#548035 (C++17) No.1222 -101

• 問題: No.1222 -101
• ユーザー: jell
• 提出日時: 2020-09-04 22:56:17
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 63 ms / 2,000 ms
• コード長: 22,584 bytes
• コンパイル時間: 2,834 ms
• コンパイル使用メモリ: 267,004 KB
• 最終ジャッジ日時: 2025-01-14 06:19:09
• ジャッジサーバーID （参考情報）: judge2 / judge3

ファイルパターン	結果
sample	AC * 4
other	AC * 35

ソースコード

#line 1 "yu.cpp"
#include <bits/extc++.h>

#line 5 "Library\\config.hpp"
namespace config {
const auto start_time{std::chrono::system_clock::now()};
int64_t elapsed()
{
    using namespace std::chrono;
    const auto end_time{system_clock::now()};
    return duration_cast<milliseconds>(end_time - start_time).count();
}
__attribute__((constructor)) void setup()
{
    using namespace std;
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(15);
#ifdef _buffer_check
    atexit([]{ ofstream cnsl("CON"); char bufc; if(cin >> bufc) cnsl << "\n\033[43m\033[30mwarning: buffer not empty.\033[0m\n\n"; });
#endif
}
unsigned cases(void), caseid = 1;
template <class C> void main() { for(const unsigned total = cases(); caseid <= total; ++caseid) C(); }
} // namespace config
#line 3 "Library\\gcc_builtin.hpp"
namespace workspace {
constexpr int clz32(const uint32_t &n) noexcept { return __builtin_clz(n); }
constexpr int clz64(const uint64_t &n) noexcept{ return __builtin_clzll(n); }
constexpr int ctz(const uint64_t &n) noexcept { return __builtin_ctzll(n); }
constexpr int popcnt(const uint64_t &n) noexcept { return __builtin_popcountll(n); }
} // namespace workspace
#line 2 "Library\\gcc_option.hpp"
#ifdef ONLINE_JUDGE
    #pragma GCC optimize("O3")
    #pragma GCC target("avx,avx2")
    #pragma GCC optimize("unroll-loops")
#endif
#line 5 "Library\\utils\\binary_search.hpp"
namespace workspace {
// binary search on discrete range.
template <class iter_type, class pred_type, std::enable_if_t<std::is_convertible_v<std::invoke_result_t<pred_type, iter_type>, bool>, std::nullptr_t> = nullptr>
iter_type binary_search(iter_type ok, iter_type ng, pred_type pred)
{
    assert(ok != ng);
    intmax_t dist(ng - ok);
    while(std::abs(dist) > 1)
    {
        iter_type mid(ok + dist / 2);
        if(pred(mid)) ok = mid, dist -= dist / 2;
        else ng = mid, dist /= 2;
    }
    return ok;
}
// binary search on real numbers.
template <class real_type, class pred_type, std::enable_if_t<std::is_convertible_v<std::invoke_result_t<pred_type, real_type>, bool>, std::nullptr_t> = nullptr>
real_type binary_search(real_type ok, real_type ng, const real_type eps, pred_type pred)
{
    assert(ok != ng);
    while(std::abs(ok - ng) > eps)
    {
        real_type mid{(ok + ng) / 2};
        (pred(mid) ? ok : ng) = mid;
    }
    return ok;
}
} // namespace workspace
#line 3 "Library\\utils\\casefmt.hpp"
namespace workspace {
std::ostream &casefmt(std::ostream& os) { return os << "Case #" << config::caseid << ": "; }
} // namespace workspace
#line 3 "Library\\utils\\chval.hpp"
namespace workspace {
template <class T, class Comp = std::less<T>> bool chle(T &x, const T &y, Comp comp = Comp()) { return comp(y, x) ? x = y, true : false; }
template <class T, class Comp = std::less<T>> bool chge(T &x, const T &y, Comp comp = Comp()) { return comp(x, y) ? x = y, true : false; }
} // namespace workspace
#line 3 "Library\\utils\\fixed_point.hpp"
namespace workspace {
// specify the return type of lambda.
template <class lambda_type>
class fixed_point
{
    lambda_type func;
public:
    fixed_point(lambda_type &&f) : func(std::move(f)) {}
    template <class... Args> auto operator()(Args &&... args) const { return func(*this, std::forward<Args>(args)...); }
};
} // namespace workspace
#line 2 "Library\\utils\\sfinae.hpp"
#include <type_traits>
template <class type, template <class> class trait>
using enable_if_trait_type = typename std::enable_if<trait<type>::value>::type;
template <class Container>
using element_type = std::remove_const_t<std::remove_reference_t<decltype(*std::begin(std::declval<Container&>()))>>;
#line 7 "Library\\utils\\hash.hpp"
namespace workspace {
template <class T, class = void>
struct hash : std::hash<T> {};
template <class Unique_bits_type>
struct hash<Unique_bits_type, enable_if_trait_type<Unique_bits_type, std::has_unique_object_representations>>
{
    size_t operator()(uint64_t x) const
    {
        static const uint64_t m = std::random_device{}();
        x ^= x >> 23;
        // x *= 0x2127599bf4325c37ULL;
        x ^= m;
        x ^= x >> 47;
        return x - (x >> 32);
    }
};
template <class Key>
size_t hash_combine(const size_t &seed, const Key &key)
{
    return seed ^ (hash<Key>()(key) + 0x9e3779b9 /* + (seed << 6) + (seed >> 2) */ );
}
template <class T1, class T2>
struct hash<std::pair<T1, T2>>
{
    size_t operator()(const std::pair<T1, T2> &pair) const
    {
        return hash_combine(hash<T1>()(pair.first), pair.second);
    }
};
template <class... T>
class hash<std::tuple<T...>>
{
    template <class Tuple, size_t index = std::tuple_size<Tuple>::value - 1> struct tuple_hash { static uint64_t apply(const Tuple &t) { return hash_combine(tuple_hash<Tuple, index - 1>::apply(t), std::get<index>(t)); } };
    template <class Tuple> struct tuple_hash<Tuple, size_t(-1)> { static uint64_t apply(const Tuple &t) { return 0; } };
public:
    uint64_t operator()(const std::tuple<T...> &t) const { return tuple_hash<std::tuple<T...>>::apply(t); }
};
template <class hash_table>
struct hash_table_wrapper : hash_table
{
    using key_type = typename hash_table::key_type;
    size_t count(const key_type &key) const { return hash_table::find(key) != hash_table::end(); }
    template <class... Args> auto emplace(Args&&... args) { return hash_table::insert(typename hash_table::value_type(args...)); }
};
template <class Key, class Mapped = __gnu_pbds::null_type>
using cc_hash_table = hash_table_wrapper<__gnu_pbds::cc_hash_table<Key, Mapped, hash<Key>>>;
template <class Key, class Mapped = __gnu_pbds::null_type>
using gp_hash_table = hash_table_wrapper<__gnu_pbds::gp_hash_table<Key, Mapped, hash<Key>>>;
template <class Key, class Mapped>
using unordered_map = std::unordered_map<Key, Mapped, hash<Key>>;
template <class Key>
using unordered_set = std::unordered_set<Key, hash<Key>>;
} // namespace workspace
#line 3 "Library\\utils\\iostream_overload.hpp"
namespace std
{
    template <class T, class U> istream &operator>>(istream &is, pair<T, U> &p) { return is >> p.first >> p.second; }
    template <class T, class U> ostream &operator<<(ostream &os, const pair<T, U> &p) { return os << p.first << ' ' << p.second; }
    template <class tuple_t, size_t index> struct tuple_is { static istream &apply(istream &is, tuple_t &t) { tuple_is<tuple_t, index - 1>::apply(is, t); return is >> get<index>(t); } };
    template <class tuple_t> struct tuple_is<tuple_t, SIZE_MAX> { static istream &apply(istream &is, tuple_t &t) { return is; } };
    template <class... T> istream &operator>>(istream &is, tuple<T...> &t) { return tuple_is<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(is, t); }
    template <class tuple_t, size_t index> struct tuple_os { static ostream &apply(ostream &os, const tuple_t &t) { tuple_os<tuple_t, index - 1>::apply(os, t); return os << ' ' << get<index>(t); } };
    template <class tuple_t> struct tuple_os<tuple_t, 0> { static ostream &apply(ostream &os, const tuple_t &t) { return os << get<0>(t); } };
    template <class tuple_t> struct tuple_os<tuple_t, SIZE_MAX> { static ostream &apply(ostream &os, const tuple_t &t) { return os; } };
    template <class... T> ostream &operator<<(ostream &os, const tuple<T...> &t) { return tuple_os<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(os, t); }
    template <class Container, typename Value = typename Container::value_type, enable_if_t<!is_same<decay_t<Container>, string>::value, nullptr_t> = nullptr>
    istream& operator>>(istream& is, Container &cont) { for(auto&& e : cont) is >> e; return is; }
    template <class Container, typename Value = typename Container::value_type, enable_if_t<!is_same<decay_t<Container>, string>::value, nullptr_t> = nullptr>
    ostream& operator<<(ostream& os, const Container &cont) { bool flag = 1; for(auto&& e : cont) flag ? flag = 0 : (os << ' ', 0), os << e; return os; }
} // namespace std
#line 3 "Library\\utils\\read.hpp"
namespace workspace {
// read with std::cin.
template <class T = void>
struct read
{
    typename std::remove_const<T>::type value;
    template <class... types>
    read(types... args) : value(args...) { std::cin >> value; }
    operator T() const { return value; }
};
template <>
struct read<void>
{
    template <class T>
    operator T() const { T value; std::cin >> value; return value; }
};
} // namespace workspace
#line 13 "yu.cpp"

namespace workspace {
constexpr char eol = '\n';
using namespace std;
using i64 = int_least64_t;
using p32 = pair<int, int>;
using p64 = pair<i64, i64>;
template <class T, class Comp = std::less<T>>
using priority_queue = std::priority_queue<T, std::vector<T>, Comp>;
template <class T> using stack = std::stack<T, std::vector<T>>;
struct solver;
}  // namespace workspace
int main() { config::main<workspace::solver>(); }
unsigned config::cases() {
  // return -1; // not specify
  // int t; std::cin >> t; return t; // given
  return 1;
}

#line 4 "Library\\data_structure\\union_find\\basic.hpp"
struct union_find
{
    union_find(const size_t &n = 0) : link(n, -1) {}

    size_t find(const size_t &x)
    {
        assert(x < size());
        return link[x] < 0 ? x : (link[x] = find(link[x]));
    }

    size_t size() const { return link.size(); }

    size_t size(const size_t &x)
    {
        assert(x < size());
        return -link[find(x)];
    }

    bool same(const size_t &x, const size_t &y)
    {
        assert(x < size() && y < size());
        return find(x) == find(y);
    }

    virtual bool unite(size_t x, size_t y)
    {
        assert(x < size() && y < size());
        x = find(x), y = find(y);
        if(x == y) return false;
        if(link[x] > link[y]) std::swap(x, y);
        link[x] += link[y];
        link[y] = x;
        return true;
    }

protected:
    std::vector<int> link;
}; // class union_find
#line 5 "Library\\graph\\directed\\strongly_connected_components.hpp"
struct strongly_connected_components
{
    strongly_connected_components(size_t n) : graph(n), low(n), made() {}

    // add an edge from the vertex s to the vertex t.
    void add_edge(size_t src, size_t dst)
    {
        assert(src < size()); assert(dst < size());
        graph[src].emplace_back(dst);
        made = false;
    }

    // the number of the components.
    size_t count() { make(); return comp_cnt; }

    size_t size() const { return graph.size(); }

    // the component which the vertex v belongs to.
    size_t operator[](size_t v) { make(); return low[v]; }

    // the directed acyclic graph consisting of the components.
    const std::vector<std::vector<size_t>> &shrinked_dag() { make(); return dag; }

protected:
    std::vector<std::vector<size_t>> graph, dag;
    std::vector<size_t> low;
    size_t comp_cnt;
    bool made;

    void make()
    {
        if(made) return;
        made = true, comp_cnt = 0;
        low.assign(size(), 0);
        size_t *itr = new size_t[size()];
        bool *const used = new bool[size()];
        for(size_t v{}, c{}; v != size(); ++v) affix(v, c, itr, used + size());
        delete[] itr;
        delete[] used;
        for(auto &e : low) e += comp_cnt;
        reverse(begin(dag), end(dag));
        for(auto &arcs : dag)
            for(auto &to : arcs)
                to += comp_cnt;
    }

    size_t affix(size_t src, size_t &c, size_t* &itr, bool *used)
    {
        if(low[src]) return low[src];
        size_t idx = ++c; low[src] = idx; *itr++ = src;
        for(size_t dst : graph[src]) low[src] = std::min(low[src], affix(dst, c, itr, used));
        if(low[src] == idx)
        {
            ++comp_cnt;
            used[-comp_cnt] = true;
            dag.emplace_back(0);
            auto srcp = itr;
            do { low[*--srcp] = -comp_cnt; } while(*srcp != src);
            while(itr != srcp)
            {
                auto now = *--itr;
                for(auto to : graph[now])
                {
                    if(!used[(int)low[to]])
                    {
                        dag.back().emplace_back(low[to]);
                        used[(int)low[to]] = true;
                    }
                }
            }
            for(int c : dag.back()) used[c] = false;
            used[-comp_cnt] = false;
            return idx;
        }
        return low[src];
    }
}; // class strongly_connected_components
#line 4 "Library\\modulus\\modint.hpp"
template <int_fast64_t mod = 0> // compile-time defined modulo.
struct modint
{
    static_assert(mod > 0);
    template <bool i32, class = void> struct modif { using value_type = int_least32_t; };
    template <class void_t> struct modif<false, void_t> { using value_type = int_least64_t; };
    using value_type = typename modif<mod < (1 << 30)>::value_type;
    constexpr static modint one() noexcept { return 1; }
    constexpr operator value_type() const noexcept { return value; }
    constexpr modint() noexcept = default;
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    constexpr modint(int_type n) noexcept : value((n %= mod) < 0 ? mod + n : n) {}
    constexpr modint operator++(int) noexcept { modint t{*this}; return operator+=(1), t; }
    constexpr modint operator--(int) noexcept { modint t{*this}; return operator-=(1), t; }
    constexpr modint &operator++() noexcept { return operator+=(1); }
    constexpr modint &operator--() noexcept { return operator-=(1); }
    constexpr modint operator-() const noexcept { return value ? mod - value : 0; }
    constexpr modint &operator+=(const modint &rhs) noexcept { return (value += rhs.value) < mod ? 0 : value -= mod, *this; }
    constexpr modint &operator-=(const modint &rhs) noexcept { return (value += mod - rhs.value) < mod ? 0 : value -= mod, *this; }
    constexpr modint &operator*=(const modint &rhs) noexcept { return value = (int_fast64_t)value * rhs.value % mod, *this; }
    constexpr modint &operator/=(const modint &rhs) noexcept { return operator*=(rhs.inverse()); }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    constexpr modint operator+(const int_type &rhs) const noexcept { return modint{*this} += rhs; }
    constexpr modint operator+(const modint &rhs) const noexcept { return modint{*this} += rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    constexpr modint operator-(const int_type &rhs) const noexcept { return modint{*this} -= rhs; }
    constexpr modint operator-(const modint &rhs) const noexcept { return modint{*this} -= rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    constexpr modint operator*(const int_type &rhs) const noexcept { return modint{*this} *= rhs; }
    constexpr modint operator*(const modint &rhs) const noexcept { return modint{*this} *= rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    constexpr modint operator/(const int_type &rhs) const noexcept { return modint{*this} /= rhs; }
    constexpr modint operator/(const modint &rhs) const noexcept { return modint{*this} /= rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    constexpr friend modint operator+(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) + rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    constexpr friend modint operator-(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) - rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    constexpr friend modint operator*(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) * rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    constexpr friend modint operator/(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) / rhs; }
    constexpr modint inverse() const noexcept
    {
        assert(value);
        value_type a{mod}, b{value}, u{}, v{1}, t{};
        while(b) t = a / b, a ^= b ^= (a -= t * b) ^= b, u ^= v ^= (u -= t * v) ^= v;
        return {u};
    }
    constexpr static modint pow(modint rhs, int_fast64_t e) noexcept
    {
        if(e < 0) e = e % (mod - 1) + mod - 1;
        modint res{1};
        while(e) { if(e & 1) res *= rhs; rhs *= rhs, e >>= 1; }
        return res;
    }
    friend std::ostream &operator<<(std::ostream &os, const modint &rhs) noexcept { return os << rhs.value; }
    friend std::istream &operator>>(std::istream &is, modint &rhs) noexcept { int_fast64_t value; rhs = (is >> value, value); return is; }
protected:
    value_type value = 0;
}; // class modint
template <> // runtime defined modulo as default(mod = 0).
struct modint<0>
{
    using value_type = int_fast64_t;
    static value_type &mod() noexcept { static value_type mod{}; return mod; }
    static modint one() noexcept { return 1; }
    operator value_type() const noexcept { return value; }
    modint() noexcept = default;
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    modint(int_type n) noexcept : value{ (assert(mod()), n %= mod() < 0 ? n + mod() : n) } {}
    modint operator++(int) noexcept { modint t{*this}; return operator+=(1), t; }
    modint operator--(int) noexcept { modint t{*this}; return operator-=(1), t; }
    modint &operator++() noexcept { return operator+=(1); }
    modint &operator--() noexcept { return operator-=(1); }
    modint operator-() const noexcept { return value ? mod() - value : 0; }
    modint &operator+=(const modint &rhs) noexcept { return (value += rhs.value) < mod() ? 0 : value -= mod(), *this; }
    modint &operator-=(const modint &rhs) noexcept { return (value += mod() - rhs.value) < mod() ? 0 : value -= mod(), *this; }
    modint &operator*=(const modint &rhs) noexcept { return (value *= rhs.value) %= mod(), *this; }
    modint &operator/=(const modint &rhs) noexcept { return operator*=(rhs.inverse()); }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    modint operator+(const int_type &rhs) const noexcept { return modint{*this} += rhs; }
    modint operator+(const modint &rhs) const noexcept { return modint{*this} += rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    modint operator-(const int_type &rhs) const noexcept { return modint{*this} -= rhs; }
    modint operator-(const modint &rhs) const noexcept { return modint{*this} -= rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    modint operator*(const int_type &rhs) const noexcept { return modint{*this} *= rhs; }
    modint operator*(const modint &rhs) const noexcept { return modint{*this} *= rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    modint operator/(const int_type &rhs) const noexcept { return modint{*this} /= rhs; }
    modint operator/(const modint &rhs) const noexcept { return modint{*this} /= rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    friend modint operator+(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) + rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    friend modint operator-(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) - rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    friend modint operator*(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) * rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    friend modint operator/(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) / rhs; }
    modint inverse() const noexcept
    {
        assert(mod() && value);
        value_type a{mod()}, b{value}, u{}, v{1}, t{};
        while(b) t = a / b, a ^= b ^= (a -= t * b) ^= b, u ^= v ^= (u -= t * v) ^= v;
        return {u};
    }
    static modint pow(modint rhs, int_fast64_t e) noexcept
    {
        if(e < 0) e = e % (mod() - 1) + mod() - 1;
        modint res{1};
        while(e) { if(e & 1) res *= rhs; rhs *= rhs, e >>= 1; }
        return res;
    }
    friend std::ostream &operator<<(std::ostream &os, const modint &rhs) noexcept { return os << rhs.value; }
    friend std::istream &operator>>(std::istream &is, modint &rhs) noexcept { int_fast64_t value; rhs = modint((is >> value, value)); return is; }
protected:
    value_type value = 0;
}; // class modint<0>
using modint_runtime = modint<0>;
#line 35 "yu.cpp"

struct workspace::solver {
  using mint = modint<1000000007>;

  solver() {
    // start here!
    int n, m;
    cin >> n >> m;
    vector<p32> same, diff;
    vector<int> zero(n + 1, 0);
    for (int i = 0; i < m; i++) {
      int l, r, p;
      cin >> l >> r >> p;
      if (p) {
        if (p > 0)
          same.emplace_back(l - 1, r);
        else
          diff.emplace_back(l - 1, r);
      } else {
        zero[r - 1] = l;
      }
    }

    vector<int> nonz(1 + n);
    for (auto [l, r] : same) {
      nonz[l]++;
      nonz[r]--;
    }
    for (auto [l, r] : diff) {
      nonz[l]++;
      nonz[r]--;
    }
    partial_sum(begin(nonz), end(nonz), begin(nonz));

    mint ans{1};
    // 0-exclusive
    {
      int cnt = 0;
      for (int i = 0; i < n; i++) {
        if (nonz[i]) {
          cnt++;
        }
      }
      cnt -= size(same);
      cnt -= size(diff);
      ans = mint::pow(2, cnt);
    }
    // 0 can exist
    {
      mint acc;
      vector<mint> dp(n + 1);
      acc = dp[0] = 1;
      mint ip2 = 1, p2 = 1;
      vector<mint> ip2s{1};
      for (int i = 0, j = 0; i < n; i++) {
        if (!nonz[i]) {
          dp[i + 1] = acc * p2;
          p2 *= 2;
          ip2 /= 2;
          acc += dp[i + 1] * ip2;
        }
        ip2s.emplace_back(ip2);
        while (j < zero[i]) {
          acc -= dp[j] * ip2s[j];
          j++;
        }
      }
      ans *= acc * p2;
    }
    cout << ans << eol;
  }
};