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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#60977#4887. Fast BridgesQingyuCompile Error//C++1410.4kb2022-11-08 23:49:112022-11-08 23:49:12

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  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2022-11-08 23:49:12]
  • 评测
  • [2022-11-08 23:49:11]
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answer

/**
 *    author:  tourist
 *    created: 01.09.2022 11:45:36       
**/
#undef _GLIBCXX_DEBUG

#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];
}*/

template <typename T>
class fenwick {
 public:
  vector<T> fenw;
  int n;

  fenwick(int _n) : n(_n) {
    fenw.resize(n);
  }

  void modify(int x, T v) {
    while (x < n) {
      fenw[x] += v;
      x |= (x + 1);
    }
  }

  T get(int x) {
    T v{};
    while (x >= 0) {
      v += fenw[x];
      x = (x & (x + 1)) - 1;
    }
    return v;
  }
};

struct node {
  int a = 0;

  inline void operator += (node &other) {
    a = max(a, other.a);
  }
};

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, k;
  cin >> n >> k;
  vector<int> xa(n), ya(n), xb(n), yb(n);
  for (int i = 0; i < n; i++) {
    cin >> xa[i] >> ya[i] >> xb[i] >> yb[i];
  }
  mt19937_64 rng(787788);
  vector<uint64_t> coeff(n);
  for (int i = 0; i < n; i++) {
    coeff[i] = rng();
  }
  Mint ans = 0;
  for (int rot = 0; rot < 2; rot++) {
    vector<int> ids;
    vector<int> xs;
    vector<int> ys;
    for (int i = 0; i < n; i++) {
      if (ya[i] < yb[i]) {
        ids.push_back(i);
        xs.push_back(xa[i]);
        ys.push_back(ya[i]);
      }
    }
    sort(xs.begin(), xs.end());
    xs.resize(unique(xs.begin(), xs.end()) - xs.begin());
    sort(ys.begin(), ys.end());
    ys.resize(unique(ys.begin(), ys.end()) - ys.begin());
    xs.insert(xs.begin(), 0);
    ys.insert(ys.begin(), 0);
    vector<int> ya_c(n);
    vector<int> yb_c(n);
    for (int i = 0; i < n; i++) {
      ya_c[i] = (int) (lower_bound(ys.begin(), ys.end(), ya[i]) - ys.begin());
      yb_c[i] = (int) (lower_bound(ys.begin(), ys.end(), yb[i]) - ys.begin());
    }
    int nx = (int) xs.size();
    int ny = (int) ys.size();
    unordered_map<uint64_t, Mint> mp;
    vector<array<int, 3>> events;
    for (int i : ids) {
      events.push_back({xa[i], ya[i], i});
      events.push_back({xb[i], yb[i], ~i});
    }
    sort(events.begin(), events.end());
    vector<int> dp(n);
    for (int x = 1; x < nx; x++) {
      for (int y = 1; y < ny; y++) {
        Mint cell_area = Mint(xs[x] - xs[x - 1]) * (ys[y] - ys[y - 1]);
        long long h = 0;
        int cnt = 0;
        for (int i : ids) {
          if (xa[i] >= xs[x] && ya[i] >= ys[y]) {
            h ^= coeff[i];
            cnt += 1;
          }
        }
        auto iter = mp.find(h);
        if (iter != mp.end()) {
          ans += cell_area * iter->second;
          continue;
        }
        Mint res = 0;
        fenwick<node> fenw(ny);
        vector<int> lim(cnt + 1, k + 1);
        for (auto& e : events) {
          int i = e[2];
          if (i >= 0) {
            if (xa[i] >= xs[x] && ya[i] >= ys[y]) {
              dp[i] = 1 + fenw.get(ya_c[i]).a;
            }
          } else {
            i = ~i;
            if (xa[i] >= xs[x] && ya[i] >= ys[y]) {
              fenw.modify(yb_c[i], {dp[i]});
              if (yb[i] < lim[dp[i]]) {
                res += Mint(lim[dp[i]] - yb[i]) * (k - xb[i] + 1);
                lim[dp[i]] = yb[i];
              }
            }
          }
        }
        ans += cell_area * res;
        mp[h] = res;
      }
    }
    for (int i = 0; i < n; i++) {
      ya[i] = k - ya[i] + 1;
      yb[i] = k - yb[i] + 1;
    }
  }
  Mint total = Mint(k) * k * k * (k - 1) * (k + 1) / 3;
  cout << total - ans << '\n';
  return 0;
}

Details

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