結果

問題 No.2033 Chromatic Duel
ユーザー Iván SotoIván Soto
提出日時 2022-08-06 12:20:48
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 49 ms / 2,000 ms
コード長 9,234 bytes
コンパイル時間 2,114 ms
コンパイル使用メモリ 205,068 KB
実行使用メモリ 5,036 KB
最終ジャッジ日時 2023-10-14 13:56:22
合計ジャッジ時間 4,758 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge15
このコードへのチャレンジ
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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 AC 48 ms
5,036 KB
testcase_01 AC 49 ms
4,884 KB
testcase_02 AC 1 ms
4,352 KB
testcase_03 AC 2 ms
4,352 KB
testcase_04 AC 2 ms
4,348 KB
testcase_05 AC 32 ms
4,348 KB
testcase_06 AC 26 ms
4,348 KB
testcase_07 AC 44 ms
4,688 KB
testcase_08 AC 43 ms
4,740 KB
testcase_09 AC 2 ms
4,352 KB
testcase_10 AC 45 ms
4,716 KB
testcase_11 AC 2 ms
4,352 KB
testcase_12 AC 38 ms
4,704 KB
testcase_13 AC 35 ms
4,352 KB
testcase_14 AC 38 ms
4,624 KB
testcase_15 AC 25 ms
4,348 KB
testcase_16 AC 2 ms
4,352 KB
testcase_17 AC 2 ms
4,348 KB
testcase_18 AC 1 ms
4,348 KB
testcase_19 AC 2 ms
4,352 KB
testcase_20 AC 2 ms
4,352 KB
testcase_21 AC 23 ms
4,352 KB
testcase_22 AC 25 ms
4,348 KB
testcase_23 AC 2 ms
4,348 KB
testcase_24 AC 2 ms
4,352 KB
testcase_25 AC 23 ms
4,348 KB
testcase_26 AC 2 ms
4,348 KB
testcase_27 AC 2 ms
4,348 KB
testcase_28 AC 1 ms
4,352 KB
testcase_29 AC 2 ms
4,352 KB
testcase_30 AC 2 ms
4,352 KB
testcase_31 AC 17 ms
4,352 KB
testcase_32 AC 2 ms
4,352 KB
testcase_33 AC 30 ms
4,352 KB
testcase_34 AC 31 ms
4,348 KB
testcase_35 AC 10 ms
4,348 KB
testcase_36 AC 44 ms
4,784 KB
testcase_37 AC 34 ms
4,708 KB
testcase_38 AC 5 ms
4,348 KB
testcase_39 AC 43 ms
4,620 KB
testcase_40 AC 34 ms
4,736 KB
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 <bits/stdc++.h>

using namespace std;

#ifdef LOCAL
#include <algo/debug.h>
#else
#define debug(...) 42
#endif

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>
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>>;
 
vector<Mint> fact(1, 1);
vector<Mint> inv_fact(1, 1);
 
Mint C(int n, int k) {
  if (k < 0 || k > n) {
    return 0;
  }
  while ((int) fact.size() < n + 1) {
    fact.push_back(fact.back() * (int) fact.size());
    inv_fact.push_back(1 / fact.back());
  }
  return fact[n] * inv_fact[k] * inv_fact[n - k];
}

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int n, b, w;
  cin >> n >> b >> w;
  int t = n - b - w;
  if (t < 0) {
    cout << 0 << '\n';
    return 0;
  }
  Mint ans = 0;
  // first B = 1st, last B < N
  // 0x + 1y + 2z = t - 1
  // x + y + z = b - 1
  // t + b <= n - 1
  // ...
  // x - z = b - t
  // x = b - t + z
  debug(t);
  if (true || t - 1 + b <= n - 1) {
    for (int z = 0; z <= n; z++) {
      int x = b - t + z;
      if (x < 0) {
        continue;
      }
      int y = b - 1 - x - z;
      if (y < 0 || y != t - 1 - 2 * z) {
        continue;
      }
      debug(x, y, z);
      // C(w + z, z)
      ans += (w == 0 ? 1 : C(w + z, z)) * C(b - 1, x) * C(b - 1 - x, y);
    }
  }
  // first B = 1st, last B = N
  // 0x + 1y + 2z = t
  // x + y + z = b - 1
  // b - 1 spaces
  // add condition?
  if (true || t + b <= n) {
    for (int z = 0; z <= n; z++) {
      int x = b - 1 - t + z;
      if (x < 0) {
        continue;
      }
      int y = b - 1 - x - z;
      if (y < 0 || y != t - 2 * z) {
        continue;
      }
      debug(x, y, z);
      ans += (w == 0 ? 1 : C(w + z - 1, z - 1)) * C(b - 1, x) * C(b - 1 - x, y);
    }
  }
  // first B > 1st, last B < N
  // 0x + 1y + 2z = t - 2
  // x + y + z = b - 1
  // 1 + (t - 2) + b <= n - 1
  // x - z = b - 1 - (t - 2)
  // x - z = b - t + 1
  // add condition?
  if (true || t - 2 + b <= n - 2) {
    for (int z = 0; z <= n; z++) {
      int x = b - t + 1 + z;
      if (x < 0) {
        continue;
      }
      int y = b - 1 - x - z;
      if (y < 0 || y != t - 2 - 2 * z) {
        continue;
      }
      debug(x, y, z);
      ans += (w == 0 ? 1 : C(w + z + 1, z + 1)) * C(b - 1, x) * C(b - 1 - x, y);
    }
  }
  // first B > 1st, last B = N
  // 0x + 1y + 2z = t - 1
  // x + y + z = b - 1
  // 1 + t - 1 + b <= n
  // x - z = b - 1 - (t - 1)
  // x - z = b - t
  if (true || 1 + t - 1 + b <= n) {
    for (int z = 0; z <= n; z++) {
      int x = b - t + z;
      if (x < 0) {
        continue;
      }
      int y = b - 1 - x - z;
      if (y < 0 || y != t - 1 - 2 * z) {
        continue;
      }
      debug(x, y, z);
      ans += (w == 0 ? 1 : C(w + z, z)) * C(b - 1, x) * C(b - 1 - x, y);
    }
  }
  cout << ans << '\n';
  return 0;
}
0