) No.950 行列累乗

提出ソース

結果

問題	No.950 行列累乗
ユーザー	ei1333333
提出日時	2019-12-13 01:20:48
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	TLE
実行時間	-
コード長	8,189 bytes
コンパイル時間	2,547 ms
コンパイル使用メモリ	224,240 KB
実行使用メモリ	9,224 KB
最終ジャッジ日時	2023-09-08 09:32:40
合計ジャッジ時間	132,847 ms
ジャッジサーバーID （参考情報）	judge13 / 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	TLE	-
testcase_01	TLE	-
testcase_02	AC	1 ms 4,376 KB
testcase_03	TLE	-
testcase_04	TLE	-
testcase_05	AC	2 ms 4,380 KB
testcase_06	TLE	-
testcase_07	AC	1 ms 4,380 KB
testcase_08	AC	58 ms 4,376 KB
testcase_09	TLE	-
testcase_10	AC	2 ms 4,380 KB
testcase_11	AC	2 ms 4,384 KB
testcase_12	TLE	-
testcase_13	AC	953 ms 4,384 KB
testcase_14	TLE	-
testcase_15	TLE	-
testcase_16	AC	39 ms 4,380 KB
testcase_17	AC	2 ms 4,376 KB
testcase_18	TLE	-
testcase_19	AC	2 ms 4,376 KB
testcase_20	AC	1 ms 4,380 KB
testcase_21	TLE	-
testcase_22	TLE	-
testcase_23	TLE	-
testcase_24	TLE	-
testcase_25	TLE	-
testcase_26	TLE	-
testcase_27	TLE	-
testcase_28	TLE	-
testcase_29	TLE	-
testcase_30	TLE	-
testcase_31	TLE	-
testcase_32	TLE	-
testcase_33	TLE	-
testcase_34	TLE	-
testcase_35	TLE	-
testcase_36	TLE	-
testcase_37	TLE	-
testcase_38	TLE	-
testcase_39	TLE	-
testcase_40	TLE	-
testcase_41	TLE	-
testcase_42	TLE	-
testcase_43	TLE	-
testcase_44	TLE	-
testcase_45	TLE	-
testcase_46	TLE	-
testcase_47	AC	2 ms 4,380 KB
testcase_48	TLE	-
testcase_49	TLE	-
testcase_50	TLE	-
testcase_51	TLE	-
testcase_52	TLE	-
testcase_53	TLE	-
testcase_54	AC	1 ms 4,376 KB
testcase_55	AC	1 ms 4,380 KB
testcase_56	TLE	-
testcase_57	AC	2 ms 4,376 KB
testcase_58	AC	1 ms 4,376 KB
testcase_59	TLE	-
testcase_60	TLE	-

権限があれば一括ダウンロードができます

ソースコード

raw source code

#include <bits/stdc++.h>

using namespace std;

using int64 = __int128_t;
const int mod = 1e9 + 7;
// const int mod = 998244353;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;


template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 > &p) {
  os << p.first << " " << p.second;
  return os;
}

template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
  is >> p.first >> p.second;
  return is;
}

template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
  for(int i = 0; i < (int) v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
  for(T &in : v) is >> in;
  return is;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

template< typename T = int64 >
vector< T > make_v(size_t a) {
  return vector< T >(a);
}

template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
  return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}

template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
  t = v;
}

template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
  for(auto &e : t) fill_v(e, v);
}

template< typename F >
struct FixPoint : F {
  FixPoint(F &&f) : F(forward< F >(f)) {}

  template< typename... Args >
  decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, forward< Args >(args)...);
  }
};

template< typename F >
inline decltype(auto) MFP(F &&f) {
  return FixPoint< F >{forward< F >(f)};
}

template< class T >
struct Matrix {
  vector< vector< T > > A;

  Matrix() {}

  Matrix(size_t n, size_t m) : A(n, vector< T >(m, 0)) {}

  Matrix(size_t n) : A(n, vector< T >(n, 0)) {};

  size_t height() const {
    return (A.size());
  }

  size_t width() const {
    return (A[0].size());
  }

  inline const vector< T > &operator[](int k) const {
    return (A.at(k));
  }

  inline vector< T > &operator[](int k) {
    return (A.at(k));
  }

  static Matrix I(size_t n) {
    Matrix mat(n);
    for(int i = 0; i < n; i++) mat[i][i] = 1;
    return (mat);
  }

  Matrix &operator+=(const Matrix &B) {
    size_t n = height(), m = width();
    assert(n == B.height() && m == B.width());
    for(int i = 0; i < n; i++)
      for(int j = 0; j < m; j++)
        (*this)[i][j] += B[i][j];
    return (*this);
  }

  Matrix &operator-=(const Matrix &B) {
    size_t n = height(), m = width();
    assert(n == B.height() && m == B.width());
    for(int i = 0; i < n; i++)
      for(int j = 0; j < m; j++)
        (*this)[i][j] -= B[i][j];
    return (*this);
  }

  Matrix &operator*=(const Matrix &B) {
    size_t n = height(), m = B.width(), p = width();
    assert(p == B.height());
    vector< vector< T > > C(n, vector< T >(m, 0));
    for(int i = 0; i < n; i++)
      for(int j = 0; j < m; j++)
        for(int k = 0; k < p; k++)
          C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
    A.swap(C);
    return (*this);
  }

  Matrix &operator^=(int64 k) {
    Matrix B = Matrix::I(height());
    while(k > 0) {
      if(k & 1) B *= *this;
      *this *= *this;
      k >>= 1LL;
    }
    A.swap(B.A);
    return (*this);
  }

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

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

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

  Matrix operator^(const long long k) const {
    return (Matrix(*this) ^= k);
  }

  friend ostream &operator<<(ostream &os, Matrix &p) {
    size_t n = p.height(), m = p.width();
    for(int i = 0; i < n; i++) {
      os << "[";
      for(int j = 0; j < m; j++) {
        os << p[i][j] << (j + 1 == m ? "]\n" : ",");
      }
    }
    return (os);
  }


  T determinant() {
    Matrix B(*this);
    assert(width() == height());
    T ret = 1;
    for(int i = 0; i < width(); i++) {
      int idx = -1;
      for(int j = i; j < width(); j++) {
        if(B[j][i] != 0) idx = j;
      }
      if(idx == -1) return (0);
      if(i != idx) {
        ret *= -1;
        swap(B[i], B[idx]);
      }
      ret *= B[i][i];
      T vv = B[i][i];
      for(int j = 0; j < width(); j++) {
        B[i][j] /= vv;
      }
      for(int j = i + 1; j < width(); j++) {
        T a = B[j][i];
        for(int k = 0; k < width(); k++) {
          B[j][k] -= B[i][k] * a;
        }
      }
    }
    return (ret);
  }
};


struct ArbitraryModInt {

  int64 x;

  ArbitraryModInt() : x(0) {}

  ArbitraryModInt(int64 y) : x(y >= 0 ? y % mod() : (mod() - (-y) % mod()) % mod()) {}

  static int64 &mod() {
    static int64 mod = 0;
    return mod;
  }

  static void set_mod(int md) {
    mod() = md;
  }

  ArbitraryModInt &operator+=(const ArbitraryModInt &p) {
    if((x += p.x) >= mod()) x -= mod();
    return *this;
  }

  ArbitraryModInt &operator-=(const ArbitraryModInt &p) {
    if((x += mod() - p.x) >= mod()) x -= mod();
    return *this;
  }

  ArbitraryModInt &operator*=(const ArbitraryModInt &p) {
    x = (__int128_t) x * p.x % mod();
    return *this;
  }

  ArbitraryModInt &operator/=(const ArbitraryModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ArbitraryModInt operator-() const { return ArbitraryModInt(-x); }

  ArbitraryModInt operator+(const ArbitraryModInt &p) const { return ArbitraryModInt(*this) += p; }

  ArbitraryModInt operator-(const ArbitraryModInt &p) const { return ArbitraryModInt(*this) -= p; }

  ArbitraryModInt operator*(const ArbitraryModInt &p) const { return ArbitraryModInt(*this) *= p; }

  ArbitraryModInt operator/(const ArbitraryModInt &p) const { return ArbitraryModInt(*this) /= p; }

  bool operator==(const ArbitraryModInt &p) const { return x == p.x; }

  bool operator!=(const ArbitraryModInt &p) const { return x != p.x; }

  ArbitraryModInt inverse() const {
    int64 a = x, b = mod(), u = 1, v = 0, t;
    while(b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ArbitraryModInt(u);
  }

  ArbitraryModInt pow(int64 n) const {
    ArbitraryModInt ret(1), mul(x);
    while(n > 0) {
      if(n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ArbitraryModInt &p) {
    return os << (int64_t) p.x;
  }

  friend istream &operator>>(istream &is, ArbitraryModInt &a) {
    int64_t t;
    is >> t;
    a = ArbitraryModInt(t);
    return (is);
  }
};


template< typename T >
void mod_log(T a, T b, int64 p) {
  int64 ok = p, ng = -1;
  while(ok - ng > 1) {
    auto mid = (ok + ng) / 2;
    if(mid * mid >= p) ok = mid;
    else ng = mid;
  }
  map< tuple< int64, int64, int64, int64 >, int64 > baby;
  T factor = T::I(2);
  T e(b);
  for(int64 i = 0; i < ok; i++) {
    baby[{e[0][0].x, e[0][1].x, e[1][0].x, e[1][1].x}] = i;
    factor *= a;
    e *= a;
  }
  e = factor;
  int64 ret = infll;
  for(int64 i = 1; i <= ok; i++) {
    auto it = baby.find({e[0][0].x, e[0][1].x, e[1][0].x, e[1][1].x});
    if(it != end(baby)) {
      int64 x = i * ok - it->second;
      auto tap = a ^x;
      if(tap[0] == b[0] && tap[1] == b[1]) {
        chmin(ret, x);
      }
    }
    e *= factor;
  }
  if(ret == infll) cout << -1 << endl;
  else cout << (int64_t) ret << endl;
}

int main() {
  int P;
  cin >> P;
  ArbitraryModInt::set_mod(P);
  Matrix< ArbitraryModInt > A(2), B(2);
  for(int i = 0; i < 2; i++) cin >> A[i];
  for(int i = 0; i < 2; i++) cin >> B[i];

  Matrix< ArbitraryModInt > C = Matrix< ArbitraryModInt >::I(2);
  for(int i = 1; i <= 10000000; i++) {
    C *= A;
    if(C[0] == B[0] && C[1] == B[1]) {
      cout << i << endl;
      return 0;
    }
  }

  mod_log(A, B, P);
}

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結果

テストケース

ソースコード