結果

問題 No.75 回数の期待値の問題
ユーザー suisen
提出日時 2022-12-12 03:51:34
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 3 ms / 5,000 ms
コード長 7,484 bytes
コンパイル時間 2,460 ms
コンパイル使用メモリ 209,772 KB
最終ジャッジ日時 2025-02-09 09:57:35
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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ファイルパターン 結果
sample AC * 4
other AC * 16
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

diff # 

#line 1 "test/matrix/gaussian_elimination/yuki129.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/system_of_linear_equations"

#line 2 "src/math/Modint.hpp"
#define CUT
#line 2 "src/Template.hpp"

#define CUT
#include <bits/stdc++.h>

using namespace std;

#define rep(i, l, r) for (int i = (l); i < (r); ++i)
#define rrep(i, l, r) for (int i = (r); i --> (l);)
#define all(c) begin(c), end(c)

#ifdef LOCAL
#define debug(...) debug_impl(#__VA_ARGS__, __VA_ARGS__)
template <class H, class... Ts> void debug_impl(string s, H&& h, Ts&&... ts) {
  cerr << '(' << s << "): (" << forward<H>(h);
  ((cerr << ", " << forward<Ts>(ts)), ..., (cerr << ")\n"));
}
#else
#define debug(...) void(0)
#endif

template <class T> bool chmax(T& a, const T& b) { return b > a ? (a = b, true) : false; }
template <class T> bool chmin(T& a, const T& b) { return b < a ? (a = b, true) : false; }

template <class T> istream& operator>>(istream& in, vector<T>& v) {
  for (auto& e : v) in >> e;
  return in;
}
template <class ...Args> void read(Args&... args) {
  (cin >> ... >> args);
}
template <class T> ostream& operator<<(ostream& out, const vector<T>& v) {
  int n = v.size();
  rep(i, 0, n) {
    out << v[i];
    if (i + 1 != n) out << ' ';
  }
  return out;
}
template <class H, class ...Ts> void print(H&& h, Ts &&... ts) {
  cout << h, ((cout << ' ' << forward<Ts>(ts)), ..., (cout << '\n'));
}

struct io_setup_ {
  io_setup_() {
    ios::sync_with_stdio(false), cin.tie(nullptr);
    cout << fixed << setprecision(10);
  }
} io_setup{};
#undef CUT

#define NOTE compile command: \texttt{g++ -std=gnu++17 -Wall -Wextra -g -fsanitize=address -fsanitize=undefined \$\{file\} -o \$\{fileDirname\}/\$\{fileBasenameNoExtension\}}
#undef NOTE
#define NOTE \texttt{-DLOCAL} を加えると \texttt{debug(...)} による出力が有効となる
#undef NOTE
#line 3 "src/math/ExtGCD.hpp"

#define CUT
constexpr long safe_mod(long long x, long long m) {
  return (x %= m) < 0 ? x + m : x;
}
// Returns `(x,g)` s.t. `g=\gcd(a,b)`, `xa\equiv g \pmod{b}`, and `0\leq x< \frac{b}{g}`
constexpr pair<long long, long long> inv_gcd(long long a, long long b) {
  assert(b > 0);
  a = safe_mod(a, b);
  if (a == 0) return { 0, b };
  long long s = b, t = a, x = 0, y = 1, tmp = 0;
  while (t) {
    long long u = s / t;
    s -= t * u;
    x -= y * u;
    tmp = s, s = t, t = tmp;
    tmp = x, x = y, y = tmp;
  }
  if (x < 0) x += b / s;
  return { x, s };
}
// Returns `x` s.t. `xa\equiv 1 \pmod{m}`.
// Requirement: `\gcd(a, m) = 1`.
constexpr long long inv_mod(long long a, long long m) {
  auto [x, g] = inv_gcd(a, m);
  assert(g == 1);
  return x;
}
// Returns `(x_0,y_0,g)` s.t. `g=\gcd(a,b)`, `ax_0 + by_0 = g`, and `0\leq x_0<\frac{b}{g}`.
// 一般解は `(x,y)=(x_0+k\cdot\dfrac{b}{g}, y_0-k\cdot\dfrac{a}{g})\;(k\in\mathbb{Z})` なので、`(x_0,y_0)` は `x` が非負の下で最小の解
constexpr tuple<long long, long long, long long> ext_gcd(long long a, long long b) {
  auto [x, g] = inv_gcd(a, b);
  return { x, (g - x * a) / b, g };
}
#undef CUT
#line 4 "src/math/Modint.hpp"

constexpr long long pow_mod(long long x, long long b, int m) {
  long long p = safe_mod(x, m), r = 1;
  for (; b; b >>= 1) {
    if (b & 1) (r *= p) %= m;
    (p *= p) %= m;
  }
  return r;
}

template <int mod> struct modint {
  unsigned x;
  modint(): x(0) {}
  modint(long long v): x(safe_mod(v, mod)) {}
  
  int val() const { return x; }

  static modint raw(unsigned v) {
    modint res;
    res.x = v;
    return v;
  }

  modint operator-() const {
    return raw(x ? mod - x : 0);
  }

  modint& operator+=(modint t) {
    if ((x += t.x) >= mod) x -= mod;
    return *this;
  }
  modint& operator-=(modint t) {
    if ((x += mod - t.x) >= mod) x -= mod;
    return *this;
  }
  modint& operator*=(modint t) {
    x = (unsigned long long) x * t.x % mod;
    return *this;
  }
  modint& operator/=(modint t) { return *this *= t.inv(); }
  friend modint operator+(modint x, modint y) { return x += y; }
  friend modint operator-(modint x, modint y) { return x -= y; }
  friend modint operator*(modint x, modint y) { return x *= y; }
  friend modint operator/(modint x, modint y) { return x /= y; }
  friend bool operator==(modint x, modint y) { return x.x == y.x; }
  friend bool operator!=(modint x, modint y) { return x.x != y.x; }

  modint inv() const { return inv_mod(x, mod); }
  modint pow(long long b) const {
    assert(b >= 0);
    return pow_mod(x, b, mod);
  }
};
#undef CUT
#line 3 "src/matrix/GaussianElimination.hpp"
#define CUT
template <class T>
struct GaussianElimination {
  vector<T> sol;
  vector<vector<T>> bases;
  // 解が一つも存在しないかどうか
  bool empty = false;

  GaussianElimination(vector<vector<T>> A, const vector<T>& b) {
    int n = A.size();
    for (int i = 0; i < n; ++i) A[i].push_back(b[i]);
    solve(A);
  }
private:
  static constexpr bool is_fp = is_floating_point_v<T>;
  static bool is_zero(T x) {
    if constexpr (is_fp) {
      return abs(x) < 1e-9;
    } else {
      return x == 0;
    }
  }

  void solve(vector<vector<T>>& Ab) {
    const int n = Ab.size(), m = Ab[0].size() - 1;

    auto pivoting = [&](int l, int k) {
      int pos = m, res = n;

      // 浮動小数点数型のとき
      T max_val = 0;

      rep(i, k, n) {
        const auto& v = Ab[i];

        // 浮動小数点数型のとき
        if constexpr (is_fp) {
          if (pos < m and abs(v[pos]) > max_val) {
            res = i, max_val = abs(v[pos]);
          }
        }

        rep(j, l, pos) {
          if (not is_zero(Ab[k][j])) {
            pos = j, res = i;

            // 浮動小数点数型のとき
            if constexpr (is_fp) {
              max_val = abs(Ab[i][j]);
            }

            break;
          }
        }
      }
      return pair{ pos, res };
    };

    int l = 0;
    rep(i, 0, n) {
      auto [mse, k] = pivoting(l, i);
      l = mse + 1;

      if (k == n) break;
      Ab[i].swap(Ab[k]);
      T cinv = T{ 1 } / Ab[i][mse];
      rep(row, i + 1, n) if (not is_zero(Ab[row][mse])) {
        T c = Ab[row][mse] * cinv;
        rep(col, mse, m + 1) Ab[row][col] -= c * Ab[i][col];
      }
    }

    int basis_num = m;
    vector<int8_t> down(m);
    sol.assign(m, T{0});
    rrep(i, 0, n) {
      int mse = m + 1;
      rep(col, 0, m + 1) if (not is_zero(Ab[i][col])) {
        mse = col;
        break;
      }
      if (mse < m) {
        T cinv = T{ 1 } / Ab[i][mse];
        rep(row, 0, i) if (not is_zero(Ab[row][mse])) {
          T c = Ab[row][mse] * cinv;
          rep(col, mse, m + 1) Ab[row][col] -= c * Ab[i][col];
        }
        rep(col, mse, m + 1) Ab[i][col] *= cinv;
        sol[mse] = Ab[i][m];
        down[mse] = true;
        --basis_num;
      } else if (mse == m) {
        empty = true;
        return;
      }
    }
    bases.assign(basis_num, vector<T>(m));
    int id = 0;
    rep(j, 0, m) if (not down[j]) {
      int i = 0;
      rep(j2, 0, m) bases[id][j2] = down[j2] ? Ab[i++][j] : 0;
      bases[id++][j] = -1;
    }
  }
};
#undef CUT
#line 5 "test/matrix/gaussian_elimination/yuki129.test.cpp"

int main() {
  int k;
  read(k);

  vector A(k, vector<double>(k));
  vector<double> b(k, 1);

  rep(i, 0, k) {
    rep(v, 1, 7) {
      if (i + v == k) {
        
      } else {
        int j = i + v;
        if (j > k) j = 0;
        A[i][j] -= 1. / 6.;
      }
    }
    A[i][i] += 1;
  }
  GaussianElimination<double> gauss(A, b);
  print(gauss.sol[0]);
  return 0;
}
0