結果

問題 No.75 回数の期待値の問題
コンテスト
ユーザー HEXAebmr
提出日時 2021-02-11 08:30:45
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 6 ms / 5,000 ms
コード長 4,783 bytes
コンパイル時間 1,384 ms
コンパイル使用メモリ 137,380 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-07-17 21:44:57
合計ジャッジ時間 2,197 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
このコードへのチャレンジ
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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 # 

#include <algorithm>
//#include <atcoder/all>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <cstdint>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <queue>
#include <random>
#include <regex>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
//using namespace atcoder;
using ll = long long;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using vll = vector<ll>;
using vvll = vector<vector<ll>>;
using vvvll = vector<vector<vector<ll>>>;
using vii = vector<int>;
using vvii = vector<vector<int>>;
using vvvii = vector<vector<vector<int>>>;
using vdd = vector<double>;
using vvdd = vector<vector<double>>;
using vvvdd = vector<vector<vector<double>>>;
using vbb = vector<bool>;
using vvbb = vector<vector<bool>>;
using vvvbb = vector<vector<vector<bool>>>;
#define pb push_back
#define mp make_pair
#define sc second
#define fr first
#define endl '\n'
#define stpr std::fixed << setprecision
#define cYES cout << "YES" << endl
#define cNO cout << "NO" << endl
#define cYes cout << "Yes" << endl
#define cNo cout << "No" << endl
#define rep(i, n) for (ll i = 0; i < (n); ++i)
#define drep(i, a, b, d) for (ll i = (a); i <= (b); i += d)
#define Rep(i, a, b) for (ll i = (a); i < (b); ++i)
#define rrep(i, n) for (ll i = n - 1; i >= 0; i--)
#define drrep(i, a, b, d) for (ll i = (a); i >= (b); i -= d)
#define rRep(i, a, b) for (ll i = a; i >= b; i--)
#define crep(i) for (char i = 'a'; i <= 'z'; ++i)
#define Crep(i) for (char i = 'A'; i <= 'Z'; ++i)
#define ALL(x) (x).begin(), (x).end()
#define rALL(x) (x).rbegin(), (x).rend()
#define sort2(A, N) \
  sort(A, A + N,    \
       [](const pii &a, const pii &b) { return a.second < b.second; });
#define debug(v)      \
  cout << #v << ":";  \
  for (auto x : v) {  \
    cout << x << ' '; \
  }                   \
  cout << endl;
int ctoi(const char c) {
  if ('0' <= c && c <= '9') return (c - '0');
  return -1;
}
ll gcd(ll a, ll b) { return (b == 0 ? a : gcd(b, a % b)); }
ll lcm(ll a, ll b) { return a * b / gcd(a, b); }
constexpr ll MOD = 1000000007;
constexpr ll INF = 1000000011;
constexpr ll MOD2 = 998244353;
constexpr ll LINF = 1001002003004005006ll;
constexpr ld EPS = 10e-10;
template <class T, class U>
inline bool chmax(T &lhs, const U &rhs) {
  if (lhs < rhs) {
    lhs = rhs;
    return 1;
  }
  return 0;
}
template <class T, class U>
inline bool chmin(T &lhs, const U &rhs) {
  if (lhs > rhs) {
    lhs = rhs;
    return 1;
  }
  return 0;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto &&x : v) is >> x;
  return is;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first;
  is >> p.second;
  return is;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << ' ' << p.second;
  return os;
}
template <class T>
ostream &operator<<(ostream &os, vector<T> &v) {
  for (auto i = begin(v); i != end(v); ++i) {
    if (i != begin(v)) os << ' ';
    os << *i;
  }
  return os;
}

// 連立方程式の形をそのまま入れる
vdd gauss_jordan(vvdd &A, const vdd &b) {
  int n_ = A.size(), m_ = A[0].size();
  if (n_ < m_) {
    return vdd();
  }
  vvdd B(n_, vdd(m_ + 1));
  auto c = b;
  for (int i = 0; i < n_; i++) {
    for (int j = 0; j < m_; j++) {
      B[i][j] = A[i][j];
    }
  }
  for (int i = 0; i < n_; i++) {
    B[i][m_] = b[i];
  }
  for (int i = 0; i < m_; i++) {
    int pivot = i;
    for (int j = i; j < n_; j++) {
      if (abs(B[j][i]) > abs(B[pivot][i])) {
        pivot = j;
      }
    }
    swap(B[i], B[pivot]);
    swap(c[i], c[pivot]);

    if (abs(B[i][i]) < EPS) {
      return vdd();
    }

    for (int j = i + 1; j <= m_; j++) {
      B[i][j] /= B[i][i];
    }
    for (int j = 0; j < n_; j++) {
      if (i != j) {
        for (int k = i + 1; k <= m_; k++) {
          B[j][k] -= B[j][i] * B[i][k];
        }
      }
    }
  }
  vdd x(m_);
  for (int i = 0; i < m_; i++) {
    x[i] = B[i][m_];
  }
  bool T = 0;
  for (int i = m_; i < n_; i++) {
    ld sum = 0;
    for (int j = 0; j < m_; j++) {
      sum += x[j] * B[i][j];
    }
    if (sum - c[i] > EPS) {
      return vdd();
    }
  }
  return x;
}

int main() {
  ll K;
  cin >> K;
  vvdd A(K + 1, vdd(K + 1, 0));
  vdd B(K + 1, -1.0);
  rep(i, K) {
    A[i][i] = -1.0;
    rep(j, 6) {
      ll t = i + j + 1;
      if (t > K) {
        t = 0;
      }
      A[i][t] += 1.0 / 6.0;
    }
  }
  A[K][K] = 1;
  B[K] = 0;
  auto V = gauss_jordan(A, B);
  cout << stpr(15) << V[0] << endl;
}
0