#841204 (C++17) No.2222 Respawn

• 問題: No.2222 Respawn
• ユーザー: NyaanNyaan
• 提出日時: 2023-02-17 22:32:08
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 147 ms / 2,000 ms
• コード長: 10,881 bytes
• コンパイル時間: 2,222 ms
• コンパイル使用メモリ: 252,552 KB
• 実行使用メモリ: 13,312 KB
• 最終ジャッジ日時: 2024-07-19 13:41:35
• 合計ジャッジ時間: 3,507 ms
• ジャッジサーバーID （参考情報）: judge3 / judge2

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 6,816 KB
testcase_01	AC	1 ms; 6,940 KB
testcase_02	AC	2 ms; 6,944 KB
testcase_03	AC	1 ms; 6,944 KB
testcase_04	AC	2 ms; 6,948 KB
testcase_05	AC	2 ms; 6,940 KB
testcase_06	AC	1 ms; 6,940 KB
testcase_07	AC	2 ms; 6,944 KB
testcase_08	AC	2 ms; 6,944 KB
testcase_09	AC	2 ms; 6,940 KB
testcase_10	AC	1 ms; 6,940 KB
testcase_11	AC	2 ms; 6,940 KB
testcase_12	AC	2 ms; 6,940 KB
testcase_13	AC	9 ms; 10,240 KB
testcase_14	AC	6 ms; 8,064 KB
testcase_15	AC	4 ms; 6,944 KB
testcase_16	AC	6 ms; 7,680 KB
testcase_17	AC	4 ms; 6,944 KB
testcase_18	AC	12 ms; 13,056 KB
testcase_19	AC	12 ms; 13,056 KB
testcase_20	AC	13 ms; 13,184 KB
testcase_21	AC	11 ms; 13,184 KB
testcase_22	AC	11 ms; 13,056 KB
testcase_23	AC	13 ms; 13,056 KB
testcase_24	AC	13 ms; 13,056 KB
testcase_25	AC	13 ms; 13,184 KB
testcase_26	AC	13 ms; 13,056 KB
testcase_27	AC	13 ms; 13,184 KB
testcase_28	AC	19 ms; 13,184 KB
testcase_29	AC	17 ms; 13,056 KB
testcase_30	AC	22 ms; 13,184 KB
testcase_31	AC	12 ms; 13,184 KB
testcase_32	AC	147 ms; 13,312 KB

ソースコード

/**
 *  date : 2023-02-17 22:32:02
 */

#define NDEBUG
using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  template <typename S>
  P &operator*=(const S &r) {
    first *= r, second *= r;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }
  P operator*(const P &r) const { return P(*this) *= r; }
  template <typename S>
  P operator*(const S &r) const {
    return P(*this) *= r;
  }
  P operator-() const { return P{-first, -second}; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N,F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

vector<int> mkiota(int n) {
  vector<int> ret(n);
  iota(begin(ret), end(ret), 0);
  return ret;
}

template <typename T>
T mkrev(const T &v) {
  T w{v};
  reverse(begin(w), end(w));
  return w;
}

template <typename T>
bool nxp(vector<T> &v) {
  return next_permutation(begin(v), end(v));
}

template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;

}  // namespace Nyaan

// bit operation
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan

// inout
namespace Nyaan {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}

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

istream &operator>>(istream &is, __int128_t &x) {
  string S;
  is >> S;
  x = 0;
  int flag = 0;
  for (auto &c : S) {
    if (c == '-') {
      flag = true;
      continue;
    }
    x *= 10;
    x += c - '0';
  }
  if (flag) x = -x;
  return is;
}

istream &operator>>(istream &is, __uint128_t &x) {
  string S;
  is >> S;
  x = 0;
  for (auto &c : S) {
    x *= 10;
    x += c - '0';
  }
  return is;
}

ostream &operator<<(ostream &os, __int128_t x) {
  if (x == 0) return os << 0;
  if (x < 0) os << '-', x = -x;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
  if (x == 0) return os << 0;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
  cin >> t;
  in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

void outr() {}
template <typename T, class... U, char sep = ' '>
void outr(const T &t, const U &...u) {
  cout << t;
  outr(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan

// debug

#ifdef NyaanDebug
#define trc(...) (void(0))
#else
#define trc(...) (void(0))
#endif

#ifdef NyaanLocal
#define trc2(...) (void(0))
#else
#define trc2(...) (void(0))
#endif

// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)

namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }

//

using namespace Nyaan;

void q() {
  // 最後にセーブしたのが i とする
  // dp[i]
  // = sum_{i <= j < N} (地点 j に着く) * (1/3) * (j までの手数 + 1 + dp[j])
  //   + (リスポーンする確率) * (リスポーンにかかる手数 + dp[i])
  //  + (ゴールに着く確率) * (それまでにかかる手数)
  // =  (リスポーンする確率) * dp[i] + (1/3) * dp[i]
  // + sum_{i < j < N} (地点 j に着く) * (1/3) * (j までの手数 + 1 + dp[j])
  // + (リスポーンする確率) * (リスポーンにかかる手数) + 1/3
  //  + (ゴールに着く確率) * (それまでにかかる手数)
  //
  // dp[i] (2/3 - (リスポーンする確率)) = hoge + huga + piyo + 1/3
  ini(N);
  ins(S);
  S.push_back('#');

  V<double> p1(N + 1), pe1(N + 1), p2(N + 1), pe2(N + 1), p3(N + 1), pe3(N + 1);
  p2[N] = 1;
  p3[N - 1] = 1;
  repr(i, N - 1) {
    if (S[i] == '#') {
      p2[i] = 1;
      continue;
    }
    // dp_i から respawn する確率
    double respawn = 0;
    double hoge = 0;
    double huga = 0;
    double piyo = 0;
    rep1(t, 2) {
      respawn += p2[i + t] / 3.;
      hoge += (p1[i + t] + pe1[i + t]) / 3.;
      huga += (p2[i + t] + pe2[i + t]) / 3.;
      piyo += (p3[i + t] + pe3[i + t]) / 3.;

      p1[i] += p1[i + t] / 3.;
      p2[i] += p2[i + t] / 3.;
      p3[i] += p3[i + t] / 3.;

      pe1[i] += (p1[i + t] + pe1[i + t]) / 3.;
      pe2[i] += (p2[i + t] + pe2[i + t]) / 3.;
      pe3[i] += (p3[i + t] + pe3[i + t]) / 3.;
    }
    double dpi = (hoge + huga + piyo + 1. / 3.);
    dpi /= 2. / 3. - respawn;
    trc(respawn, hoge, huga, piyo, dpi);

    if (i == 0) die(dpi);
    p1[i] += 1. / 3.;
    pe1[i] += (dpi + 1) / 3.;
  }
}

void Nyaan::solve() {
  int t = 1;
  // in(t);
  while (t--) q();
}