#379817 (C++14) No.147 試験監督（2）

提出ソース
結果

問題	No.147 試験監督（2）
ユーザー	fumiphys
提出日時	2019-09-16 17:53:06
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	830 ms / 2,000 ms
コード長	12,197 bytes
コンパイル時間	2,449 ms
コンパイル使用メモリ	189,488 KB
実行使用メモリ	6,940 KB
最終ジャッジ日時	2024-07-07 02:26:04
合計ジャッジ時間	6,029 ms
ジャッジサーバーID （参考情報）	judge1 / judge3
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	824 ms 6,816 KB
testcase_01	AC	824 ms 6,812 KB
testcase_02	AC	830 ms 6,940 KB
testcase_03	AC	2 ms 6,940 KB
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ソースコード

raw source code
// includes
#include <bits/stdc++.h>
using namespace std;

// macros
#define pb emplace_back
#define mk make_pair
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define rep(i, n) FOR(i, 0, n)
#define rrep(i, n) for(int i=((int)(n)-1);i>=0;i--)
#define irep(itr, st) for(auto itr = (st).begin(); itr != (st).end(); ++itr)
#define irrep(itr, st) for(auto itr = (st).rbegin(); itr != (st).rend(); ++itr)
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())
#define bit(n) (1LL<<(n))
// functions
template <class T>bool chmax(T &a, const T &b){if(a < b){a = b; return 1;} return 0;}
template <class T>bool chmin(T &a, const T &b){if(a > b){a = b; return 1;} return 0;}
template <typename T> istream &operator>>(istream &is, vector<T> &vec){for(auto &v: vec)is >> v; return is;}
template <typename T> ostream &operator<<(ostream &os, const vector<T>& vec){for(int i = 0; i < vec.size(); i++){ os << vec[i]; if(i + 1 != vec.size())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
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> ostream &operator<<(ostream &os, const map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const unordered_map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}
//  types
using ll = long long int;
using P = pair<int, int>;
// constants
const int inf = 1e9;
const ll linf = 1LL << 50;
const double EPS = 1e-10;
const int mod = 1000000007;
const int dx[4] = {-1, 0, 1, 0};
const int dy[4] = {0, -1, 0, 1};
// io
struct fast_io{
  fast_io(){ios_base::sync_with_stdio(false); cin.tie(0); cout << fixed << setprecision(20);}
} fast_io_;

const ll B = 10000;
const int BW = 4;
struct BigInt{
  vector<ll> digit;
  BigInt(ll a = 0){
    digit.emplace_back(a);
    normalize();
  }
  BigInt(const string &s){
    from_string(s);
  }
  void from_string(const string &s){
    digit.clear();
    int i;
    for(i = (int)s.size() - BW; i >= 0; i-=BW){
      digit.emplace_back(stol(s.substr(i, BW)));
    }
    i += BW;
    if(i > 0)digit.emplace_back(stol(s.substr(0, i)));
  }
  void normalize(){
    ll c = 0;
    for(int i = 0; i < digit.size(); i++){
      while(digit[i] < 0){
        if(i + 1 == digit.size())digit.emplace_back(0);
        digit[i+1]--;
        digit[i] += B;
      }
      ll a = digit[i] + c;
      digit[i] = a % B;
      c = a / B;
    }
    while(c){
      digit.emplace_back(c % B);
      c /= B;
    }
    for(int i = (int)digit.size() - 1; i >= 1; i--){
      if(digit[i] == 0){
        digit.pop_back();
      }else{
        break;
      }
    }
  }
  size_t size(){
    return digit.size();
  }
  BigInt& operator=(ll a){
    digit.resize(1, a);
    normalize();
    return *this;
  }
  BigInt& operator=(const string &s){
    from_string(s);
    return *this;
  }
} ZERO(0), ONE(1);

ostream &operator<<(ostream &os, const BigInt &b){
  os << b.digit[b.digit.size() - 1];
  for(int i = (int)b.digit.size() - 2; i >= 0; i--){
    os << setw(BW) << setfill('0') << b.digit[i];
  }
  return os;
}

istream & operator>>(istream &is, BigInt &b){
  string s;
  is >> s;
  b.from_string(s);
  return is;
}

bool operator<(const BigInt &x, const BigInt &y){
  if(x.digit.size() != y.digit.size())return x.digit.size() < y.digit.size();
  for(int i = x.digit.size() - 1; i >= 0; i--){
    if(x.digit[i] != y.digit[i])return x.digit[i] < y.digit[i];
  }
  return false;
}

bool operator>(const BigInt &x, const BigInt y){
  return y < x;
}

bool operator<=(const BigInt &x, const BigInt &y){
  return !(y < x);
}

bool operator>=(const BigInt &x, const BigInt &y){
  return !(x < y);
}

bool operator!=(const BigInt &x, const BigInt &y){
  return x < y || y < x;
}

bool operator==(const BigInt &x, const BigInt &y){
  return !(x < y) && !(y < x);
}

BigInt operator+(const BigInt &x, ll a){
  BigInt res = x;
  res.digit[0] += a;
  res.normalize();
  return res;
}

BigInt operator+(const BigInt &x, const BigInt &y){
  BigInt res = x;
  while(res.digit.size() < y.digit.size())res.digit.emplace_back(0);
  for(int i = 0; i < y.digit.size(); i++)res.digit[i] += y.digit[i];
  res.normalize();
  return res;
}

BigInt operator-(const BigInt &x, const BigInt &y){
  BigInt res = x;
  assert(res.digit.size() >= y.digit.size());
  for(int i = 0; i < y.digit.size(); i++)res.digit[i] -= y.digit[i];
  res.normalize();
  return res;
}

BigInt operator*(const BigInt &x, const BigInt &y){
  BigInt z;
  z.digit.assign(x.digit.size() + y.digit.size(), 0);
  for(int i = 0; i < x.digit.size(); i++){
    for(int j = 0; j < y.digit.size(); j++){
      z.digit[i+j] += x.digit[i] * y.digit[j];
    }
  }
  z.normalize();
  return z;
}

BigInt operator*(const BigInt &x, ll a){
  BigInt res = x;
  for(int i = 0; i < res.digit.size(); i++)res.digit[i] *= a;
  res.normalize();
  return res;
}

pair<BigInt, ll> divmod(const BigInt &x, ll a){
  ll c = 0;
  BigInt res = x;
  for(int i = (int)res.digit.size() - 1; i >= 0; i--){
    ll t = B * c + res.digit[i];
    res.digit[i] = t / a;
    c = t % a;
  }
  res.normalize();
  return make_pair(res, c);
}

BigInt operator/(const BigInt &x, ll a){
  return divmod(x, a).first;
}

BigInt operator%(const BigInt &x, ll a){
  return divmod(x, a).second;
}

pair<BigInt, BigInt> divmod(const BigInt &x, const BigInt &y){
  BigInt rx = x, ry = y;
  if(x.digit.size() < y.digit.size())return make_pair(ZERO, x);
  int F = B / (y.digit[y.digit.size() - 1] + 1);
  rx = rx * F; ry = ry * F;
  BigInt z;
  z.digit.assign(rx.digit.size() - ry.digit.size() + 1, 0);
  for(int k = (int)z.digit.size() - 1, i = (int)rx.digit.size() - 1; k >= 0; k--, i--){
    z.digit[k] = (i + 1 < rx.digit.size() ? rx.digit[i+1]: 0) * B + rx.digit[i];
    z.digit[k] /= ry.digit[ry.digit.size() - 1];
    BigInt t;
    t.digit.assign(k + ry.digit.size(), 0);
    for(int m = 0; m < ry.digit.size(); m++){
      t.digit[k+m] = z.digit[k] * ry.digit[m];
    }
    t.normalize();
    while(rx < t){
      z.digit[k] -= 1;
      for(int m = 0; m < ry.digit.size(); m++){
        t.digit[k+m] -= ry.digit[m];
      }
      t.normalize();
    }
    rx = rx - t;
  }
  z.normalize();
  return make_pair(z, rx / F);
}

BigInt operator/(const BigInt &x, const BigInt &y){
  return divmod(x, y).first;
}

BigInt operator%(const BigInt &x, const BigInt &y){
  return divmod(x, y).second;
}

BigInt& operator+=(BigInt &x, ll a){
  x = x + a;
  return x;
}

BigInt &operator+=(BigInt &x, const BigInt &y){
  x = x + y;
  return x;
}

BigInt &operator-=(BigInt &x, const BigInt &y){
  x = x - y;
  return x;
}

BigInt& operator*=(BigInt &x, const BigInt &y){
  x = x * y;
  return x;
}

BigInt& operator/=(BigInt &x, const BigInt &y){
  x = x / y;
  return x;
}

BigInt& operator%=(BigInt &x, const BigInt &y){
  x = x % y;
  return x;
}

BigInt& operator/=(BigInt &x, ll a){
  x = x / a;
  return x;
}

BigInt& operator%=(BigInt &x, ll a){
  x = x % a;
  return x;
}

BigInt sqrt(const BigInt &x){
  BigInt l = 1;
  BigInt r = x;
  while(r - l > BigInt(1)){
    BigInt m = (r + l) / 2;
    if(m * m > x)r = m;
    else l = m;
  }
  return l;
}

template<typename T>
T extgcd(T a, T b, T &x, T &y){ 
  T d = a;
  if(b != 0){
    d = extgcd(b, a % b, y, x);
    y -= (a / b) * x;
  }else{
    x = 1, y = 0;
  }
  return d;
}

template <typename T>
T modinv(T a, T m){
  long long x = 0, y = 0;
  extgcd<long long>(a, m, x, y);
  x %= m;
  if(x < 0)x += m;
  return x;
}


template <int MOD = int(1e9+7)>
struct LMatrix{
  vector<vector<long long>> v;
  int n, m;
  LMatrix(int n_, int m_ = -1): n(n_), m(m_){
    if(m < 0)m = n;
    v.resize(n);
    for(int i = 0; i < n; i++)v[i].resize(m);
  }
  void identity(){
    assert(n == m);
    for(int i = 0; i < n; i++){
      for(int j = 0; j < n; j++){
        v[i][j] = (i == j ? 1: 0);
      }
    }
  }
  vector<long long> &operator[](size_t i){
    return v[i];
  }
  const vector<long long> &operator[](size_t i) const{
    return v[i];
  }
  LMatrix operator*(const LMatrix &r) const{
    assert(m == r.n);
    int l = r.m;
    LMatrix res(n, l);
    for(int i = 0; i < n; i++){
      for(int j = 0; j < l; j++){
        res.v[i][j] = 0;
        for(int k = 0; k < m; k++){
          res.v[i][j] = (res.v[i][j] + v[i][k] * r.v[k][j] % MOD) % MOD;
        }
      }
    }
    return res;
  }
  LMatrix operator+(const LMatrix &r) const{
    assert(n == r.n);
    assert(m == r.m);
    LMatrix res(n, m);
    for(int i = 0; i < n; i++){
      for(int j = 0; j < m; j++){
        res[i][j] = (v[i][j] + r[i][j]) % MOD;
      }
    }
    return res;
  }
  LMatrix operator-(const LMatrix &r) const{
    assert(n == r.n);
    assert(m == r.m);
    LMatrix res(n, m);
    for(int i = 0; i < n; i++){
      for(int j = 0; j < m; j++){
        res[i][j] = (v[i][j] - r[i][j]) % MOD;
        if(res[i][j] < 0)res[i][j] += MOD;
      }
    }
    return res;
  }
  template <typename T>
  LMatrix operator*(T a) const{
    LMatrix res = *this;
    for(int i = 0; i < n; i++){
      for(int j = 0; j < n; j++){
        res[i][j] = a * res[i][j] % MOD;
      }
    }
    return res;
  }
  LMatrix inv2() const{
    assert(n == 2 && m == 2);
    long long det = v[0][0] * v[1][1] % MOD - v[0][1] * v[1][0] % MOD;
    if(det < 0)det += MOD;
    assert(det != 0);
    LMatrix res(2, 2);
    long long inv = modinv(det, (long long)MOD);
    res[0][0] = v[1][1];
    res[1][1] = v[0][0];
    res[1][0] = - v[1][0];
    res[0][1] = - v[0][1];
    for(int i = 0; i < n; i++){
      for(int j = 0; j < m; j++){
        res[i][j] %= MOD;
        res[i][j] = res[i][j] * inv % MOD;
        if(res[i][j] < 0)res[i][j] += MOD;
      }
    }
    return res;
  }
};

template <typename T, int MOD = int(1e9+7)>
LMatrix<MOD> operator*(T a, const LMatrix<MOD> b){
  return b * a;
}

template <int MOD = int(1e9+7)>
LMatrix<MOD> powerm(LMatrix<MOD> &a, long long n){
  long long tmp = n;
  LMatrix<MOD> curr = a;
  LMatrix<MOD> res(a.n);
  res.identity();
  while(tmp){
    if(tmp % 2 == 1){
      res = res * curr;
    }
    curr = curr * curr;
    tmp /= 2;
  }
  return res;
}

template <typename T>
T power(T a, T n, T mod) {
  T res = 1;
  T tmp = n;
  T curr = a;
  while(tmp){
    if(tmp % 2 == 1){
      res = (T)(res * curr % mod);
    }
    curr = (T)(curr * curr % mod);
    tmp >>= 1;
  }

  return res;
}


// dp[i][0] = dp[i-1][0] + dp[i-1][1]
// dp[i][1] = dp[i-1][0]
// | 1 1 |
// | 1 0 |

int main(int argc, char const* argv[])
{
  int n;
  cin >> n;
  ll res = 1;
  LMatrix<> lm(2, 2);
  lm[0][0] = 1;
  lm[1][0] = 1;
  lm[0][1] = 1;
  BigInt MOD = BigInt(mod);
  rep(i, n){
    ll c;
    string d;
    cin >> c >> d;
    BigInt D(d);
    D %= (MOD - 1);
    ll dd = 0;
    ll ba = 1;
    for(int j = 0; j < min(3, (int)D.digit.size()); j++){
      dd = (dd + ba * D.digit[j] % mod) % mod;
      ba = ba * (ll)B % mod;
    }
    auto p = powerm(lm, c);
    ll tmp = (p[0][0] + p[1][0]) % mod;
    if(tmp > 0)tmp = power<ll>(tmp, dd, mod);
    res = res * tmp % mod;
  }
  cout << res << endl;
  return 0;
}
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結果

テストケース

ソースコード
