proconlib

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:heavy_check_mark: tests/lazy_sparse_segtree/binary_search.test.cpp

Depends on

Code

// competitive-verifier: STANDALONE

#include <iostream>
#include <random>
#include <tuple>
#include <utility>
#include <vector>
#include "tools/assert_that.hpp"
#include "tools/inversion_number.hpp"
#include "tools/lazy_sparse_segtree.hpp"

struct SM {
  using T = std::tuple<int, int, int>;
  static T op(const T& x, const T& y) {
    return {std::get<0>(x) + std::get<0>(y), std::get<1>(x) + std::get<1>(y), std::get<2>(x) + std::get<2>(y) + std::get<1>(x) * std::get<0>(y)};
  }
  static T e() {
    return {0, 0, 0};
  }
};
using S = typename SM::T;

struct FM {
  using T = bool;
  static T op(const T f, const T g) {
    return f ^ g;
  }
  static T e() {
    return false;
  }
};
using F = typename FM::T;

S mapping(const F f, const S& e) {
  return f ? std::make_tuple(std::get<1>(e), std::get<0>(e), std::get<0>(e) * std::get<1>(e) - std::get<2>(e)) : e;
}

int main() {
  std::cin.tie(nullptr);
  std::ios_base::sync_with_stdio(false);

  std::random_device seed_gen;
  std::mt19937 engine(seed_gen());

  std::uniform_int_distribution<int> t_dist(0, 2);
  for (int N = 0; N < 50; ++N) {
    std::vector<int> a(N, 0);
    tools::lazy_sparse_segtree<SM, FM, mapping> seg(0, N, {1, 0, 0});

    std::vector<std::pair<int, int>> lr;
    for (int l = 0; l <= N; ++l) {
      for (int r = l; r <= N; ++r) {
        lr.emplace_back(l, r);
      }
    }

    std::uniform_int_distribution<int> p_dist(0, N);
    std::uniform_int_distribution<int> lr_dist(0, (N + 1) * (N + 2) / 2 - 1);
    for (int q = 0; q < (N + 1) * (N + 2) * 3; ++q) {
      const auto t = t_dist(engine);
      if (t == 0) {
        const auto [l, r] = lr[lr_dist(engine)];
        for (int i = l; i < r; ++i) a[i] ^= 1;
        seg.apply(l, r, true);
      } else if (t == 1) {
        const auto l = p_dist(engine);
        const auto x = std::uniform_int_distribution<int>(0, (N - l) * (N - l - 1) / 2)(engine);
        auto ok = l;
        auto ng = N + 1;
        while (ng - ok > 1) {
          const auto mid = (ok + ng) / 2;
          if (tools::inversion_number(std::ranges::subrange(a.begin() + l, a.begin() + mid)) <= x) {
            ok = mid;
          } else {
            ng = mid;
          }
        }
        assert_that(seg.max_right(l, [&](const S& e) { return std::get<2>(e) <= x; }) == ok);
      } else {
        const auto r = p_dist(engine);
        const auto x = std::uniform_int_distribution<int>(0, r * (r - 1) / 2)(engine);
        auto ok = r;
        auto ng = -1;
        while (ok - ng > 1) {
          const auto mid = (ok + ng) / 2;
          if (tools::inversion_number(std::ranges::subrange(a.begin() + mid, a.begin() + r)) <= x) {
            ok = mid;
          } else {
            ng = mid;
          }
        }
        assert_that(seg.min_left(r, [&](const S& e) { return std::get<2>(e) <= x; }) == ok);
      }
    }
  }

  return 0;
}

#line 1 "tests/lazy_sparse_segtree/binary_search.test.cpp"
// competitive-verifier: STANDALONE

#include <iostream>
#include <random>
#include <tuple>
#include <utility>
#include <vector>
#line 1 "tools/assert_that.hpp"



#line 5 "tools/assert_that.hpp"
#include <cstdlib>

#define assert_that_impl(cond, file, line, func) do {\
  if (!cond) {\
    ::std::cerr << file << ':' << line << ": " << func << ": Assertion `" << #cond << "' failed." << '\n';\
    ::std::exit(EXIT_FAILURE);\
  }\
} while (false)
#define assert_that(...) assert_that_impl((__VA_ARGS__), __FILE__, __LINE__, __func__)


#line 1 "tools/inversion_number.hpp"



#include <algorithm>
#include <iterator>
#include <ranges>
#line 1 "lib/ac-library/atcoder/fenwicktree.hpp"



#include <cassert>
#line 6 "lib/ac-library/atcoder/fenwicktree.hpp"

#line 1 "lib/ac-library/atcoder/internal_type_traits.hpp"



#line 5 "lib/ac-library/atcoder/internal_type_traits.hpp"
#include <numeric>
#include <type_traits>

namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                  is_signed_int128<T>::value ||
                                                  is_unsigned_int128<T>::value,
                                              std::true_type,
                                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

}  // namespace atcoder


#line 8 "lib/ac-library/atcoder/fenwicktree.hpp"

namespace atcoder {

// Reference: https://en.wikipedia.org/wiki/Fenwick_tree
template <class T> struct fenwick_tree {
    using U = internal::to_unsigned_t<T>;

  public:
    fenwick_tree() : _n(0) {}
    explicit fenwick_tree(int n) : _n(n), data(n) {}

    void add(int p, T x) {
        assert(0 <= p && p < _n);
        p++;
        while (p <= _n) {
            data[p - 1] += U(x);
            p += p & -p;
        }
    }

    T sum(int l, int r) {
        assert(0 <= l && l <= r && r <= _n);
        return sum(r) - sum(l);
    }

  private:
    int _n;
    std::vector<U> data;

    U sum(int r) {
        U s = 0;
        while (r > 0) {
            s += data[r - 1];
            r -= r & -r;
        }
        return s;
    }
};

}  // namespace atcoder


#line 1 "tools/compress.hpp"



#line 1 "tools/lower_bound.hpp"



#line 6 "tools/lower_bound.hpp"

namespace tools {

  template <class ForwardIterator, class T>
  auto lower_bound(ForwardIterator first, ForwardIterator last, const T& value) {
    return ::std::distance(first, ::std::lower_bound(first, last, value));
  }

  template <class ForwardIterator, class T, class Compare>
  auto lower_bound(ForwardIterator first, ForwardIterator last, const T& value, Compare comp) {
    return ::std::distance(first, ::std::lower_bound(first, last, value, comp));
  }
}


#line 8 "tools/compress.hpp"

namespace tools {
  template <::std::ranges::range R, typename OutputIterator>
  void compress(R&& a, OutputIterator result) {
    using T = typename ::std::ranges::range_value_t<R>;
    if constexpr (::std::ranges::forward_range<R>) {
      ::std::vector<T> sorted(::std::ranges::begin(a), ::std::ranges::end(a));
      ::std::ranges::sort(sorted);
      sorted.erase(::std::unique(sorted.begin(), sorted.end()), sorted.end());
      for (auto it = ::std::ranges::begin(a); it != ::std::ranges::end(a); ++it, ++result) {
        *result = ::tools::lower_bound(sorted.begin(), sorted.end(), *it);
      }
    } else {
      ::tools::compress(::std::vector<T>(::std::ranges::begin(a), ::std::ranges::end(a)), result);
    }
  }
}


#line 10 "tools/inversion_number.hpp"

namespace tools {

  template <::std::ranges::range R>
  long long inversion_number(R&& a) {
    ::std::vector<int> compressed;
    ::tools::compress(a, ::std::back_inserter(compressed));

    if (compressed.empty()) return 0;

    const auto max = *::std::ranges::max_element(compressed);
    ::atcoder::fenwick_tree<int> fw(max + 1);
    long long res = 0;
    for (const auto x : compressed) {
      res += fw.sum(x + 1, max + 1);
      fw.add(x, 1);
    }

    return res;
  }
}


#line 1 "tools/lazy_sparse_segtree.hpp"



#line 5 "tools/lazy_sparse_segtree.hpp"
#include <array>
#line 7 "tools/lazy_sparse_segtree.hpp"
#include <functional>
#line 11 "tools/lazy_sparse_segtree.hpp"
#include <variant>
#line 1 "tools/ceil_log2.hpp"



#line 1 "tools/bit_width.hpp"



#include <bit>
#line 1 "tools/is_integral.hpp"



#line 5 "tools/is_integral.hpp"

namespace tools {
  template <typename T>
  struct is_integral : ::std::is_integral<T> {};

  template <typename T>
  inline constexpr bool is_integral_v = ::tools::is_integral<T>::value;
}


#line 1 "tools/is_signed.hpp"



#line 5 "tools/is_signed.hpp"

namespace tools {
  template <typename T>
  struct is_signed : ::std::is_signed<T> {};

  template <typename T>
  inline constexpr bool is_signed_v = ::tools::is_signed<T>::value;
}


#line 1 "tools/make_unsigned.hpp"



#line 5 "tools/make_unsigned.hpp"

namespace tools {
  template <typename T>
  struct make_unsigned : ::std::make_unsigned<T> {};

  template <typename T>
  using make_unsigned_t = typename ::tools::make_unsigned<T>::type;
}


#line 10 "tools/bit_width.hpp"

namespace tools {
  template <typename T>
  constexpr int bit_width(T) noexcept;

  template <typename T>
  constexpr int bit_width(const T x) noexcept {
    static_assert(::tools::is_integral_v<T> && !::std::is_same_v<::std::remove_cv_t<T>, bool>);
    if constexpr (::tools::is_signed_v<T>) {
      assert(x >= 0);
      return ::tools::bit_width<::tools::make_unsigned_t<T>>(x);
    } else {
      return ::std::bit_width(x);
    }
  }
}


#line 6 "tools/ceil_log2.hpp"

namespace tools {
  template <typename T>
  constexpr T ceil_log2(T x) noexcept {
    assert(x > 0);
    return ::tools::bit_width(x - 1);
  }
}


#line 1 "tools/fix.hpp"



#line 6 "tools/fix.hpp"

namespace tools {
  template <typename F>
  struct fix : F {
    template <typename G>
    fix(G&& g) : F({::std::forward<G>(g)}) {
    }

    template <typename... Args>
    decltype(auto) operator()(Args&&... args) const {
      return F::operator()(*this, ::std::forward<Args>(args)...);
    }
  };

  template <typename F>
  fix(F&&) -> fix<::std::decay_t<F>>;
}


#line 1 "tools/nop_monoid.hpp"



#line 5 "tools/nop_monoid.hpp"

namespace tools {
  struct nop_monoid {
    using T = ::std::monostate;
    static T op(T, T) {
      return {};
    }
    static T e() {
      return {};
    }
  };
}


#line 16 "tools/lazy_sparse_segtree.hpp"

namespace tools {
  template <typename SM, typename FM, auto mapping>
  class lazy_sparse_segtree {
    using S = typename SM::T;
    using F = typename FM::T;
    static_assert(
      ::std::is_convertible_v<decltype(mapping), ::std::function<S(F, S)>>,
      "mapping must work as S(F, S)");

    template <typename T>
    static constexpr bool has_data = !::std::is_same_v<T, ::tools::nop_monoid>;
    template <typename T>
    static constexpr bool has_lazy = !::std::is_same_v<T, ::tools::nop_monoid>;

    struct regular_node {
      S data;
      ::std::array<int, 2> children;
    };
    struct dual_node {
      F lazy;
      ::std::array<int, 2> children;
    };
    struct lazy_node {
      S data;
      F lazy;
      ::std::array<int, 2> children;
    };
    using node = ::std::conditional_t<has_data<SM>, ::std::conditional_t<has_lazy<FM>, lazy_node, regular_node>, dual_node>;

    ::std::vector<node> m_nodes;
    long long m_offset;
    long long m_size;
    int m_height;
    int m_root;

    long long capacity() const {
      return 1LL << this->m_height;
    }
    bool is_mutable(const int k) const {
      assert(0 <= k && ::std::cmp_less(k, this->m_nodes.size()));
      return this->m_height < k;
    }
    void make_mutable() {
      if (this->is_mutable(this->m_root)) return;
      this->m_nodes.push_back(this->m_nodes[this->m_root]);
      this->m_root = this->m_nodes.size() - 1;
    }
    void make_mutable(const int k, const int d) {
      assert(0 <= k && ::std::cmp_less(k, this->m_nodes.size()));
      assert(0 <= d && d < 2);
      assert(!this->is_leaf(k));
      if (this->is_mutable(this->m_nodes[k].children[d])) return;
      this->m_nodes.push_back(this->m_nodes[this->m_nodes[k].children[d]]);
      this->m_nodes[k].children[d] = this->m_nodes.size() - 1;
    }
    bool is_leaf(const int k) const {
      assert(0 <= k && ::std::cmp_less(k, this->m_nodes.size()));
      const auto& node = this->m_nodes[k];
      return node.children[0] < 0 && node.children[1] < 0;
    }
    template <typename SFINAE = FM> requires (has_lazy<SFINAE>)
    void push(const int k) {
      assert(0 <= k && ::std::cmp_less(k, this->m_nodes.size()));
      assert(this->is_mutable(k));
      assert(!this->is_leaf(k));
      auto& node = this->m_nodes[k];
      this->all_apply(node.children[0], node.lazy);
      this->all_apply(node.children[1], node.lazy);
      node.lazy = FM::e();
    }
    template <typename SFINAE = FM> requires (has_lazy<SFINAE>)
    void all_apply(const int k, const F& f) {
      assert(0 <= k && ::std::cmp_less(k, this->m_nodes.size()));
      assert(this->is_mutable(k));
      auto& node = this->m_nodes[k];
      if constexpr (has_data<SM>) {
        node.data = mapping(f, node.data);
      }
      node.lazy = FM::op(f, node.lazy);
    }
    template <typename SFINAE = SM> requires (has_data<SFINAE>)
    void update(const int k) {
      assert(0 <= k && ::std::cmp_less(k, this->m_nodes.size()));
      assert(this->is_mutable(k));
      assert(!this->is_leaf(k));
      auto& node = this->m_nodes[k];
      node.data = SM::op(this->m_nodes[node.children[0]].data, this->m_nodes[node.children[1]].data);
    }

  public:
    lazy_sparse_segtree() = default;
    template <typename SFINAE = SM> requires (has_data<SFINAE>)
    lazy_sparse_segtree(const long long l_star, const long long r_star) : lazy_sparse_segtree(l_star, r_star, SM::e()) {
    }
    template <typename SFINAE = SM> requires (has_data<SFINAE>)
    lazy_sparse_segtree(const long long l_star, const long long r_star, const S& x) :
        m_offset(l_star), m_size(r_star - l_star), m_height(::tools::ceil_log2(::std::max(1LL, r_star - l_star))) {
      assert(l_star <= r_star);
      if constexpr (has_lazy<FM>) {
        this->m_nodes.push_back({x, FM::e(), {-1, -1}});
        for (int k = 1; k <= this->m_height; ++k) {
          this->m_nodes.push_back({SM::op(this->m_nodes.back().data, this->m_nodes.back().data), FM::e(), {k - 1, k - 1}});
        }
      } else {
        this->m_nodes.push_back({x, {-1, -1}});
        for (int k = 1; k <= this->m_height; ++k) {
          this->m_nodes.push_back({SM::op(this->m_nodes.back().data, this->m_nodes.back().data), {k - 1, k - 1}});
        }
      }
      this->m_root = this->m_height;
    }
    template <typename SFINAE = SM> requires (!has_data<SFINAE>)
    lazy_sparse_segtree(const long long l_star, const long long r_star) :
        m_offset(l_star), m_size(r_star - l_star), m_height(::tools::ceil_log2(::std::max(1LL, r_star - l_star))) {
      assert(l_star <= r_star);
      this->m_nodes.push_back({FM::e(), {-1, -1}});
      for (int k = 1; k <= this->m_height; ++k) {
        this->m_nodes.push_back({FM::e(), {k - 1, k - 1}});
      }
      this->m_root = this->m_height;
    }

    long long lower_bound() const {
      return this->m_offset;
    }
    long long upper_bound() const {
      return this->m_offset + this->m_size;
    }
    template <typename SFINAE = SM> requires (has_data<SFINAE>)
    void set(long long p, const S& x) {
      assert(this->lower_bound() <= p && p < this->upper_bound());
      p -= this->m_offset;

      this->make_mutable();
      ::tools::fix([&](auto&& dfs, const int h, const int k) -> void {
        assert(this->is_mutable(k));
        if (h > 0) {
          assert(!this->is_leaf(k));
          if constexpr (has_lazy<FM>) {
            this->make_mutable(k, 0);
            this->make_mutable(k, 1);
            this->push(k);
          } else {
            this->make_mutable(k, ((this->capacity() + p) >> (h - 1)) & 1);
          }
          dfs(h - 1, this->m_nodes[k].children[((this->capacity() + p) >> (h - 1)) & 1]);
          this->update(k);
        } else {
          assert(this->is_leaf(k));
          this->m_nodes[k].data = x;
        }
      })(this->m_height, this->m_root);
    }
    template <typename SFINAE = SM> requires (has_data<SFINAE>)
    S get(const long long p) {
      return this->prod(p, p + 1);
    }
    template <typename SFINAE = SM> requires (!has_data<SFINAE>)
    F get(long long p) {
      assert(this->lower_bound() <= p && p < this->upper_bound());
      p -= this->m_offset;

      this->make_mutable();
      return ::tools::fix([&](auto&& dfs, const int h, const int k) -> F {
        assert(this->is_mutable(k));
        if (h > 0) {
          assert(!this->is_leaf(k));
          this->make_mutable(k, 0);
          this->make_mutable(k, 1);
          this->push(k);
          return dfs(h - 1, this->m_nodes[k].children[((this->capacity() + p) >> (h - 1)) & 1]);
        } else {
          assert(this->is_leaf(k));
          return this->m_nodes[k].lazy;
        }
      })(this->m_height, this->m_root);
    }
    template <typename SFINAE = SM> requires (has_data<SFINAE>)
    S prod(long long l, long long r) {
      assert(this->lower_bound() <= l && l <= r && r <= this->upper_bound());
      if (l == r) return SM::e();
      l -= this->m_offset;
      r -= this->m_offset;

      if constexpr (has_lazy<FM>) {
        this->make_mutable();
      }
      return ::tools::fix([&](auto&& dfs, const int k, const long long kl, const long long kr) -> S {
        assert(kl < kr);
        if (l <= kl && kr <= r) return this->m_nodes[k].data;
        if constexpr (has_lazy<FM>) {
          this->make_mutable(k, 0);
          this->make_mutable(k, 1);
          this->push(k);
        }
        const auto km = ::std::midpoint(kl, kr);
        S res = SM::e();
        if (l < km) res = SM::op(res, dfs(this->m_nodes[k].children[0], kl, km));
        if (km < r) res = SM::op(res, dfs(this->m_nodes[k].children[1], km, kr));
        return res;
      })(this->m_root, 0, this->capacity());
    }
    template <typename SFINAE = SM> requires (has_data<SFINAE>)
    S all_prod() const {
      return this->m_nodes[this->m_root].data;
    }
    template <typename SFINAE = FM> requires (has_lazy<SFINAE>)
    void apply(const long long p, const F& f) {
      this->apply(p, p + 1, f);
    }
    template <typename SFINAE = FM> requires (has_lazy<SFINAE>)
    void apply(long long l, long long r, const F& f) {
      assert(this->lower_bound() <= l && l <= r && r <= this->upper_bound());
      if (l == r) return;
      l -= this->m_offset;
      r -= this->m_offset;

      this->make_mutable();
      ::tools::fix([&](auto&& dfs, const int k, const long long kl, const long long kr) -> void {
        assert(kl < kr);
        if (l <= kl && kr <= r) {
          this->all_apply(k, f);
          return;
        }
        this->make_mutable(k, 0);
        this->make_mutable(k, 1);
        this->push(k);
        const auto km = ::std::midpoint(kl, kr);
        if (l < km) dfs(this->m_nodes[k].children[0], kl, km);
        if (km < r) dfs(this->m_nodes[k].children[1], km, kr);
        if constexpr (has_data<SM>) {
          this->update(k);
        }
      })(this->m_root, 0, this->capacity());
    }
    template <typename G, typename SFINAE = SM> requires (has_data<SFINAE>)
    long long max_right(long long l, const G& g) {
      assert(this->lower_bound() <= l && l <= this->upper_bound());
      assert(g(SM::e()));
      if (l == this->upper_bound()) return l;
      l -= this->m_offset;

      if constexpr (has_lazy<FM>) {
        this->make_mutable();
      }
      return this->m_offset + ::std::min(::tools::fix([&](auto&& dfs, const S& c, const int k, const long long kl, const long long kr) -> ::std::pair<S, long long> {
        assert(kl < kr);
        if (kl < l) {
          assert(kl < l && l < kr);
          if constexpr (has_lazy<FM>) {
            this->make_mutable(k, 0);
            this->make_mutable(k, 1);
            this->push(k);
          }
          const auto km = ::std::midpoint(kl, kr);
          if (l < km) {
            const auto [hc, hr] = dfs(c, this->m_nodes[k].children[0], kl, km);
            assert(l <= hr && hr <= km);
            if (hr < km) return {hc, hr};
            return dfs(hc, this->m_nodes[k].children[1], km, kr);
          } else {
            return dfs(c, this->m_nodes[k].children[1], km, kr);
          }
        } else {
          if (const auto wc = SM::op(c, this->m_nodes[k].data); g(wc)) return {wc, kr};
          if (kr - kl == 1) return {c, kl};
          if constexpr (has_lazy<FM>) {
            this->make_mutable(k, 0);
            this->make_mutable(k, 1);
            this->push(k);
          }
          const auto km = ::std::midpoint(kl, kr);
          const auto [hc, hr] = dfs(c, this->m_nodes[k].children[0], kl, km);
          assert(l <= hr && hr <= km);
          if (hr < km) return {hc, hr};
          return dfs(hc, this->m_nodes[k].children[1], km, kr);
        }
      })(SM::e(), this->m_root, 0, this->capacity()).second, this->m_size);
    }
    template <typename G, typename SFINAE = SM> requires (has_data<SFINAE>)
    long long min_left(long long r, const G& g) {
      assert(this->lower_bound() <= r && r <= this->upper_bound());
      assert(g(SM::e()));
      if (r == this->lower_bound()) return r;
      r -= this->m_offset;

      if constexpr (has_lazy<FM>) {
        this->make_mutable();
      }
      return this->m_offset + ::tools::fix([&](auto&& dfs, const S& c, const int k, const long long kl, const long long kr) -> ::std::pair<S, long long> {
        assert(kl < kr);
        if (r < kr) {
          assert(kl < r && r < kr);
          if constexpr (has_lazy<FM>) {
            this->make_mutable(k, 0);
            this->make_mutable(k, 1);
            this->push(k);
          }
          const auto km = ::std::midpoint(kl, kr);
          if (km < r) {
            const auto [hc, hl] = dfs(c, this->m_nodes[k].children[1], km, kr);
            assert(km <= hl && hl <= r);
            if (km < hl) return {hc, hl};
            return dfs(hc, this->m_nodes[k].children[0], kl, km);
          } else {
            return dfs(c, this->m_nodes[k].children[0], kl, km);
          }
        } else {
          if (const auto wc = SM::op(this->m_nodes[k].data, c); g(wc)) return {wc, kl};
          if (kr - kl == 1) return {c, kr};
          if constexpr (has_lazy<FM>) {
            this->make_mutable(k, 0);
            this->make_mutable(k, 1);
            this->push(k);
          }
          const auto km = ::std::midpoint(kl, kr);
          const auto [hc, hl] = dfs(c, this->m_nodes[k].children[1], km, kr);
          assert(km <= hl && hl <= r);
          if (km < hl) return {hc, hl};
          return dfs(hc, this->m_nodes[k].children[0], kl, km);
        }
      })(SM::e(), this->m_root, 0, this->capacity()).second;
    }
  };
}


#line 11 "tests/lazy_sparse_segtree/binary_search.test.cpp"

struct SM {
  using T = std::tuple<int, int, int>;
  static T op(const T& x, const T& y) {
    return {std::get<0>(x) + std::get<0>(y), std::get<1>(x) + std::get<1>(y), std::get<2>(x) + std::get<2>(y) + std::get<1>(x) * std::get<0>(y)};
  }
  static T e() {
    return {0, 0, 0};
  }
};
using S = typename SM::T;

struct FM {
  using T = bool;
  static T op(const T f, const T g) {
    return f ^ g;
  }
  static T e() {
    return false;
  }
};
using F = typename FM::T;

S mapping(const F f, const S& e) {
  return f ? std::make_tuple(std::get<1>(e), std::get<0>(e), std::get<0>(e) * std::get<1>(e) - std::get<2>(e)) : e;
}

int main() {
  std::cin.tie(nullptr);
  std::ios_base::sync_with_stdio(false);

  std::random_device seed_gen;
  std::mt19937 engine(seed_gen());

  std::uniform_int_distribution<int> t_dist(0, 2);
  for (int N = 0; N < 50; ++N) {
    std::vector<int> a(N, 0);
    tools::lazy_sparse_segtree<SM, FM, mapping> seg(0, N, {1, 0, 0});

    std::vector<std::pair<int, int>> lr;
    for (int l = 0; l <= N; ++l) {
      for (int r = l; r <= N; ++r) {
        lr.emplace_back(l, r);
      }
    }

    std::uniform_int_distribution<int> p_dist(0, N);
    std::uniform_int_distribution<int> lr_dist(0, (N + 1) * (N + 2) / 2 - 1);
    for (int q = 0; q < (N + 1) * (N + 2) * 3; ++q) {
      const auto t = t_dist(engine);
      if (t == 0) {
        const auto [l, r] = lr[lr_dist(engine)];
        for (int i = l; i < r; ++i) a[i] ^= 1;
        seg.apply(l, r, true);
      } else if (t == 1) {
        const auto l = p_dist(engine);
        const auto x = std::uniform_int_distribution<int>(0, (N - l) * (N - l - 1) / 2)(engine);
        auto ok = l;
        auto ng = N + 1;
        while (ng - ok > 1) {
          const auto mid = (ok + ng) / 2;
          if (tools::inversion_number(std::ranges::subrange(a.begin() + l, a.begin() + mid)) <= x) {
            ok = mid;
          } else {
            ng = mid;
          }
        }
        assert_that(seg.max_right(l, [&](const S& e) { return std::get<2>(e) <= x; }) == ok);
      } else {
        const auto r = p_dist(engine);
        const auto x = std::uniform_int_distribution<int>(0, r * (r - 1) / 2)(engine);
        auto ok = r;
        auto ng = -1;
        while (ok - ng > 1) {
          const auto mid = (ok + ng) / 2;
          if (tools::inversion_number(std::ranges::subrange(a.begin() + mid, a.begin() + r)) <= x) {
            ok = mid;
          } else {
            ng = mid;
          }
        }
        assert_that(seg.min_left(r, [&](const S& e) { return std::get<2>(e) <= x; }) == ok);
      }
    }
  }

  return 0;
}
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