Submission #263033

#	Time	Username	Problem	Language	Result	Execution time	Memory
263033		KoD	Boat (APIO16_boat)	C++11	100 / 100	573 ms	4480 KiB

boat

/**
 * @title Template
 */

#include <iostream>
#include <algorithm>
#include <utility>
#include <numeric>
#include <vector>
#include <array>
#include <cassert>


template <class T, class U>
bool chmin(T &lhs, const U &rhs) {
  if (lhs > rhs) { 
    lhs = rhs; 
    return true; 
  }
  return false;
}

template <class T, class U>
bool chmax(T &lhs, const U &rhs) {
  if (lhs < rhs) { 
    lhs = rhs; 
    return true; 
  }
  return false;
}

/**
 * @title Chmin/Chmax
 */


class range {
public:
  class iterator {
  private:
    int64_t M_position;

  public:
    iterator(int64_t position) noexcept: M_position(position) { }
    void operator ++ () noexcept { ++M_position; }
    bool operator != (iterator other) const noexcept { return M_position != other.M_position; }
    int64_t operator * () const noexcept { return M_position; }

  };

  class reverse_iterator {
  private:
    int64_t M_position;
  
  public:
    reverse_iterator(int64_t position) noexcept: M_position(position) { }
    void operator ++ () noexcept { --M_position; }
    bool operator != (reverse_iterator other) const noexcept { return M_position != other.M_position; }
    int64_t operator * () const noexcept { return M_position; }

  };
  
private:
  const iterator M_first, M_last;

public:
  range(int64_t first, int64_t last) noexcept: M_first(first), M_last(std::max(first, last)) { }
  iterator begin() const noexcept { return M_first; }
  iterator end() const noexcept { return M_last; }
  reverse_iterator rbegin() const noexcept { return reverse_iterator(*M_last - 1); } 
  reverse_iterator rend() const noexcept { return reverse_iterator(*M_first - 1); } 

};

/**
 * @title Range
 */

#include <type_traits>
#include <iterator>

template <class T>
class rev_impl {
public:
  using iterator = decltype(std::declval<T>().rbegin());

private:
  const iterator M_begin;
  const iterator M_end;

public:
  rev_impl(T &&cont) noexcept: M_begin(cont.rbegin()), M_end(cont.rend()) { }
  iterator begin() const noexcept { return M_begin; }
  iterator end() const noexcept { return M_end; }

};

template <class T>
rev_impl<T> rev(T &&cont) {
  return rev_impl<T>(std::forward<T>(cont));
}

/**
 * @title Reverser
 */

#include <cstdint>

template <class Modulus>
class modular {
public:
  using value_type = uint32_t;
  using cover_type = uint64_t;
  static constexpr value_type mod() { return Modulus::value(); }

  template <class T>
  static value_type normalize(T value_) noexcept {
    if (value_ < 0) {
      value_ = -value_;
      value_ %= mod();
      if (value_ == 0) return 0;
      return mod() - value_;
    }
    return value_ % mod();
  }

private:
  value_type value;

public:
  modular() noexcept : value(0) { }
  template <class T>
  explicit modular(T value_) noexcept : value(normalize(value_)) { }
  template <class T>
  explicit operator T() const noexcept { return static_cast<T>(value); }

  value_type get() const noexcept { return value; }
  modular operator - () const noexcept { return modular(mod() - value); }
  modular operator ~ () const noexcept { return inverse(); }

  value_type &extract() noexcept { return value; }
  modular inverse() const noexcept { return power(mod() - 2); }
  modular power(cover_type exp) const noexcept {
    modular res(1), mult(*this);
    while (exp > 0) {
      if (exp & 1) res *= mult;
      mult *= mult;
      exp >>= 1;
    }
    return res;
  }

  modular operator + (const modular &rhs) const noexcept { return modular(*this) += rhs; }
  modular& operator += (const modular &rhs) noexcept { 
    if ((value += rhs.value) >= mod()) value -= mod(); 
    return *this; 
  }

  modular operator - (const modular &rhs) const noexcept { return modular(*this) -= rhs; }
  modular& operator -= (const modular &rhs) noexcept { 
    if ((value += mod() - rhs.value) >= mod()) value -= mod(); 
    return *this; 
  }

  modular operator * (const modular &rhs) const noexcept { return modular(*this) *= rhs; }
  modular& operator *= (const modular &rhs) noexcept { 
    value = (cover_type) value * rhs.value % mod();
    return *this;
  }

  modular operator / (const modular &rhs) const noexcept { return modular(*this) /= rhs; }
  modular& operator /= (const modular &rhs) noexcept { return (*this) *= rhs.inverse(); }

  bool zero() const noexcept { return value == 0; }
  bool operator == (const modular &rhs) const noexcept { return value == rhs.value; }
  bool operator != (const modular &rhs) const noexcept { return value != rhs.value; }

  friend std::ostream& operator << (std::ostream &stream, const modular &rhs) { return stream << rhs.value; }
  friend modular power(modular val, cover_type exp) noexcept { return val.power(exp); }
  friend modular inverse(modular val) noexcept { return val.inverse(); }

};

template <uint32_t Val>
struct modulus_impl { static constexpr uint32_t value() noexcept { return Val; } };
template <uint32_t Val>
using mint32_t = modular<modulus_impl<Val>>;

struct runtime_mod { static uint32_t &value() noexcept { static uint32_t val = 0; return val; } };
using rmint32_t = modular<runtime_mod>;

/**
 * @title Modint
 */

#include <cstddef>

template <class T, size_t N>
class factorials {
public:
  using value_type = T;
  static constexpr size_t size = N;

public:
  std::array<value_type, size + 1> fact{};
  std::array<value_type, size + 1> fact_inv{};

  factorials() {
    fact.front() = value_type(1);
    for (size_t i = 1; i <= size; ++i) {
      fact[i] = fact[i - 1] * value_type(i);
    }
    fact_inv.back() = ~fact.back();
    for (size_t i = size; i > 0; --i) {
      fact_inv[i - 1] = fact_inv[i] * value_type(i);
    }
  }

  value_type operator () (size_t n, size_t r) const {
    return fact[n] * fact_inv[n - r] * fact_inv[r];
  }

};

/**
 * @title Factorial
 */

using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;

constexpr i32 inf32 = (i32(1) << 30) - 1;
constexpr i64 inf64 = (i64(1) << 62) - 1;

using m32 = mint32_t<1000000007>;
factorials<m32, 500> fact;

int main() {
  i32 N;
  std::cin >> N;
  std::vector<i32> L(N), R(N);
  std::vector<i32> comp;
  comp.reserve(2 * N);
  for (auto i: range(0, N)) {
    std::cin >> L[i] >> R[i];
    ++R[i];
    comp.push_back(L[i]);
    comp.push_back(R[i]);
  }
  std::sort(comp.begin(), comp.end());
  comp.erase(std::unique(comp.begin(), comp.end()), comp.end());
  for (auto i: range(0, N)) {
    L[i] = std::lower_bound(comp.cbegin(), comp.cend(), L[i]) - comp.cbegin();
    R[i] = std::lower_bound(comp.cbegin(), comp.cend(), R[i]) - comp.cbegin();
  }
  const i32 size = comp.size() - 1;
  std::vector<i32> len(size);
  std::vector<std::vector<m32>> dp(size);
  std::vector<std::vector<m32>> coeff(size);
  for (auto i: range(0, size)) {
    len[i] = comp[i + 1] - comp[i];
    dp[i].resize(std::min(N, len[i]) + 1);
    coeff[i].resize(std::min(N, len[i]) + 1);
    m32 cur(1);
    for (auto j: range(1, std::min(N, len[i]) + 1)) {
      cur *= m32(len[i] - j + 1);
      coeff[i][j] = cur * fact.fact_inv[j];
    }
  }
  for (auto i: range(0, N)) {
    m32 sum;
    for (auto j: range(0, L[i])) {
      for (auto k: range(1, std::min(N, len[j]) + 1)) {
        sum += dp[j][k] * coeff[j][k];
      }
    }
    for (auto j: range(L[i], R[i])) {
      m32 add;
      for (auto k: range(1, std::min(N, len[j]) + 1)) {
        add += dp[j][k] * coeff[j][k];
      }
      for (auto k: rev(range(1, std::min(N, len[j])))) {
        dp[j][k + 1] += dp[j][k];
      }
      dp[j][1] += sum + m32(1);
      sum += add;
    }
  }
  m32 ans;
  for (auto j: range(0, size)) {
    for (auto k: range(1, std::min(N, len[j]) + 1)) {
      ans += dp[j][k] * coeff[j][k];
    }
  }
  std::cout << ans << '\n';
  return 0;
}

• Subtask 1: 9 / 9
• Subtask 2: 22 / 22
• Subtask 3: 27 / 27
• Subtask 4: 42 / 42