結果

問題 No.1222 -101
ユーザー KoD
提出日時 2020-09-04 22:41:02
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 445 ms / 2,000 ms
コード長 16,928 bytes
コンパイル時間 966 ms
コンパイル使用メモリ 86,116 KB
最終ジャッジ日時 2025-01-14 06:05:49
ジャッジサーバーID
(参考情報)
judge4 / judge4
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ファイルパターン 結果
sample AC * 4
other AC * 35
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ソースコード

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プレゼンテーションモードにする

#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/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/Programming/Library/other/range.cpp"
#line 4 "/Users/kodamankod/Desktop/Programming/Library/other/range.cpp"
class range {
public:
class iterator {
private:
int64_t M_position;
public:
constexpr iterator(int64_t position) noexcept: M_position(position) { }
constexpr void operator ++ () noexcept { ++M_position; }
constexpr bool operator != (iterator other) const noexcept { return M_position != other.M_position; }
constexpr int64_t operator * () const noexcept { return M_position; }
};
class reverse_iterator {
private:
int64_t M_position;
public:
constexpr reverse_iterator(int64_t position) noexcept: M_position(position) { }
constexpr void operator ++ () noexcept { --M_position; }
constexpr bool operator != (reverse_iterator other) const noexcept { return M_position != other.M_position; }
constexpr int64_t operator * () const noexcept { return M_position; }
};
private:
const iterator M_first, M_last;
public:
constexpr range(int64_t first, int64_t last) noexcept: M_first(first), M_last(std::max(first, last)) { }
constexpr iterator begin() const noexcept { return M_first; }
constexpr iterator end() const noexcept { return M_last; }
constexpr reverse_iterator rbegin() const noexcept { return reverse_iterator(*M_last - 1); }
constexpr reverse_iterator rend() const noexcept { return reverse_iterator(*M_first - 1); }
};
/**
* @title Range
*/
#line 2 "/Users/kodamankod/Desktop/Programming/Library/other/rev.cpp"
#include <type_traits>
#include <iterator>
#line 6 "/Users/kodamankod/Desktop/Programming/Library/other/rev.cpp"
template <class T>
class rev_impl {
public:
using iterator = decltype(std::rbegin(std::declval<T>()));
private:
const iterator M_begin;
const iterator M_end;
public:
constexpr rev_impl(T &&cont) noexcept: M_begin(std::rbegin(cont)), M_end(std::rend(cont)) { }
constexpr iterator begin() const noexcept { return M_begin; }
constexpr iterator end() const noexcept { return M_end; }
};
template <class T>
constexpr decltype(auto) rev(T &&cont) {
return rev_impl<T>(std::forward<T>(cont));
}
/**
* @title Reverser
*/
#line 2 "/Users/kodamankod/Desktop/Programming/Library/algebraic/modular.cpp"
#include <cstdint>
#line 5 "/Users/kodamankod/Desktop/Programming/Library/algebraic/modular.cpp"
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 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;
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(modular val) noexcept { return power(val, mod() - 2); }
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 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
*/
#line 2 "/Users/kodamankod/Desktop/Programming/Library/container/lazy_propagation_segment_tree.cpp"
#line 2 "/Users/kodamankod/Desktop/Programming/Library/other/bit_operation.cpp"
#include <cstddef>
#line 5 "/Users/kodamankod/Desktop/Programming/Library/other/bit_operation.cpp"
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 2 "/Users/kodamankod/Desktop/Programming/Library/other/monoid.cpp"
#include <type_traits>
#line 5 "/Users/kodamankod/Desktop/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]] constexpr 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:
static constexpr typename T::type convert(const typename T::type &value) { return value; }
static constexpr typename T::type revert(const typename T::type &value) { return value; }
};
template <class T>
class fixed_monoid_impl<T, false>: private T {
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 T>
using fixed_monoid = fixed_monoid_impl<T, has_identity<T>::value>;
template <class T, bool HasIdentity>
class fixed_combined_monoid_impl {
public:
using value_structure = typename T::value_structure;
using operator_structure = fixed_monoid<typename T::operator_structure>;
template <class... Args>
static constexpr typename value_structure::type operation(
const typename value_structure::type &val,
const typename operator_structure::type &op,
Args&&... args) {
return T::operation(val, op, std::forward<Args>(args)...);
}
};
template <class T>
class fixed_combined_monoid_impl<T, false> {
public:
using value_structure = typename T::value_structure;
using operator_structure = fixed_monoid<typename T::operator_structure>;
template <class... Args>
static constexpr typename value_structure::type operation(
const typename value_structure::type &val,
const typename operator_structure::type &op,
Args&&... args) {
if (!op.state) return val;
return T::operation(val, op.value, std::forward<Args>(args)...);
}
};
template <class T>
using fixed_combined_monoid = fixed_combined_monoid_impl<T, has_identity<typename T::operator_structure>::value>;
/**
* @title Monoid Utility
*/
#line 5 "/Users/kodamankod/Desktop/Programming/Library/container/lazy_propagation_segment_tree.cpp"
#line 10 "/Users/kodamankod/Desktop/Programming/Library/container/lazy_propagation_segment_tree.cpp"
template <class CombinedMonoid>
class lazy_propagation_segment_tree {
public:
using structure = CombinedMonoid;
using value_monoid = typename CombinedMonoid::value_structure;
using operator_monoid = typename CombinedMonoid::operator_structure;
using value_type = typename CombinedMonoid::value_structure::type;
using operator_type = typename CombinedMonoid::operator_structure::type;
using size_type = size_t;
private:
using fixed_structure = fixed_combined_monoid<structure>;
using fixed_operator_monoid = typename fixed_structure::operator_structure;
using fixed_operator_type = typename fixed_operator_monoid::type;
class node_type {
public:
value_type value;
fixed_operator_type lazy;
node_type(
const value_type &value = value_monoid::identity(),
const fixed_operator_type &lazy = fixed_operator_monoid::identity()
): value(value), lazy(lazy) { }
};
static void S_apply(node_type &node, const fixed_operator_type &op, const size_type length) {
node.value = fixed_structure::operation(node.value, op, length);
node.lazy = fixed_operator_monoid::operation(node.lazy, op);
}
void M_propagate(const size_type index, const size_type length) {
S_apply(M_tree[index << 1 | 0], M_tree[index].lazy, length);
S_apply(M_tree[index << 1 | 1], M_tree[index].lazy, length);
M_tree[index].lazy = fixed_operator_monoid::identity();
}
void M_fix_change(const size_type index) {
M_tree[index].value =
value_monoid::operation(M_tree[index << 1 | 0].value, M_tree[index << 1 | 1].value);
}
void M_pushdown(const size_type index) {
const size_type lsb = bit_ctzr(index);
for (size_type story = bit_width(index); story != lsb; --story) {
M_propagate(index >> story, 1 << (story - 1));
}
}
void M_pullup(size_type index) {
index >>= bit_ctzr(index);
while (index != 1) {
index >>= 1;
M_fix_change(index);
}
}
std::vector<node_type> M_tree;
public:
lazy_propagation_segment_tree() = default;
explicit lazy_propagation_segment_tree(const size_type size) { initialize(size); }
template <class InputIterator>
explicit lazy_propagation_segment_tree(InputIterator first, InputIterator last) { construct(first, last); }
void initialize(const size_type size) {
clear();
M_tree.assign(size << 1, node_type());
}
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, node_type());
for (; first != last; ++first) {
M_tree.emplace_back(*first, fixed_operator_monoid::identity());
}
for (size_type index = size - 1; index != 0; --index) {
M_fix_change(index);
}
}
value_type fold(size_type first, size_type last) {
first += size();
last += size();
M_pushdown(first);
M_pushdown(last);
value_type fold_l = value_monoid::identity();
value_type fold_r = value_monoid::identity();
while (first != last) {
if (first & 1) {
fold_l = value_monoid::operation(fold_l, M_tree[first].value);
++first;
}
if (last & 1) {
--last;
fold_r = value_monoid::operation(M_tree[last].value, fold_r);
}
first >>= 1;
last >>= 1;
}
return value_monoid::operation(fold_l, fold_r);
}
void operate(size_type first, size_type last, const operator_type &op_) {
const auto op = fixed_operator_monoid::convert(op_);
first += size();
last += size();
M_pushdown(first);
M_pushdown(last);
const size_type first_c = first;
const size_type last_c = last;
for (size_type story = 0; first != last; ++story) {
if (first & 1) {
S_apply(M_tree[first], op, 1 << story);
++first;
}
if (last & 1) {
--last;
S_apply(M_tree[last], op, 1 << story);
}
first >>= 1;
last >>= 1;
}
M_pullup(first_c);
M_pullup(last_c);
}
void assign(size_type index, const value_type &val) {
index += size();
for (size_type story = bit_width(index); story != 0; --story) {
M_propagate(index >> story, 1 << (story - 1));
}
M_tree[index].value = val;
M_tree[index].lazy = fixed_operator_monoid::identity();
while (index != 1) {
index >>= 1;
M_fix_change(index);
}
}
void clear() {
M_tree.clear();
M_tree.shrink_to_fit();
}
size_type size() const {
return M_tree.size() >> 1;
}
};
/**
* @title Lazy Propagation Segment Tree
*/
#line 19 "main.cpp"
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>;
struct lst_monoid {
struct value_structure {
using type = m32;
static type identity() { return m32(0); }
static type operation(const type& v1, const type& v2) {
return v1 + v2;
}
};
struct operator_structure {
using type = m32;
static type identity() { return m32(1); }
static type operation(const type& v1, const type& v2) {
return v1 * v2;
}
};
static typename value_structure::type operation(
const typename value_structure::type &val,
const typename operator_structure::type &op,
const size_t length = 1) {
return val * op;
}
};
int main() {
i32 N, M;
std::cin >> N >> M;
std::vector<i32> usage(N + 1);
i32 nonzero = 0;
std::vector<std::vector<i32>> Qs(N + 1);
for (auto i: range(0, M)) {
i32 l, r, p;
std::cin >> l >> r >> p;
--l;
if (p == 0) {
Qs[r].push_back(l);
}
else {
++nonzero;
++usage[l];
--usage[r];
}
}
m32 ans(1);
for (auto i: range(0, N)) {
usage[i + 1] += usage[i];
if (usage[i] > 0) {
ans *= m32(2);
}
}
ans /= power(m32(2), nonzero);
lazy_propagation_segment_tree<lst_monoid> dp(N + 1);
dp.assign(0, m32(1));
for (auto i: range(1, N + 1)) {
if (usage[i - 1] == 0) {
dp.assign(i, dp.fold(0, i));
dp.operate(0, i, m32(2));
}
for (auto l: Qs[i]) {
dp.operate(0, l + 1, m32(0));
}
}
std::cout << ans * dp.fold(0, N + 1) << '\n';
return 0;
}
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