#156878 (C++11) No.492 IOI数列

• 問題: No.492 IOI数列
• ユーザー: ei1333333
• 提出日時: 2017-03-10 23:26:50
• 言語: C++11 (gcc 11.4.0)
• 結果: AC
• 実行時間: 8 ms / 1,000 ms
• コード長: 10,293 bytes
• コンパイル時間: 2,546 ms
• コンパイル使用メモリ: 194,300 KB
• 実行使用メモリ: 6,944 KB
• 最終ジャッジ日時: 2024-06-24 08:46:42
• 合計ジャッジ時間: 3,217 ms
• ジャッジサーバーID （参考情報）: judge2 / judge4

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 6,812 KB
testcase_01	AC	8 ms; 6,940 KB
testcase_02	AC	8 ms; 6,940 KB
testcase_03	AC	8 ms; 6,940 KB
testcase_04	AC	5 ms; 6,940 KB
testcase_05	AC	5 ms; 6,940 KB
testcase_06	AC	7 ms; 6,944 KB
testcase_07	AC	8 ms; 6,940 KB
testcase_08	AC	7 ms; 6,940 KB
testcase_09	AC	7 ms; 6,944 KB
testcase_10	AC	1 ms; 6,944 KB
testcase_11	AC	2 ms; 6,940 KB
testcase_12	AC	3 ms; 6,944 KB
testcase_13	AC	1 ms; 6,940 KB
testcase_14	AC	2 ms; 6,940 KB
testcase_15	AC	2 ms; 6,940 KB
testcase_16	AC	2 ms; 6,940 KB
testcase_17	AC	2 ms; 6,940 KB
testcase_18	AC	3 ms; 6,944 KB
testcase_19	AC	3 ms; 6,940 KB
testcase_20	AC	3 ms; 6,944 KB
testcase_21	AC	4 ms; 6,940 KB

ソースコード

#include<bits/stdc++.h>

using namespace std;

// ごめんなさいその2

const int base = 1000000000;
const int base_digits = 9;

struct bigint
{
  vector< int > a;
  int sign;

  bigint() :
      sign(1)
  {
  }

  bigint(long long v)
  {
    *this = v;
  }

  bigint(const string &s)
  {
    read(s);
  }

  void operator=(const bigint &v)
  {
    sign = v.sign;
    a = v.a;
  }

  void operator=(long long v)
  {
    sign = 1;
    if(v < 0)
      sign = -1, v = -v;
    for(; v > 0; v = v / base)
      a.push_back(v % base);
  }

  bigint operator+(const bigint &v) const
  {
    if(sign == v.sign) {
      bigint res = v;

      for(int i = 0, carry = 0; i < (int) max(a.size(), v.a.size()) || carry; ++i) {
        if(i == (int) res.a.size())
          res.a.push_back(0);
        res.a[i] += carry + (i < (int) a.size() ? a[i] : 0);
        carry = res.a[i] >= base;
        if(carry)
          res.a[i] -= base;
      }
      return res;
    }
    return *this - (-v);
  }

  bigint operator-(const bigint &v) const
  {
    if(sign == v.sign) {
      if(abs() >= v.abs()) {
        bigint res = *this;
        for(int i = 0, carry = 0; i < (int) v.a.size() || carry; ++i) {
          res.a[i] -= carry + (i < (int) v.a.size() ? v.a[i] : 0);
          carry = res.a[i] < 0;
          if(carry)
            res.a[i] += base;
        }
        res.trim();
        return res;
      }
      return -(v - *this);
    }
    return *this + (-v);
  }

  void operator*=(int v)
  {
    if(v < 0)
      sign = -sign, v = -v;
    for(int i = 0, carry = 0; i < (int) a.size() || carry; ++i) {
      if(i == (int) a.size())
        a.push_back(0);
      long long cur = a[i] * (long long) v + carry;
      carry = (int) (cur / base);
      a[i] = (int) (cur % base);
      //asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur), "c"(base));
    }
    trim();
  }

  bigint operator*(int v) const
  {
    bigint res = *this;
    res *= v;
    return res;
  }

  friend pair< bigint, bigint > divmod(const bigint &a1, const bigint &b1)
  {
    int norm = base / (b1.a.back() + 1);
    bigint a = a1.abs() * norm;
    bigint b = b1.abs() * norm;
    bigint q, r;
    q.a.resize(a.a.size());

    for(int i = a.a.size() - 1; i >= 0; i--) {
      r *= base;
      r += a.a[i];
      int s1 = r.a.size() <= b.a.size() ? 0 : r.a[b.a.size()];
      int s2 = r.a.size() <= b.a.size() - 1 ? 0 : r.a[b.a.size() - 1];
      int d = ((long long) base * s1 + s2) / b.a.back();
      r -= b * d;
      while(r < 0)
        r += b, --d;
      q.a[i] = d;
    }

    q.sign = a1.sign * b1.sign;
    r.sign = a1.sign;
    q.trim();
    r.trim();
    return make_pair(q, r / norm);
  }

  bigint operator/(const bigint &v) const
  {
    return divmod(*this, v).first;
  }

  bigint operator%(const bigint &v) const
  {
    return divmod(*this, v).second;
  }

  void operator/=(int v)
  {
    if(v < 0)
      sign = -sign, v = -v;
    for(int i = (int) a.size() - 1, rem = 0; i >= 0; --i) {
      long long cur = a[i] + rem * (long long) base;
      a[i] = (int) (cur / v);
      rem = (int) (cur % v);
    }
    trim();
  }

  bigint operator/(int v) const
  {
    bigint res = *this;
    res /= v;
    return res;
  }

  int operator%(int v) const
  {
    if(v < 0)
      v = -v;
    int m = 0;
    for(int i = a.size() - 1; i >= 0; --i)
      m = (a[i] + m * (long long) base) % v;
    return m * sign;
  }

  void operator+=(const bigint &v)
  {
    *this = *this + v;
  }

  void operator-=(const bigint &v)
  {
    *this = *this - v;
  }

  void operator*=(const bigint &v)
  {
    *this = *this * v;
  }

  void operator/=(const bigint &v)
  {
    *this = *this / v;
  }

  bool operator<(const bigint &v) const
  {
    if(sign != v.sign)
      return sign < v.sign;
    if(a.size() != v.a.size())
      return a.size() * sign < v.a.size() * v.sign;
    for(int i = a.size() - 1; i >= 0; i--)
      if(a[i] != v.a[i])
        return a[i] * sign < v.a[i] * sign;
    return false;
  }

  bool operator>(const bigint &v) const
  {
    return v < *this;
  }

  bool operator<=(const bigint &v) const
  {
    return !(v < *this);
  }

  bool operator>=(const bigint &v) const
  {
    return !(*this < v);
  }

  bool operator==(const bigint &v) const
  {
    return !(*this < v) && !(v < *this);
  }

  bool operator!=(const bigint &v) const
  {
    return *this < v || v < *this;
  }

  void trim()
  {
    while(!a.empty() && !a.back())
      a.pop_back();
    if(a.empty())
      sign = 1;
  }

  bool isZero() const
  {
    return a.empty() || (a.size() == 1 && !a[0]);
  }

  bigint operator-() const
  {
    bigint res = *this;
    res.sign = -sign;
    return res;
  }

  bigint abs() const
  {
    bigint res = *this;
    res.sign *= res.sign;
    return res;
  }

  long long longValue() const
  {
    long long res = 0;
    for(int i = a.size() - 1; i >= 0; i--)
      res = res * base + a[i];
    return res * sign;
  }

  friend bigint gcd(const bigint &a, const bigint &b)
  {
    return b.isZero() ? a : gcd(b, a % b);
  }

  friend bigint lcm(const bigint &a, const bigint &b)
  {
    return a / gcd(a, b) * b;
  }

  void read(const string &s)
  {
    sign = 1;
    a.clear();
    int pos = 0;
    while(pos < (int) s.size() && (s[pos] == '-' || s[pos] == '+')) {
      if(s[pos] == '-')
        sign = -sign;
      ++pos;
    }
    for(int i = s.size() - 1; i >= pos; i -= base_digits) {
      int x = 0;
      for(int j = max(pos, i - base_digits + 1); j <= i; j++)
        x = x * 10 + s[j] - '0';
      a.push_back(x);
    }
    trim();
  }

  friend istream &operator>>(istream &stream, bigint &v)
  {
    string s;
    stream >> s;
    v.read(s);
    return stream;
  }

  friend ostream &operator<<(ostream &stream, const bigint &v)
  {
    if(v.sign == -1)
      stream << '-';
    stream << (v.a.empty() ? 0 : v.a.back());
    for(int i = (int) v.a.size() - 2; i >= 0; --i)
      stream << setw(base_digits) << setfill('0') << v.a[i];
    return stream;
  }

  static vector< int > convert_base(const vector< int > &a, int old_digits, int new_digits)
  {
    vector< long long > p(max(old_digits, new_digits) + 1);
    p[0] = 1;
    for(int i = 1; i < (int) p.size(); i++)
      p[i] = p[i - 1] * 10;
    vector< int > res;
    long long cur = 0;
    int cur_digits = 0;
    for(int i = 0; i < (int) a.size(); i++) {
      cur += a[i] * p[cur_digits];
      cur_digits += old_digits;
      while(cur_digits >= new_digits) {
        res.push_back(int(cur % p[new_digits]));
        cur /= p[new_digits];
        cur_digits -= new_digits;
      }
    }
    res.push_back((int) cur);
    while(!res.empty() && !res.back())
      res.pop_back();
    return res;
  }

  typedef vector< long long > vll;

  static vll karatsubaMultiply(const vll &a, const vll &b)
  {
    int n = a.size();
    vll res(n + n);
    if(n <= 32) {
      for(int i = 0; i < n; i++)
        for(int j = 0; j < n; j++)
          res[i + j] += a[i] * b[j];
      return res;
    }

    int k = n >> 1;
    vll a1(a.begin(), a.begin() + k);
    vll a2(a.begin() + k, a.end());
    vll b1(b.begin(), b.begin() + k);
    vll b2(b.begin() + k, b.end());

    vll a1b1 = karatsubaMultiply(a1, b1);
    vll a2b2 = karatsubaMultiply(a2, b2);

    for(int i = 0; i < k; i++)
      a2[i] += a1[i];
    for(int i = 0; i < k; i++)
      b2[i] += b1[i];

    vll r = karatsubaMultiply(a2, b2);
    for(int i = 0; i < (int) a1b1.size(); i++)
      r[i] -= a1b1[i];
    for(int i = 0; i < (int) a2b2.size(); i++)
      r[i] -= a2b2[i];

    for(int i = 0; i < (int) r.size(); i++)
      res[i + k] += r[i];
    for(int i = 0; i < (int) a1b1.size(); i++)
      res[i] += a1b1[i];
    for(int i = 0; i < (int) a2b2.size(); i++)
      res[i + n] += a2b2[i];
    return res;
  }

  bigint operator*(const bigint &v) const
  {
    vector< int > a6 = convert_base(this->a, base_digits, 6);
    vector< int > b6 = convert_base(v.a, base_digits, 6);
    vll a(a6.begin(), a6.end());
    vll b(b6.begin(), b6.end());
    while(a.size() < b.size())
      a.push_back(0);
    while(b.size() < a.size())
      b.push_back(0);
    while(a.size() & (a.size() - 1))
      a.push_back(0), b.push_back(0);
    vll c = karatsubaMultiply(a, b);
    bigint res;
    res.sign = sign * v.sign;
    for(int i = 0, carry = 0; i < (int) c.size(); i++) {
      long long cur = c[i] + carry;
      res.a.push_back((int) (cur % 1000000));
      carry = (int) (cur / 1000000);
    }
    res.a = convert_base(res.a, 6, base_digits);
    res.trim();
    return res;
  }
};


struct Matrix
{
  bigint m;
  vector< vector< bigint > > a;

  Matrix(int N, bigint mod)
  {
    m = mod;
    a.resize(N, vector< bigint >(N));
  }

  Matrix operator+(const Matrix &kj)
  {
    Matrix ret(a.size(), m);
    for(int i = 0; i < a.size(); i++) {
      for(int j = 0; j < a.size(); j++) {
        ret.a[i][j] = a[i][j] + kj.a[i][j];
        ret.a[i][j] = ret.a[i][j] % m;
      }
    }
    return (ret);
  }

  Matrix operator*(const Matrix &kj)
  {
    Matrix ret = Matrix::Zero(a.size(), m);
    for(int i = 0; i < a.size(); i++) {
      for(int j = 0; j < a.size(); j++) {
        for(int k = 0; k < a.size(); k++) {
          ret.a[i][j] = (ret.a[i][j] + a[i][k] * kj.a[k][j]) % m;
        }
      }
    }
    return (ret);
  }

  Matrix operator^(long long n)
  {
    Matrix ret = Matrix::I(a.size(), m);
    Matrix x = *this;
    while(n > 0) {
      if(n & 1) (ret = ret * x);
      x = x * x;
      n >>= 1;
    }
    return (ret);
  }

  static Matrix Zero(int N, bigint m)
  {
    Matrix ret(N, m);
    for(int i = 0; i < N; i++) {
      for(int j = 0; j < N; j++) ret.a[i][j] = 0;
    }
    return (ret);
  }

  static Matrix I(int N, bigint m)
  {
    Matrix ret(N, m);
    for(int i = 0; i < N; i++) {
      for(int j = 0; j < N; j++) ret.a[i][j] = i == j;
    }
    return (ret);
  }
};

int main()
{
  Matrix tt1(2, bigint("1000000007"));
  Matrix tt2(2, bigint("101010101010101010101"));

  tt1.a = {{100, 0, 1},
           {1,   0, 0},
           {0,   0, 1}};
  tt2.a = {{100, 0, 1},
           {1,   0, 0},
           {0,   0, 1}};


  long long N;
  cin >> N;
  N--;
  auto p = tt1 ^N;
  auto q = tt2 ^N;

  cout << (p.a[0][0] + p.a[0][2]) % bigint("1000000007") << endl;
  cout << (q.a[0][0] + q.a[0][2]) % bigint("101010101010101010101") << endl;

}