#582271 (C++17) No.1294 マウンテン数列

提出ソース
結果

問題	No.1294 マウンテン数列
ユーザー	KoD
提出日時	2020-11-21 00:27:17
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	482 ms / 2,000 ms
コード長	17,785 bytes
コンパイル時間	1,141 ms
コンパイル使用メモリ	86,152 KB
実行使用メモリ	5,376 KB
最終ジャッジ日時	2024-07-23 14:10:45
合計ジャッジ時間	5,173 ms
ジャッジサーバーID （参考情報）	judge1 / judge5
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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	2 ms 5,248 KB
testcase_01	AC	2 ms 5,248 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	AC	2 ms 5,376 KB
testcase_04	AC	2 ms 5,376 KB
testcase_05	AC	35 ms 5,376 KB
testcase_06	AC	53 ms 5,376 KB
testcase_07	AC	2 ms 5,376 KB
testcase_08	AC	2 ms 5,376 KB
testcase_09	AC	2 ms 5,376 KB
testcase_10	AC	477 ms 5,376 KB
testcase_11	AC	478 ms 5,376 KB
testcase_12	AC	477 ms 5,376 KB
testcase_13	AC	482 ms 5,376 KB
testcase_14	AC	407 ms 5,376 KB
testcase_15	AC	453 ms 5,376 KB
testcase_16	AC	412 ms 5,376 KB
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ソースコード

raw source code
#line 1 "main.cpp"

/**
 * @title Template
 */

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

#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/chmin_chmax.cpp"

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

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

/**
 * @title Chmin/Chmax
 */
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/range.cpp"

#line 4 "/Users/kodamankod/Desktop/cpp_programming/Library/other/range.cpp"

class range {
  struct iter {
    std::size_t itr;
    constexpr iter(std::size_t pos) noexcept: itr(pos) { }
    constexpr void operator ++ () noexcept { ++itr; }
    constexpr bool operator != (iter other) const noexcept { return itr != other.itr; }
    constexpr std::size_t operator * () const noexcept { return itr; }
  };

  struct reviter {
    std::size_t itr;
    constexpr reviter(std::size_t pos) noexcept: itr(pos) { }
    constexpr void operator ++ () noexcept { --itr; }
    constexpr bool operator != (reviter other) const noexcept { return itr != other.itr; }
    constexpr std::size_t operator * () const noexcept { return itr; }
  };

  const iter first, last;

public:
  constexpr range(std::size_t first, std::size_t last) noexcept: first(first), last(std::max(first, last)) { }
  constexpr iter begin() const noexcept { return first; }
  constexpr iter end() const noexcept { return last; }
  constexpr reviter rbegin() const noexcept { return reviter(*last - 1); } 
  constexpr reviter rend() const noexcept { return reviter(*first - 1); } 
};

/**
 * @title Range
 */
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/container/segment_tree.cpp"

#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/monoid.cpp"

#include <type_traits>
#line 5 "/Users/kodamankod/Desktop/cpp_programming/Library/other/monoid.cpp"
#include <stdexcept>

template <class T, class = void>
class has_identity: public std::false_type { };

template <class T>
class has_identity<T, typename std::conditional<false, decltype(T::identity()), void>::type>: public std::true_type { };

template <class T>
constexpr typename std::enable_if<has_identity<T>::value, typename T::type>::type empty_exception() {
  return T::identity();
}
template <class T>
[[noreturn]] typename std::enable_if<!has_identity<T>::value, typename T::type>::type empty_exception() {
  throw std::runtime_error("type T has no identity");
}

template <class T, bool HasIdentity>
class fixed_monoid_impl: public T {
public:
  using type = typename T::type;

  static constexpr type convert(const type &value) { return value; }
  static constexpr type revert(const type &value) { return value; }

  template <class Mapping, class Value, class... Args>
  static constexpr void operate(Mapping &&func, Value &value, const type &op, Args&&... args) {
    value = func(value, op, std::forward<Args>(args)...);
  }
  template <class Constraint>
  static constexpr bool satisfies(Constraint &&func, const type &value) {
    return func(value);
  }
};

template <class T>
class fixed_monoid_impl<T, false> {
public:
  class type {
  public:
    typename T::type value;
    bool state;
  
    explicit constexpr type(): value(typename T::type { }), state(false) { }
    explicit constexpr type(const typename T::type &value): value(value), state(true) { }
  };

  static constexpr type convert(const typename T::type &value) { return type(value); }
  static constexpr typename T::type revert(const type &value) { 
    if (!value.state) throw std::runtime_error("attempted to revert identity to non-monoid"); 
    return value.value; 
  }

  static constexpr type identity() { return type(); }
  static constexpr type operation(const type &v1, const type &v2) {
    if (!v1.state) return v2;
    if (!v2.state) return v1;
    return type(T::operation(v1.value, v2.value));
  }

  template <class Mapping, class Value, class... Args>
  static constexpr void operate(Mapping &&func, Value &value, const type &op, Args&&... args) {
    if (!op.state) return;
    value = func(value, op.value, std::forward<Args>(args)...);
  }
  template <class Constraint>
  static constexpr bool satisfies(Constraint &&func, const type &value) {
    if (!value.state) return false;
    return func(value.value);
  }
};

template <class T>
using fixed_monoid = fixed_monoid_impl<T, has_identity<T>::value>;

/**
 * @title Monoid Utility
 */
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/bit_operation.cpp"

#include <cstddef>
#include <cstdint>

constexpr size_t bit_ppc(const uint64_t x) { return __builtin_popcountll(x); }
constexpr size_t bit_ctzr(const uint64_t x) { return x == 0 ? 64 : __builtin_ctzll(x); }
constexpr size_t bit_ctzl(const uint64_t x) { return x == 0 ? 64 : __builtin_clzll(x); }
constexpr size_t bit_width(const uint64_t x) { return 64 - bit_ctzl(x); }
constexpr uint64_t bit_msb(const uint64_t x) { return x == 0 ? 0 : uint64_t(1) << (bit_width(x) - 1); }
constexpr uint64_t bit_lsb(const uint64_t x) { return x & (-x); }
constexpr uint64_t bit_cover(const uint64_t x) { return x == 0 ? 0 : bit_msb(2 * x - 1); }

constexpr uint64_t bit_rev(uint64_t x) {
  x = ((x >> 1) & 0x5555555555555555) | ((x & 0x5555555555555555) << 1);
  x = ((x >> 2) & 0x3333333333333333) | ((x & 0x3333333333333333) << 2);
  x = ((x >> 4) & 0x0F0F0F0F0F0F0F0F) | ((x & 0x0F0F0F0F0F0F0F0F) << 4);
  x = ((x >> 8) & 0x00FF00FF00FF00FF) | ((x & 0x00FF00FF00FF00FF) << 8);
  x = ((x >> 16) & 0x0000FFFF0000FFFF) | ((x & 0x0000FFFF0000FFFF) << 16);
  x = (x >> 32) | (x << 32);
  return x;
}

/**
 * @title Bit Operations
 */
#line 5 "/Users/kodamankod/Desktop/cpp_programming/Library/container/segment_tree.cpp"

#line 8 "/Users/kodamankod/Desktop/cpp_programming/Library/container/segment_tree.cpp"
#include <iterator>
#line 11 "/Users/kodamankod/Desktop/cpp_programming/Library/container/segment_tree.cpp"
#include <type_traits>
#line 13 "/Users/kodamankod/Desktop/cpp_programming/Library/container/segment_tree.cpp"

template <class Monoid>
class segment_tree {
public:
  using structure    = Monoid;
  using value_monoid = typename Monoid::value_structure;
  using value_type   = typename Monoid::value_structure::type;
  using size_type    = size_t;

private:
  using fixed_value_monoid = fixed_monoid<value_monoid>;
  using fixed_value_type   = typename fixed_value_monoid::type;

  std::vector<fixed_value_type> M_tree;

  void M_fix_change(const size_type index) {
    M_tree[index] = fixed_value_monoid::operation(M_tree[index << 1 | 0], M_tree[index << 1 | 1]);
  }

public:
  segment_tree() = default;
  explicit segment_tree(const size_type size) { initialize(size); }
  template <class InputIterator>
  explicit segment_tree(InputIterator first, InputIterator last) { construct(first, last); }

  void initialize(const size_type size) {
    clear();
    M_tree.assign(size << 1, fixed_value_monoid::identity());
  }

  template <class InputIterator>
  void construct(InputIterator first, InputIterator last) {
    clear();
    const size_type size = std::distance(first, last);
    M_tree.reserve(size << 1);
    M_tree.assign(size, fixed_value_monoid::identity());
    std::transform(first, last, std::back_inserter(M_tree), [&](const value_type &value) {
      return fixed_value_monoid::convert(value);
    });
    for (size_type index = size - 1; index != 0; --index) {
      M_fix_change(index);
    }
  }

  void assign(size_type index, const value_type &value) {
    assert(index < size());
    index += size();
    M_tree[index] = fixed_value_monoid::convert(value);
    while (index != 1) {
      index >>= 1;
      M_fix_change(index);
    } 
  }

  value_type at(const size_type index) const { 
    assert(index < size());
    return fixed_value_monoid::revert(M_tree[index + size()]);
  }

  value_type fold(size_type first, size_type last) const {
    assert(first <= last);
    assert(last <= size());
    first += size();
    last += size();
    fixed_value_type fold_l = fixed_value_monoid::identity();
    fixed_value_type fold_r = fixed_value_monoid::identity();
    while (first != last) {
      if (first & 1) {
        fold_l = fixed_value_monoid::operation(fold_l, M_tree[first]);
        ++first;
      }
      if (last & 1) {
        --last;
        fold_r = fixed_value_monoid::operation(M_tree[last], fold_r);      
      }
      first >>= 1;
      last >>= 1;
    }
    return fixed_value_monoid::revert(fixed_value_monoid::operation(fold_l, fold_r));
  }

  template <bool ToRight = true, class Constraint, std::enable_if_t<ToRight>* = nullptr> 
  size_type satisfies(const size_type left, Constraint &&func) const {
    assert(left <= size());
    if (fixed_value_monoid::satisfies(std::forward<Constraint>(func), 
      fixed_value_monoid::identity())) return left;
    size_type first = left + size();
    size_type last = 2 * size();
    const size_type last_c = last;
    fixed_value_type fold = fixed_value_monoid::identity();
    const auto try_merge = [&](const size_type index) {
      fixed_value_type tmp = fixed_value_monoid::operation(fold, M_tree[index]);
      if (fixed_value_monoid::satisfies(std::forward<Constraint>(func), tmp)) return true;
      fold = std::move(tmp);
      return false;
    };
    const auto subtree = [&](size_type index) {
      while (index < size()) {
        index <<= 1;
        if (!try_merge(index)) ++index;
      }
      return index - size() + 1;
    };
    size_type story = 0;
    while (first < last) {
      if (first & 1) {
        if (try_merge(first)) return subtree(first);
        ++first;
      }
      first >>= 1;
      last >>= 1;
      ++story;
    }
    while (story--) {
      last = last_c >> story;
      if (last & 1) {
        --last;
        if (try_merge(last)) return subtree(last);
      }
    }
    return size() + 1;
  }

  template <bool ToRight = true, class Constraint, std::enable_if_t<!ToRight>* = nullptr> 
  size_type satisfies(const size_type right, Constraint &&func) const {
    assert(right <= size());
    if (fixed_value_monoid::satisfies(std::forward<Constraint>(func), 
      fixed_value_monoid::identity())) return right;
    size_type first = size();
    size_type last = right + size();
    const size_type first_c = first;
    fixed_value_type fold = fixed_value_monoid::identity();
    const auto try_merge = [&](const size_type index) {
      fixed_value_type tmp = fixed_value_monoid::operation(M_tree[index], fold);
      if (fixed_value_monoid::satisfies(std::forward<Constraint>(func), tmp)) return true;
      fold = std::move(tmp);
      return false;
    };
    const auto subtree = [&](size_type index) {
      while (index < size()) {
        index <<= 1;
        if (try_merge(index + 1)) ++index;
      }
      return index - size();
    };
    size_type story = 0;
    while (first < last) {
      if (first & 1) ++first;
      if (last & 1) {
        --last;
        if (try_merge(last)) return subtree(last);
      }
      first >>= 1;
      last >>= 1;
      ++story;
    }
    const size_type cover = bit_cover(first_c);
    while (story--) {
      first = (cover >> story) - ((cover - first_c) >> story);
      if (first & 1) {
        if (try_merge(first)) return subtree(first);
      }
    }
    return size_type(-1);
  }

  void clear() {
    M_tree.clear();
    M_tree.shrink_to_fit();
  }
  size_type size() const { 
    return M_tree.size() >> 1;
  }
};

/**
 * @title Segment Tree
 */
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/algebraic/modular.cpp"

#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/algebraic/mod_inv.cpp"

#line 5 "/Users/kodamankod/Desktop/cpp_programming/Library/algebraic/mod_inv.cpp"

constexpr std::pair<int64_t, int64_t> mod_inv(int64_t a, int64_t b) {
  if ((a %= b) == 0) return { b, 0 };
  int64_t s = b, t = (a < 0 ? a + b : a);
  int64_t m0 = 0, m1 = 1, tmp = 0;
  while (t > 0) {
    const auto u = s / t;
    s -= t * u; m0 -= m1 * u;
    tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp;
  }
  return { s, (m0 < 0 ? m0 + b / s : m0) };
}

/**
 * @title Extended GCD
 */
#line 4 "/Users/kodamankod/Desktop/cpp_programming/Library/algebraic/modular.cpp"

#line 8 "/Users/kodamankod/Desktop/cpp_programming/Library/algebraic/modular.cpp"
#include <type_traits>

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

  template <bool IsPrime, std::enable_if_t<IsPrime>* = nullptr>
  constexpr modular inverse_helper() const noexcept { return power(*this, mod() - 2); }
  template <bool IsPrime, std::enable_if_t<!IsPrime>* = nullptr>
  constexpr modular inverse_helper() const noexcept {
    const auto tmp = mod_inv(value, mod());
    assert(tmp.first == 1);
    return modular(tmp.second);
  }

public:
  constexpr modular() noexcept : value(0) { }
  template <class T>
  explicit constexpr modular(T value_) noexcept : value(normalize(value_)) { }
  template <class T>
  explicit constexpr operator T() const noexcept { return static_cast<T>(value); }
 
  constexpr value_type get() const noexcept { return value; }
  constexpr value_type &extract() noexcept { return value; }
  constexpr modular operator - () const noexcept { return modular(mod() - value); }
  constexpr modular operator ~ () const noexcept { return inverse(*this); }
 
  constexpr modular operator + (const modular &rhs) const noexcept { return modular(*this) += rhs; }
  constexpr modular& operator += (const modular &rhs) noexcept { 
    if ((value += rhs.value) >= mod()) value -= mod(); 
    return *this; 
  }
 
  constexpr modular operator - (const modular &rhs) const noexcept { return modular(*this) -= rhs; }
  constexpr modular& operator -= (const modular &rhs) noexcept { 
    if ((value += mod() - rhs.value) >= mod()) value -= mod(); 
    return *this; 
  }
 
  constexpr modular operator * (const modular &rhs) const noexcept { return modular(*this) *= rhs; }
  constexpr modular& operator *= (const modular &rhs) noexcept { 
    value = (cover_type) value * rhs.value % mod();
    return *this;
  }
 
  constexpr modular operator / (const modular &rhs) const noexcept { return modular(*this) /= rhs; }
  constexpr modular& operator /= (const modular &rhs) noexcept { return (*this) *= inverse(rhs); }
 
  constexpr bool zero() const noexcept { return value == 0; }
  constexpr bool operator == (const modular &rhs) const noexcept { return value == rhs.value; }
  constexpr 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 constexpr modular inverse(const modular &val) noexcept { return val.inverse_helper<Modulus::is_prime>(); }
  friend constexpr modular power(modular val, cover_type exp) noexcept { 
    modular res(1);
    for (; exp > 0; exp >>= 1, val *= val) if (exp & 1) res *= val;
    return res;
  }
 
};
 
template <uint32_t Mod, bool IsPrime = true>
struct static_modulus { 
  static constexpr uint32_t mod() noexcept { return Mod; } 
  static constexpr bool is_prime = IsPrime;
};

template <uint32_t Id = 0, bool IsPrime = false>
struct dynamic_modulus {
  static uint32_t &mod() noexcept { static uint32_t val = 0; return val; }
  static constexpr bool is_prime = IsPrime;
};

template <uint32_t Mod, bool IsPrime = true>
using mint32_t = modular<static_modulus<Mod, IsPrime>>;
using rmint32_t = modular<dynamic_modulus<>>;

/*
 * @title Modint
 */
#line 18 "main.cpp"

using i32 = std::int32_t;
using i64 = std::int64_t;
using u32 = std::uint32_t;
using u64 = std::uint64_t;
using isize = std::ptrdiff_t;
using usize = std::size_t;

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

using Fp = mint32_t<998244353>;

struct st_monoid {
  struct value_structure {
    using type = Fp;
    static type identity() { return Fp(0); }
    static type operation(const type& v1, const type& v2) { 
      return v1 + v2;
    }
  };
};

int main() {
  usize N;
  std::cin >> N;
  std::vector<usize> A(N);
  for (auto &x: A) {
    std::cin >> x;
  }
  std::reverse(A.begin(), A.end());
  usize mx = 0;
  for (auto i: range(1, N)) {
    chmax(mx, A[i - 1] - A[i]);
  }
  std::vector<Fp> ans(2500);
  for (auto max_dif: range(mx, 2500)) {
    // std::vector<std::vector<Fp>> dp(N, std::vector<Fp>(N));
    // dp[0][0] = Fp(1);
    // for (auto i: range(0, N - 1)) {
    //   for (auto j: range(0, i + 1)) {
    //     dp[i + 1][j] += dp[i][j];
    //     if (A[j] - A[i + 1] <= max_dif) {
    //       dp[i + 1][i] += dp[i][j];
    //     }
    //   }
    // }
    // for (auto i: range(0, N)) {
    //   ans[max_dif] += dp[N - 1][i];
    // }
    std::vector<usize> left(N - 1);
    {
      usize idx = 0;
      for (auto i: range(0, N - 1)) {
        while (A[idx] - A[i + 1] > max_dif) {
          idx += 1;
        }
        left[i] = idx;
      }
    }
    segment_tree<st_monoid> seg(N);
    seg.assign(0, Fp(2));
    for (auto i: range(0, N - 1)) {
      seg.assign(i, seg.fold(left[i], i + 1));
    }
    ans[max_dif] = seg.fold(0, N);
  }
  Fp sum;
  for (auto i: range(1, 2500)) {
    sum += Fp(i) * (ans[i] - ans[i - 1]);
  }
  std::cout << sum << '\n';
  return 0;
}
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