結果

問題 No.1751 Fortune Nim
ユーザー 👑 emthrmemthrm
提出日時 2021-11-19 23:00:41
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 25 ms / 2,000 ms
コード長 9,249 bytes
コンパイル時間 3,504 ms
コンパイル使用メモリ 202,432 KB
最終ジャッジ日時 2025-01-25 20:50:10
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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 * 2
other AC * 30
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 # 

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 998244353;
constexpr int DY[]{1, 0, -1, 0}, DX[]{0, -1, 0, 1};
constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1}, DX8[]{0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << fixed << setprecision(20);
  }
} iosetup;

template <int M>
struct MInt {
  unsigned int val;
  MInt(): val(0) {}
  MInt(long long x) : val(x >= 0 ? x % M : x % M + M) {}
  static constexpr int get_mod() { return M; }
  static void set_mod(int divisor) { assert(divisor == M); }
  static void init(int x = 10000000) { inv(x, true); fact(x); fact_inv(x); }
  static MInt inv(int x, bool init = false) {
    // assert(0 <= x && x < M && std::__gcd(x, M) == 1);
    static std::vector<MInt> inverse{0, 1};
    int prev = inverse.size();
    if (init && x >= prev) {
      // "x!" and "M" must be disjoint.
      inverse.resize(x + 1);
      for (int i = prev; i <= x; ++i) inverse[i] = -inverse[M % i] * (M / i);
    }
    if (x < inverse.size()) return inverse[x];
    unsigned int a = x, b = M; int u = 1, v = 0;
    while (b) {
      unsigned int q = a / b;
      std::swap(a -= q * b, b);
      std::swap(u -= q * v, v);
    }
    return u;
  }
  static MInt fact(int x) {
    static std::vector<MInt> f{1};
    int prev = f.size();
    if (x >= prev) {
      f.resize(x + 1);
      for (int i = prev; i <= x; ++i) f[i] = f[i - 1] * i;
    }
    return f[x];
  }
  static MInt fact_inv(int x) {
    static std::vector<MInt> finv{1};
    int prev = finv.size();
    if (x >= prev) {
      finv.resize(x + 1);
      finv[x] = inv(fact(x).val);
      for (int i = x; i > prev; --i) finv[i - 1] = finv[i] * i;
    }
    return finv[x];
  }
  static MInt nCk(int n, int k) {
    if (n < 0 || n < k || k < 0) return 0;
    if (n - k > k) k = n - k;
    return fact(n) * fact_inv(k) * fact_inv(n - k);
  }
  static MInt nPk(int n, int k) { return n < 0 || n < k || k < 0 ? 0 : fact(n) * fact_inv(n - k); }
  static MInt nHk(int n, int k) { return n < 0 || k < 0 ? 0 : (k == 0 ? 1 : nCk(n + k - 1, k)); }
  static MInt large_nCk(long long n, int k) {
    if (n < 0 || n < k || k < 0) return 0;
    inv(k, true);
    MInt res = 1;
    for (int i = 1; i <= k; ++i) res *= inv(i) * n--;
    return res;
  }
  MInt pow(long long exponent) const {
    MInt tmp = *this, res = 1;
    while (exponent > 0) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
      exponent >>= 1;
    }
    return res;
  }
  MInt &operator+=(const MInt &x) { if((val += x.val) >= M) val -= M; return *this; }
  MInt &operator-=(const MInt &x) { if((val += M - x.val) >= M) val -= M; return *this; }
  MInt &operator*=(const MInt &x) { val = static_cast<unsigned long long>(val) * x.val % M; return *this; }
  MInt &operator/=(const MInt &x) { return *this *= inv(x.val); }
  bool operator==(const MInt &x) const { return val == x.val; }
  bool operator!=(const MInt &x) const { return val != x.val; }
  bool operator<(const MInt &x) const { return val < x.val; }
  bool operator<=(const MInt &x) const { return val <= x.val; }
  bool operator>(const MInt &x) const { return val > x.val; }
  bool operator>=(const MInt &x) const { return val >= x.val; }
  MInt &operator++() { if (++val == M) val = 0; return *this; }
  MInt operator++(int) { MInt res = *this; ++*this; return res; }
  MInt &operator--() { val = (val == 0 ? M : val) - 1; return *this; }
  MInt operator--(int) { MInt res = *this; --*this; return res; }
  MInt operator+() const { return *this; }
  MInt operator-() const { return MInt(val ? M - val : 0); }
  MInt operator+(const MInt &x) const { return MInt(*this) += x; }
  MInt operator-(const MInt &x) const { return MInt(*this) -= x; }
  MInt operator*(const MInt &x) const { return MInt(*this) *= x; }
  MInt operator/(const MInt &x) const { return MInt(*this) /= x; }
  friend std::ostream &operator<<(std::ostream &os, const MInt &x) { return os << x.val; }
  friend std::istream &operator>>(std::istream &is, MInt &x) { long long val; is >> val; x = MInt(val); return is; }
};
namespace std { template <int M> MInt<M> abs(const MInt<M> &x) { return x; } }
using ModInt = MInt<MOD>;

template <typename T = long long>
struct Rational {
  T num, den;
  Rational(): num(0), den(1) {}
  Rational(T num, T den = 1) : num(num), den(den) { assert(den != 0); reduce(); }
  template <typename Real = long double> Real to_real() const { return static_cast<Real>(num) / den; }
  Rational &operator+=(const Rational &x) {
    T g = std::__gcd(den, x.den);
    num = num * (x.den / g) + x.num * (den / g); den *= x.den / g;
    reduce();
    return *this;
  }
  Rational &operator-=(const Rational &x) { return *this += -x; }
  Rational &operator*=(const Rational &x) {
    T g1 = std::__gcd(num, x.den), g2 = std::__gcd(den, x.num);
    num = (num / g1) * (x.num / g2); den = (den / g2) * (x.den / g1);
    reduce();
    return *this;
  }
  Rational &operator/=(const Rational &x) { return *this *= Rational(x.den, x.num); }
  bool operator==(const Rational &x) const { return num == x.num && den == x.den; }
  bool operator!=(const Rational &x) const { return !(*this == x); }
  bool operator<(const Rational &x) const { return (x - *this).num > 0; }
  bool operator<=(const Rational &x) const { return !(x < *this); }
  bool operator>(const Rational &x) const { return x < *this; }
  bool operator>=(const Rational &x) const { return !(*this < x); }
  Rational &operator++() { if ((num += den) == 0) den = 1; return *this; }
  Rational operator++(int) { Rational res = *this; ++*this; return res; }
  Rational &operator--() { if ((num -= den) == 0) den = 1; return *this; }
  Rational operator--(int) { Rational res = *this; --*this; return res; }
  Rational operator+() const { return *this; }
  Rational operator-() const { return Rational(-num, den); }
  Rational operator+(const Rational &x) const { return Rational(*this) += x; }
  Rational operator-(const Rational &x) const { return Rational(*this) -= x; }
  Rational operator*(const Rational &x) const { return Rational(*this) *= x; }
  Rational operator/(const Rational &x) const { return Rational(*this) /= x; }
  friend std::ostream &operator<<(std::ostream &os, const Rational &x) {
    if (x.den == 1) return os << x.num;
    return os << x.num << '/' << x.den;
  }
private:
  void reduce() { T g = std::__gcd(num, den); num /= g; den /= g; if (den < 0) { num = -num; den = -den; } }
};
namespace std {
template <typename T> Rational<T> abs(const Rational<T> &x) {Rational<T> res = x; if (res.num < 0) res.num = -res.num; return res; }
template <typename T> Rational<T> max(const Rational<T> &a, const Rational<T> &b) { return a < b ? b : a; }
template <typename T> Rational<T> min(const Rational<T> &a, const Rational<T> &b) { return a < b ? a : b; }
template <typename T> struct numeric_limits<Rational<T>> {
  static constexpr Rational<T> max() { return std::numeric_limits<T>::max(); }
  static constexpr Rational<T> lowest() { return std::numeric_limits<T>::lowest(); }
};
}  // std

ll p3(int n) {
  ll res = 1;
  while (n--) res *= 3;
  return res;
}

int main() {
  using rational = Rational<>;
  map<multiset<int>, rational> dp;
  auto f = [&](auto&& f, const multiset<int>& a) -> rational {
    if (dp.count(a) == 1) return dp[a];
    rational& r = dp[a];
    if (a.size() == 1) return r = rational(2, 3);
    multiset<int> b = a;
    for (const int ai : a) {
      b.erase(b.lower_bound(ai));
      chmax(r, (-f(f, b) + 2) / 3);
      FOR(na, 1, ai) {
        b.emplace(na);
        chmax(r, (-f(f, b) + 2) / 3);
        b.erase(b.lower_bound(na));
      }
      b.emplace(ai);
    }
    int x = 0;
    for (int ai : a) x ^= ai;
    if (x == 0) {
      assert(r.den == p3(accumulate(ALL(a), 0)));
    } else {
      pair<int, int> rem{0, 0};
      for (int ai : a) {
        if ((x ^ ai) <= ai) {
          chmax(rem, make_pair(ai - (x ^ ai), ai));
        }
      }
      for (int ai : a) {
        if (ai == rem.second) {
          b.erase(b.lower_bound(ai));
          if (rem.first < ai) b.emplace(ai - rem.first);
          assert(f(f, b).den * 3 == r.den);
          break;
        }
      }
    }
    return r;
  };

  auto nth = [](const ll n) -> ModInt {
    return (ModInt::inv(ModInt(3).pow(n).val) * (n % 2 == 0 ? -1 : 1) + 1) / 2;
  };
  int n; cin >> n;
  if (n == 1) {
    cout << ModInt(2) / 3 << '\n';
    return 0;
  }
  vector<int> a(n); REP(i, n) cin >> a[i];
  int x = 0;
  REP(i, n) x ^= a[i];
  if (x == 0) {
    cout << nth(accumulate(ALL(a), 0LL)) << '\n';
  } else {
    int remove = 0;
    REP(i, n) {
      if ((x ^ a[i]) <= a[i]) chmax(remove, a[i] - (x ^ a[i]));
    }
    cout << nth(accumulate(ALL(a), 0LL) - remove + 1) << '\n';
  }
  return 0;
}
0