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 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 718 ms / 2,000 ms
コード長 17,785 bytes
コンパイル時間 959 ms
コンパイル使用メモリ 83,656 KB
最終ジャッジ日時 2025-01-16 03:39:58
ジャッジサーバーID
(参考情報)
judge1 / judge5
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ファイルパターン 結果
other AC * 17
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#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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