結果

問題 No.1751 Fortune Nim
ユーザー NyaanNyaanNyaanNyaan
提出日時 2021-11-19 22:30:09
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
WA  
実行時間 -
コード長 15,220 bytes
コンパイル時間 3,219 ms
コンパイル使用メモリ 251,400 KB
実行使用メモリ 5,272 KB
最終ジャッジ日時 2023-08-30 09:16:50
合計ジャッジ時間 4,977 ms
ジャッジサーバーID
（参考情報） 		judge15 / judge14
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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 WA -
testcase_01 WA -
testcase_02 WA -
testcase_03 WA -
testcase_04 WA -
testcase_05 RE -
testcase_06 WA -
testcase_07 WA -
testcase_08 WA -
testcase_09 WA -
testcase_10 WA -
testcase_11 WA -
testcase_12 WA -
testcase_13 WA -
testcase_14 WA -
testcase_15 WA -
testcase_16 WA -
testcase_17 WA -
testcase_18 WA -
testcase_19 WA -
testcase_20 RE -
testcase_21 RE -
testcase_22 RE -
testcase_23 WA -
testcase_24 WA -
testcase_25 WA -
testcase_26 WA -
testcase_27 WA -
testcase_28 WA -
testcase_29 WA -
testcase_30 WA -
testcase_31 WA -
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ソースコード

diff # 

/**
 *  date : 2021-11-19 22:30:10
 */

#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;

  T &x() { return first; }
  const T &x() const { return first; }
  U &y() { return second; }
  const U &y() const { return 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;
  }
  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; }
};

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;
}

}  // 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;
}

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
namespace DebugImpl {

template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, typename U::iterator, void>::type>
    : true_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, decltype(U::first), void>::type>
    : true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};

void dump(const char& t) { cerr << t; }

void dump(const string& t) { cerr << t; }

void dump(const bool& t) { cerr << (t ? "true" : "false"); }

template <typename U,
          enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
  cerr << t;
}

template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
  string res;
  if (t == Nyaan::inf) res = "inf";
  if constexpr (is_signed<T>::value) {
    if (t == -Nyaan::inf) res = "-inf";
  }
  if constexpr (sizeof(T) == 8) {
    if (t == Nyaan::infLL) res = "inf";
    if constexpr (is_signed<T>::value) {
      if (t == -Nyaan::infLL) res = "-inf";
    }
  }
  if (res.empty()) res = to_string(t);
  cerr << res;
}

template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);

template <typename T>
void dump(const T& t,
          enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
  cerr << "[ ";
  for (auto it = t.begin(); it != t.end();) {
    dump(*it);
    cerr << (++it == t.end() ? "" : ", ");
  }
  cerr << " ]";
}

template <typename T, typename U>
void dump(const pair<T, U>& t) {
  cerr << "( ";
  dump(t.first);
  cerr << ", ";
  dump(t.second);
  cerr << " )";
}

template <typename T>
void dump(const pair<T*, int>& t) {
  cerr << "[ ";
  for (int i = 0; i < t.second; i++) {
    dump(t.first[i]);
    cerr << (i == t.second - 1 ? "" : ", ");
  }
  cerr << " ]";
}

void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
  cerr << " ";
  dump(head);
  if (sizeof...(tail) != 0) cerr << ",";
  trace(forward<Tail>(tail)...);
}

}  // namespace DebugImpl

#ifdef NyaanDebug
#define trc(...)                            \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc(...) (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(); }

//


template <typename T>
void walsh_hadamard_transform(vector<T>& f, bool inverse = false) {
  int n = f.size();
  for (int i = 1; i < n; i <<= 1) {
    for (int j = 0; j < n; j++) {
      if ((j & i) == 0) {
        T x = f[j], y = f[j | i];
        f[j] = x + y, f[j | i] = x - y;
      }
    }
  }
  if (inverse) {
    if constexpr (is_integral<T>::value) {
      for (auto& x : f) x /= n;
    } else {
      T invn = T(1) / T(f.size());
      for (auto& x : f) x *= invn;
    }
  }
}

/**
 * @brief Walsh Hadamard Transform
 */

template <typename T>
vector<T> xor_convolution(vector<T> a, vector<T> b) {
  walsh_hadamard_transform(a);
  walsh_hadamard_transform(b);
  for (int i = 0; i < (int)a.size(); i++) a[i] *= b[i];
  walsh_hadamard_transform(a, true);
  return a;
}

/**
 * @brief XOR Convoluion
 */

//
/**
#include "modint/montgomery-modint.hpp"

#include "modulo/binomial.hpp"

using namespace Nyaan;
using mint = LazyMontgomeryModInt<998244353>;
// using mint = LazyMontgomeryModInt<1000000007>;
Binomial<mint> C;
//*/
/**/

struct Rational {
  using R = Rational;
  using i128 = __int128_t;
  using i64 = long long;
  using u64 = unsigned long long;
  long long x, y;
  Rational() : x(0), y(1) {}
  Rational(long long _x, long long _y = 1) : x(_x), y(_y) {
    assert(y != 0);
    if (_y != 1) {
      long long g = gcd(x, y);
      if (g != 0) x /= g, y /= g;
      if (y < 0) x = -x, y = -y;
    }
  }

  u64 gcd(i64 A, i64 B) {
    u64 a = A >= 0 ? A : -A;
    u64 b = B >= 0 ? B : -B;
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a);
    int m = __builtin_ctzll(b);
    a >>= n;
    b >>= m;
    while (a != b) {
      int d = __builtin_ctzll(a - b);
      bool f = a > b;
      u64 c = f ? a : b;
      b = f ? b : a;
      a = (c - b) >> d;
    }
    return a << min(n, m);
  }

  friend R operator+(const R& l, const R& r) {
    return R(l.x * r.y + l.y * r.x, l.y * r.y);
  }
  friend R operator-(const R& l, const R& r) {
    return R(l.x * r.y - l.y * r.x, l.y * r.y);
  }
  friend R operator*(const R& l, const R& r) { return R(l.x * r.x, l.y * r.y); }
  friend R operator/(const R& l, const R& r) {
    assert(r.x != 0);
    return R(l.x * r.y, l.y * r.x);
  }
  R& operator+=(const R& r) { return (*this) = (*this) + r; }
  R& operator-=(const R& r) { return (*this) = (*this) - r; }
  R& operator*=(const R& r) { return (*this) = (*this) * r; }
  R& operator/=(const R& r) { return (*this) = (*this) / r; }
  R operator-() const {
    R r;
    r.x = -x, r.y = y;
    return r;
  }
  R inverse() const {
    assert(x != 0);
    R r;
    r.x = y, r.y = x;
    if (x < 0) r.x = -r.x, r.y = -r.y;
    return r;
  }
  R pow(long long p) const {
    R res(1), base(*this);
    while (p) {
      if (p & 1) res *= base;
      base *= base;
      p >>= 1;
    }
    return res;
  }

  friend bool operator==(const R& l, const R& r) {
    return l.x == r.x && l.y == r.y;
  };
  friend bool operator!=(const R& l, const R& r) {
    return l.x != r.x || l.y != r.y;
  };
  friend bool operator<(const R& l, const R& r) {
    return i128(l.x) * r.y < i128(l.y) * r.x;
  };
  friend bool operator<=(const R& l, const R& r) { return l < r || l == r; }
  friend bool operator>(const R& l, const R& r) {
    return i128(l.x) * r.y > i128(l.y) * r.x;
  };
  friend bool operator>=(const R& l, const R& r) { return l > r || l == r; }
  friend ostream& operator<<(ostream& os, const R& r) {
    os << r.x;
    if (r.x != 0 && r.y != 1) os << "/" << r.y;
    return os;
  }

  long long toMint(long long mod) {
    assert(mod != 0);
    i64 a = y, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return i128((u % mod + mod) % mod) * x % mod;
  }
};

struct Binomial {
  vector<Rational> fc;
  Binomial(int = 0) { fc.emplace_back(1); }

  void extend() {
    int n = fc.size();
    Rational nxt = fc.back() * n;
    fc.push_back(nxt);
  }

  Rational fac(int n) {
    while ((int)fc.size() <= n) extend();
    return fc[n];
  }
  Rational finv(int n) { return fac(n).inverse(); }
  Rational inv(int n) { return Rational{1, max(n, 1)}; }
  Rational C(int n, int r) {
    if (n < 0 or r < 0 or n < r) return Rational{0};
    return fac(n) * finv(n - r) * finv(r);
  }
};

using mint = Rational;
//*/
using namespace Nyaan;
using vm = vector<mint>;
using vvm = vector<vm>;

void Nyaan::solve() {

  auto sol = [](ll, ll S) {
    mint x = mint{-1} / 3;
    return (mint{1} - x.pow(S)) / 2;
  };

  inl(N);
  vl a(N);
  in(a);

  if (N == 1) {
    out(mint{2} / 3);
    return;
  }

  ll S = Sum(a);

  if (sz(a) % 2 == 0) {
    mint ans = sol(N, S);
    trc(ans);
    out(ans);
    return;
  }

  exit(1);

  sort(all(a));
  reverse(all(a));

  each(x, a) {
    // 奇数個 -> 勝ち
    if (S % 2 != x % 2) {
      mint bns = sol(N - 1, S - x);
      mint ans = bns * 2 / 3;
      ans += (-bns + 1) * 1 / 3;
      out(ans);
      return;
    }
  }

  // 一番小さいものを選ぶ
  {
    ll x = a.back();
    mint bns = sol(N - 1, S - x);
    mint ans = bns * 2 / 3;
    ans += (-bns + 1) * 1 / 3;
    out(ans);
    return;
  }
}
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