Submission #43441423

Source Code Expand

#include <bits/stdc++.h>

using namespace std;

#ifdef LOCAL
#include "algo/debug.h"
#endif

using i64 = long long;

template <typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a; swap(a, m);
    u -= t * v; swap(u, v);
  }
  assert(m == 1);
  return u;
}

template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;

  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U& x) {
    value = normalize(x);
  }

  template <typename U>
  static Type normalize(const U& x) {
    Type v;
    if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
    else v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }

  const Type& operator()() const { return value; }
  template <typename U>
  explicit operator U() const { return static_cast<U>(value); }
  constexpr static Type mod() { return T::value; }

  Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
  Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; }
  template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }
  template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); }
  Modular& operator++() { return *this += 1; }
  Modular& operator--() { return *this -= 1; }
  Modular operator++(int) { Modular result(*this); *this += 1; return result; }
  Modular operator--(int) { Modular result(*this); *this -= 1; return result; }
  Modular operator-() const { return Modular(-value); }

  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
#ifdef _WIN32
    uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
    uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
    asm(
      "divl %4; \n\t"
      : "=a" (d), "=d" (m)
      : "d" (xh), "a" (xl), "r" (mod())
    );
    value = m;
#else
    value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
    return *this;
  }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, long long>::value, Modular>::type& operator*=(const Modular& rhs) {
    long long q = static_cast<long long>(static_cast<long double>(value) * rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }
  template <typename U = T>
  typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular >::type& operator*=(const Modular& rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }

  Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }

  friend const Type& abs(const Modular& x) { return x.value; }

  template <typename U>
  friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);

  template <typename U>
  friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);

  template <typename V, typename U>
  friend V& operator>>(V& stream, Modular<U>& number);

 private:
  Type value;
};

template <typename T> bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
template <typename T, typename U> bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }
template <typename T, typename U> bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; }

template <typename T> bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); }

template <typename T> bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; }

template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }

template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }

template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }

template <typename T> Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }

template <typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1) res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}
template <typename T, typename U> Modular<T> operator^(const Modular<T>& lhs, U rhs) { return power(lhs, rhs); };

template <typename T>
bool IsZero(const Modular<T>& number) {
  return number() == 0;
}

template <typename T>
string to_string(const Modular<T>& number) {
  return to_string(number());
}

// U == std::ostream? but done this way because of fastoutput
template <typename U, typename T>
U& operator<<(U& stream, const Modular<T>& number) {
  return stream << number();
}

// U == std::istream? but done this way because of fastinput
template <typename U, typename T>
U& operator>>(U& stream, Modular<T>& number) {
  typename common_type<typename Modular<T>::Type, long long>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}

/*
using ModType = int;

struct VarMod { static ModType value; };
ModType VarMod::value;
ModType& md = VarMod::value;
using Mint = Modular<VarMod>;
*/

constexpr int md = 998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int n;
  cin >> n;
  string t;
  cin >> t;
  vector<Mint> f(2 * n + 1), g(2 * n + 1);
  f[n] = 1;
  for (auto c : t) {
    vector<Mint> new_f(2 * n + 1), new_g(2 * n + 1);
    for (int i = 0; i <= 2 * n; ++i) {
      if (c != '-' && i + 1 <= 2 * n) {
        new_f[i + 1] += f[i];
        new_g[i + 1] += g[i] + f[i] * abs(n - (i + 1));
      }
      if (c != '+' && i - 1 >= 0) {
        new_f[i - 1] += f[i];
        new_g[i - 1] += g[i] + f[i] * abs(n - (i - 1));
      }
    }
    f.swap(new_f);
    g.swap(new_g);
  }
  auto ans = g[n];
  cout << ans << "\n";
  return 0;
}

Submission Info

Submission Time
Task D - 1D Coulomb
User nima_aryan
Language C++ (GCC 9.2.1)
Score 600
Code Size 7622 Byte
Status AC
Exec Time 267 ms
Memory 3704 KiB

Judge Result

Set Name Sample All
Score / Max Score 0 / 0 600 / 600
Status
AC × 2
AC × 42
Set Name Test Cases
Sample sample-01.txt, sample-02.txt
All in-01.txt, in-02.txt, in-03.txt, in-04.txt, in-05.txt, in-06.txt, in-07.txt, in-08.txt, in-09.txt, in-10.txt, in-11.txt, in-12.txt, in-13.txt, in-14.txt, in-15.txt, in-16.txt, in-17.txt, in-18.txt, in-19.txt, in-20.txt, in-21.txt, in-22.txt, in-23.txt, in-24.txt, in-25.txt, in-26.txt, in-27.txt, in-28.txt, in-29.txt, in-30.txt, in-31.txt, in-32.txt, in-33.txt, in-34.txt, in-35.txt, in-36.txt, in-37.txt, in-38.txt, in-39.txt, in-40.txt, sample-01.txt, sample-02.txt
Case Name Status Exec Time Memory
in-01.txt AC 8 ms 3540 KiB
in-02.txt AC 3 ms 3584 KiB
in-03.txt AC 2 ms 3568 KiB
in-04.txt AC 2 ms 3428 KiB
in-05.txt AC 2 ms 3428 KiB
in-06.txt AC 2 ms 3584 KiB
in-07.txt AC 2 ms 3592 KiB
in-08.txt AC 2 ms 3568 KiB
in-09.txt AC 267 ms 3688 KiB
in-10.txt AC 253 ms 3592 KiB
in-11.txt AC 255 ms 3624 KiB
in-12.txt AC 253 ms 3692 KiB
in-13.txt AC 212 ms 3676 KiB
in-14.txt AC 213 ms 3692 KiB
in-15.txt AC 214 ms 3644 KiB
in-16.txt AC 174 ms 3692 KiB
in-17.txt AC 177 ms 3692 KiB
in-18.txt AC 175 ms 3528 KiB
in-19.txt AC 250 ms 3568 KiB
in-20.txt AC 249 ms 3624 KiB
in-21.txt AC 249 ms 3620 KiB
in-22.txt AC 176 ms 3572 KiB
in-23.txt AC 213 ms 3560 KiB
in-24.txt AC 172 ms 3636 KiB
in-25.txt AC 171 ms 3688 KiB
in-26.txt AC 154 ms 3616 KiB
in-27.txt AC 118 ms 3696 KiB
in-28.txt AC 2 ms 3588 KiB
in-29.txt AC 2 ms 3488 KiB
in-30.txt AC 1 ms 3624 KiB
in-31.txt AC 2 ms 3468 KiB
in-32.txt AC 1 ms 3572 KiB
in-33.txt AC 2 ms 3592 KiB
in-34.txt AC 238 ms 3640 KiB
in-35.txt AC 220 ms 3668 KiB
in-36.txt AC 176 ms 3676 KiB
in-37.txt AC 230 ms 3704 KiB
in-38.txt AC 137 ms 3684 KiB
in-39.txt AC 82 ms 3608 KiB
in-40.txt AC 94 ms 3568 KiB
sample-01.txt AC 2 ms 3584 KiB
sample-02.txt AC 2 ms 3544 KiB