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 // Copyright 2018 The Abseil Authors.
 //
 // Licensed under the Apache License, Version 2.0 (the "License");
 // you may not use this file except in compliance with the License.
 // You may obtain a copy of the License at
 //
 //      https://www.apache.org/licenses/LICENSE-2.0
 //
 // Unless required by applicable law or agreed to in writing, software
 // distributed under the License is distributed on an "AS IS" BASIS,
 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
 // A btree implementation of the STL set and map interfaces. A btree is smaller
 // and generally also faster than STL set/map (refer to the benchmarks below).
 // The red-black tree implementation of STL set/map has an overhead of 3
 // pointers (left, right and parent) plus the node color information for each
 // stored value. So a set<int32_t> consumes 40 bytes for each value stored in
 // 64-bit mode. This btree implementation stores multiple values on fixed
 // size nodes (usually 256 bytes) and doesn't store child pointers for leaf
 // nodes. The result is that a btree_set<int32_t> may use much less memory per
 // stored value. For the random insertion benchmark in btree_bench.cc, a
 // btree_set<int32_t> with node-size of 256 uses 5.1 bytes per stored value.
 //
 // The packing of multiple values on to each node of a btree has another effect
 // besides better space utilization: better cache locality due to fewer cache
 // lines being accessed. Better cache locality translates into faster
 // operations.
 //
 // CAVEATS
 //
 // Insertions and deletions on a btree can cause splitting, merging or
 // rebalancing of btree nodes. And even without these operations, insertions
 // and deletions on a btree will move values around within a node. In both
 // cases, the result is that insertions and deletions can invalidate iterators
 // pointing to values other than the one being inserted/deleted. Therefore, this
 // container does not provide pointer stability. This is notably different from
 // STL set/map which takes care to not invalidate iterators on insert/erase
 // except, of course, for iterators pointing to the value being erased.  A
 // partial workaround when erasing is available: erase() returns an iterator
 // pointing to the item just after the one that was erased (or end() if none
 // exists).
 
 #ifndef ABSL_CONTAINER_INTERNAL_BTREE_H_
 #define ABSL_CONTAINER_INTERNAL_BTREE_H_
 
 #include <algorithm>
 #include <cassert>
 #include <cstddef>
 #include <cstdint>
 #include <cstring>
 #include <functional>
 #include <iterator>
 #include <limits>
 #include <string>
 #include <type_traits>
 #include <utility>
 
 #include "absl/base/config.h"
 #include "absl/base/internal/raw_logging.h"
 #include "absl/base/macros.h"
 #include "absl/container/internal/common.h"
 #include "absl/container/internal/common_policy_traits.h"
 #include "absl/container/internal/compressed_tuple.h"
 #include "absl/container/internal/container_memory.h"
 #include "absl/container/internal/layout.h"
 #include "absl/memory/memory.h"
 #include "absl/meta/type_traits.h"
 #include "absl/strings/cord.h"
 #include "absl/strings/string_view.h"
 #include "absl/types/compare.h"
 
 namespace absl {
 ABSL_NAMESPACE_BEGIN
 namespace container_internal {
 
 #ifdef ABSL_BTREE_ENABLE_GENERATIONS
 #error ABSL_BTREE_ENABLE_GENERATIONS cannot be directly set
 #elif (defined(ABSL_HAVE_ADDRESS_SANITIZER) ||   \
        defined(ABSL_HAVE_HWADDRESS_SANITIZER) || \
        defined(ABSL_HAVE_MEMORY_SANITIZER)) &&   \
     !defined(NDEBUG_SANITIZER)  // If defined, performance is important.
 // When compiled in sanitizer mode, we add generation integers to the nodes and
 // iterators. When iterators are used, we validate that the container has not
 // been mutated since the iterator was constructed.
 #define ABSL_BTREE_ENABLE_GENERATIONS
 #endif
 
 #ifdef ABSL_BTREE_ENABLE_GENERATIONS
 constexpr bool BtreeGenerationsEnabled() { return true; }
 #else
 constexpr bool BtreeGenerationsEnabled() { return false; }
 #endif
 
 template <typename Compare, typename T, typename U>
 using compare_result_t = absl::result_of_t<const Compare(const T &, const U &)>;
 
 // A helper class that indicates if the Compare parameter is a key-compare-to
 // comparator.
 template <typename Compare, typename T>
 using btree_is_key_compare_to =
     std::is_convertible<compare_result_t<Compare, T, T>, absl::weak_ordering>;
 
 struct StringBtreeDefaultLess {
   using is_transparent = void;
 
   StringBtreeDefaultLess() = default;
 
   // Compatibility constructor.
   StringBtreeDefaultLess(std::less<std::string>) {}        // NOLINT
   StringBtreeDefaultLess(std::less<absl::string_view>) {}  // NOLINT
 
   // Allow converting to std::less for use in key_comp()/value_comp().
   explicit operator std::less<std::string>() const { return {}; }
   explicit operator std::less<absl::string_view>() const { return {}; }
   explicit operator std::less<absl::Cord>() const { return {}; }
 
   absl::weak_ordering operator()(absl::string_view lhs,
                                  absl::string_view rhs) const {
     return compare_internal::compare_result_as_ordering(lhs.compare(rhs));
   }
   StringBtreeDefaultLess(std::less<absl::Cord>) {}  // NOLINT
   absl::weak_ordering operator()(const absl::Cord &lhs,
                                  const absl::Cord &rhs) const {
     return compare_internal::compare_result_as_ordering(lhs.Compare(rhs));
   }
   absl::weak_ordering operator()(const absl::Cord &lhs,
                                  absl::string_view rhs) const {
     return compare_internal::compare_result_as_ordering(lhs.Compare(rhs));
   }
   absl::weak_ordering operator()(absl::string_view lhs,
                                  const absl::Cord &rhs) const {
     return compare_internal::compare_result_as_ordering(-rhs.Compare(lhs));
   }
 };
 
 struct StringBtreeDefaultGreater {
   using is_transparent = void;
 
   StringBtreeDefaultGreater() = default;
 
   StringBtreeDefaultGreater(std::greater<std::string>) {}        // NOLINT
   StringBtreeDefaultGreater(std::greater<absl::string_view>) {}  // NOLINT
 
   // Allow converting to std::greater for use in key_comp()/value_comp().
   explicit operator std::greater<std::string>() const { return {}; }
   explicit operator std::greater<absl::string_view>() const { return {}; }
   explicit operator std::greater<absl::Cord>() const { return {}; }
 
   absl::weak_ordering operator()(absl::string_view lhs,
                                  absl::string_view rhs) const {
     return compare_internal::compare_result_as_ordering(rhs.compare(lhs));
   }
   StringBtreeDefaultGreater(std::greater<absl::Cord>) {}  // NOLINT
   absl::weak_ordering operator()(const absl::Cord &lhs,
                                  const absl::Cord &rhs) const {
     return compare_internal::compare_result_as_ordering(rhs.Compare(lhs));
   }
   absl::weak_ordering operator()(const absl::Cord &lhs,
                                  absl::string_view rhs) const {
     return compare_internal::compare_result_as_ordering(-lhs.Compare(rhs));
   }
   absl::weak_ordering operator()(absl::string_view lhs,
                                  const absl::Cord &rhs) const {
     return compare_internal::compare_result_as_ordering(rhs.Compare(lhs));
   }
 };
 
 // See below comments for checked_compare.
 template <typename Compare, bool is_class = std::is_class<Compare>::value>
 struct checked_compare_base : Compare {
   using Compare::Compare;
   explicit checked_compare_base(Compare c) : Compare(std::move(c)) {}
   const Compare &comp() const { return *this; }
 };
 template <typename Compare>
 struct checked_compare_base<Compare, false> {
   explicit checked_compare_base(Compare c) : compare(std::move(c)) {}
   const Compare &comp() const { return compare; }
   Compare compare;
 };
 
 // A mechanism for opting out of checked_compare for use only in btree_test.cc.
 struct BtreeTestOnlyCheckedCompareOptOutBase {};
 
 // A helper class to adapt the specified comparator for two use cases:
 // (1) When using common Abseil string types with common comparison functors,
 // convert a boolean comparison into a three-way comparison that returns an
 // `absl::weak_ordering`. This helper class is specialized for
 // less<std::string>, greater<std::string>, less<string_view>,
 // greater<string_view>, less<absl::Cord>, and greater<absl::Cord>.
 // (2) Adapt the comparator to diagnose cases of non-strict-weak-ordering (see
 // https://en.cppreference.com/w/cpp/named_req/Compare) in debug mode. Whenever
 // a comparison is made, we will make assertions to verify that the comparator
 // is valid.
 template <typename Compare, typename Key>
 struct key_compare_adapter {
   // Inherit from checked_compare_base to support function pointers and also
   // keep empty-base-optimization (EBO) support for classes.
   // Note: we can't use CompressedTuple here because that would interfere
   // with the EBO for `btree::rightmost_`. `btree::rightmost_` is itself a
   // CompressedTuple and nested `CompressedTuple`s don't support EBO.
   // TODO(b/214288561): use CompressedTuple instead once it supports EBO for
   // nested `CompressedTuple`s.
   struct checked_compare : checked_compare_base<Compare> {
    private:
     using Base = typename checked_compare::checked_compare_base;
     using Base::comp;
 
     // If possible, returns whether `t` is equivalent to itself. We can only do
     // this for `Key`s because we can't be sure that it's safe to call
     // `comp()(k, k)` otherwise. Even if SFINAE allows it, there could be a
     // compilation failure inside the implementation of the comparison operator.
     bool is_self_equivalent(const Key &k) const {
       // Note: this works for both boolean and three-way comparators.
       return comp()(k, k) == 0;
     }
     // If we can't compare `t` with itself, returns true unconditionally.
     template <typename T>
     bool is_self_equivalent(const T &) const {
       return true;
     }
 
    public:
     using Base::Base;
     checked_compare(Compare comp) : Base(std::move(comp)) {}  // NOLINT
 
     // Allow converting to Compare for use in key_comp()/value_comp().
     explicit operator Compare() const { return comp(); }
 
     template <typename T, typename U,
               absl::enable_if_t<
                   std::is_same<bool, compare_result_t<Compare, T, U>>::value,
                   int> = 0>
     bool operator()(const T &lhs, const U &rhs) const {
       // NOTE: if any of these assertions fail, then the comparator does not
       // establish a strict-weak-ordering (see
       // https://en.cppreference.com/w/cpp/named_req/Compare).
       assert(is_self_equivalent(lhs));
       assert(is_self_equivalent(rhs));
       const bool lhs_comp_rhs = comp()(lhs, rhs);
       assert(!lhs_comp_rhs || !comp()(rhs, lhs));
       return lhs_comp_rhs;
     }
 
     template <
         typename T, typename U,
         absl::enable_if_t<std::is_convertible<compare_result_t<Compare, T, U>,
                                               absl::weak_ordering>::value,
                           int> = 0>
     absl::weak_ordering operator()(const T &lhs, const U &rhs) const {
       // NOTE: if any of these assertions fail, then the comparator does not
       // establish a strict-weak-ordering (see
       // https://en.cppreference.com/w/cpp/named_req/Compare).
       assert(is_self_equivalent(lhs));
       assert(is_self_equivalent(rhs));
       const absl::weak_ordering lhs_comp_rhs = comp()(lhs, rhs);
 #ifndef NDEBUG
       const absl::weak_ordering rhs_comp_lhs = comp()(rhs, lhs);
       if (lhs_comp_rhs > 0) {
         assert(rhs_comp_lhs < 0 && "lhs_comp_rhs > 0 -> rhs_comp_lhs < 0");
       } else if (lhs_comp_rhs == 0) {
         assert(rhs_comp_lhs == 0 && "lhs_comp_rhs == 0 -> rhs_comp_lhs == 0");
       } else {
         assert(rhs_comp_lhs > 0 && "lhs_comp_rhs < 0 -> rhs_comp_lhs > 0");
       }
 #endif
       return lhs_comp_rhs;
     }
   };
   using type = absl::conditional_t<
       std::is_base_of<BtreeTestOnlyCheckedCompareOptOutBase, Compare>::value,
       Compare, checked_compare>;
 };
 
 template <>
 struct key_compare_adapter<std::less<std::string>, std::string> {
   using type = StringBtreeDefaultLess;
 };
 
 template <>
 struct key_compare_adapter<std::greater<std::string>, std::string> {
   using type = StringBtreeDefaultGreater;
 };
 
 template <>
 struct key_compare_adapter<std::less<absl::string_view>, absl::string_view> {
   using type = StringBtreeDefaultLess;
 };
 
 template <>
 struct key_compare_adapter<std::greater<absl::string_view>, absl::string_view> {
   using type = StringBtreeDefaultGreater;
 };
 
 template <>
 struct key_compare_adapter<std::less<absl::Cord>, absl::Cord> {
   using type = StringBtreeDefaultLess;
 };
 
 template <>
 struct key_compare_adapter<std::greater<absl::Cord>, absl::Cord> {
   using type = StringBtreeDefaultGreater;
 };
 
 // Detects an 'absl_btree_prefer_linear_node_search' member. This is
 // a protocol used as an opt-in or opt-out of linear search.
 //
 //  For example, this would be useful for key types that wrap an integer
 //  and define their own cheap operator<(). For example:
 //
 //   class K {
 //    public:
 //     using absl_btree_prefer_linear_node_search = std::true_type;
 //     ...
 //    private:
 //     friend bool operator<(K a, K b) { return a.k_ < b.k_; }
 //     int k_;
 //   };
 //
 //   btree_map<K, V> m;  // Uses linear search
 //
 // If T has the preference tag, then it has a preference.
 // Btree will use the tag's truth value.
 template <typename T, typename = void>
 struct has_linear_node_search_preference : std::false_type {};
 template <typename T, typename = void>
 struct prefers_linear_node_search : std::false_type {};
 template <typename T>
 struct has_linear_node_search_preference<
     T, absl::void_t<typename T::absl_btree_prefer_linear_node_search>>
     : std::true_type {};
 template <typename T>
 struct prefers_linear_node_search<
     T, absl::void_t<typename T::absl_btree_prefer_linear_node_search>>
     : T::absl_btree_prefer_linear_node_search {};
 
 template <typename Compare, typename Key>
 constexpr bool compare_has_valid_result_type() {
   using compare_result_type = compare_result_t<Compare, Key, Key>;
   return std::is_same<compare_result_type, bool>::value ||
          std::is_convertible<compare_result_type, absl::weak_ordering>::value;
 }
 
 template <typename original_key_compare, typename value_type>
 class map_value_compare {
   template <typename Params>
   friend class btree;
 
   // Note: this `protected` is part of the API of std::map::value_compare. See
   // https://en.cppreference.com/w/cpp/container/map/value_compare.
  protected:
   explicit map_value_compare(original_key_compare c) : comp(std::move(c)) {}
 
   original_key_compare comp;  // NOLINT
 
  public:
   auto operator()(const value_type &lhs, const value_type &rhs) const
       -> decltype(comp(lhs.first, rhs.first)) {
     return comp(lhs.first, rhs.first);
   }
 };
 
 template <typename Key, typename Compare, typename Alloc, int TargetNodeSize,
           bool IsMulti, bool IsMap, typename SlotPolicy>
 struct common_params : common_policy_traits<SlotPolicy> {
   using original_key_compare = Compare;
 
   // If Compare is a common comparator for a string-like type, then we adapt it
   // to use heterogeneous lookup and to be a key-compare-to comparator.
   // We also adapt the comparator to diagnose invalid comparators in debug mode.
   // We disable this when `Compare` is invalid in a way that will cause
   // adaptation to fail (having invalid return type) so that we can give a
   // better compilation failure in static_assert_validation. If we don't do
   // this, then there will be cascading compilation failures that are confusing
   // for users.
   using key_compare =
       absl::conditional_t<!compare_has_valid_result_type<Compare, Key>(),
                           Compare,
                           typename key_compare_adapter<Compare, Key>::type>;
 
   static constexpr bool kIsKeyCompareStringAdapted =
       std::is_same<key_compare, StringBtreeDefaultLess>::value ||
       std::is_same<key_compare, StringBtreeDefaultGreater>::value;
   static constexpr bool kIsKeyCompareTransparent =
       IsTransparent<original_key_compare>::value || kIsKeyCompareStringAdapted;
 
   // A type which indicates if we have a key-compare-to functor or a plain old
   // key-compare functor.
   using is_key_compare_to = btree_is_key_compare_to<key_compare, Key>;
 
   using allocator_type = Alloc;
   using key_type = Key;
   using size_type = size_t;
   using difference_type = ptrdiff_t;
 
   using slot_policy = SlotPolicy;
   using slot_type = typename slot_policy::slot_type;
   using value_type = typename slot_policy::value_type;
   using init_type = typename slot_policy::mutable_value_type;
   using pointer = value_type *;
   using const_pointer = const value_type *;
   using reference = value_type &;
   using const_reference = const value_type &;
 
   using value_compare =
       absl::conditional_t<IsMap,
                           map_value_compare<original_key_compare, value_type>,
                           original_key_compare>;
   using is_map_container = std::integral_constant<bool, IsMap>;
 
   // For the given lookup key type, returns whether we can have multiple
   // equivalent keys in the btree. If this is a multi-container, then we can.
   // Otherwise, we can have multiple equivalent keys only if all of the
   // following conditions are met:
   // - The comparator is transparent.
   // - The lookup key type is not the same as key_type.
   // - The comparator is not a StringBtreeDefault{Less,Greater} comparator
   //   that we know has the same equivalence classes for all lookup types.
   template <typename LookupKey>
   constexpr static bool can_have_multiple_equivalent_keys() {
     return IsMulti || (IsTransparent<key_compare>::value &&
                        !std::is_same<LookupKey, Key>::value &&
                        !kIsKeyCompareStringAdapted);
   }
 
   enum {
     kTargetNodeSize = TargetNodeSize,
 
     // Upper bound for the available space for slots. This is largest for leaf
     // nodes, which have overhead of at least a pointer + 4 bytes (for storing
     // 3 field_types and an enum).
     kNodeSlotSpace = TargetNodeSize - /*minimum overhead=*/(sizeof(void *) + 4),
   };
 
   // This is an integral type large enough to hold as many slots as will fit a
   // node of TargetNodeSize bytes.
   using node_count_type =
       absl::conditional_t<(kNodeSlotSpace / sizeof(slot_type) >
                            (std::numeric_limits<uint8_t>::max)()),
                           uint16_t, uint8_t>;  // NOLINT
 };
 
 // An adapter class that converts a lower-bound compare into an upper-bound
 // compare. Note: there is no need to make a version of this adapter specialized
 // for key-compare-to functors because the upper-bound (the first value greater
 // than the input) is never an exact match.
 template <typename Compare>
 struct upper_bound_adapter {
   explicit upper_bound_adapter(const Compare &c) : comp(c) {}
   template <typename K1, typename K2>
   bool operator()(const K1 &a, const K2 &b) const {
     // Returns true when a is not greater than b.
     return !compare_internal::compare_result_as_less_than(comp(b, a));
   }
 
  private:
   Compare comp;
 };
 
 enum class MatchKind : uint8_t { kEq, kNe };
 
 template <typename V, bool IsCompareTo>
 struct SearchResult {
   V value;
   MatchKind match;
 
   static constexpr bool HasMatch() { return true; }
   bool IsEq() const { return match == MatchKind::kEq; }
 };
 
 // When we don't use CompareTo, `match` is not present.
 // This ensures that callers can't use it accidentally when it provides no
 // useful information.
 template <typename V>
 struct SearchResult<V, false> {
   SearchResult() = default;
   explicit SearchResult(V v) : value(v) {}
   SearchResult(V v, MatchKind /*match*/) : value(v) {}
 
   V value;
 
   static constexpr bool HasMatch() { return false; }
   static constexpr bool IsEq() { return false; }
 };
 
 // A node in the btree holding. The same node type is used for both internal
 // and leaf nodes in the btree, though the nodes are allocated in such a way
 // that the children array is only valid in internal nodes.
 template <typename Params>
 class btree_node {
   using is_key_compare_to = typename Params::is_key_compare_to;
   using field_type = typename Params::node_count_type;
   using allocator_type = typename Params::allocator_type;
   using slot_type = typename Params::slot_type;
   using original_key_compare = typename Params::original_key_compare;
 
  public:
   using params_type = Params;
   using key_type = typename Params::key_type;
   using value_type = typename Params::value_type;
   using pointer = typename Params::pointer;
   using const_pointer = typename Params::const_pointer;
   using reference = typename Params::reference;
   using const_reference = typename Params::const_reference;
   using key_compare = typename Params::key_compare;
   using size_type = typename Params::size_type;
   using difference_type = typename Params::difference_type;
 
   // Btree decides whether to use linear node search as follows:
   //   - If the comparator expresses a preference, use that.
   //   - If the key expresses a preference, use that.
   //   - If the key is arithmetic and the comparator is std::less or
   //     std::greater, choose linear.
   //   - Otherwise, choose binary.
   // TODO(ezb): Might make sense to add condition(s) based on node-size.
   using use_linear_search = std::integral_constant<
       bool, has_linear_node_search_preference<original_key_compare>::value
                 ? prefers_linear_node_search<original_key_compare>::value
             : has_linear_node_search_preference<key_type>::value
                 ? prefers_linear_node_search<key_type>::value
                 : std::is_arithmetic<key_type>::value &&
                       (std::is_same<std::less<key_type>,
                                     original_key_compare>::value ||
                        std::is_same<std::greater<key_type>,
                                     original_key_compare>::value)>;
 
   // This class is organized by absl::container_internal::Layout as if it had
   // the following structure:
   //   // A pointer to the node's parent.
   //   btree_node *parent;
   //
   //   // When ABSL_BTREE_ENABLE_GENERATIONS is defined, we also have a
   //   // generation integer in order to check that when iterators are
   //   // used, they haven't been invalidated already. Only the generation on
   //   // the root is used, but we have one on each node because whether a node
   //   // is root or not can change.
   //   uint32_t generation;
   //
   //   // The position of the node in the node's parent.
   //   field_type position;
   //   // The index of the first populated value in `values`.
   //   // TODO(ezb): right now, `start` is always 0. Update insertion/merge
   //   // logic to allow for floating storage within nodes.
   //   field_type start;
   //   // The index after the last populated value in `values`. Currently, this
   //   // is the same as the count of values.
   //   field_type finish;
   //   // The maximum number of values the node can hold. This is an integer in
   //   // [1, kNodeSlots] for root leaf nodes, kNodeSlots for non-root leaf
   //   // nodes, and kInternalNodeMaxCount (as a sentinel value) for internal
   //   // nodes (even though there are still kNodeSlots values in the node).
   //   // TODO(ezb): make max_count use only 4 bits and record log2(capacity)
   //   // to free extra bits for is_root, etc.
   //   field_type max_count;
   //
   //   // The array of values. The capacity is `max_count` for leaf nodes and
   //   // kNodeSlots for internal nodes. Only the values in
   //   // [start, finish) have been initialized and are valid.
   //   slot_type values[max_count];
   //
   //   // The array of child pointers. The keys in children[i] are all less
   //   // than key(i). The keys in children[i + 1] are all greater than key(i).
   //   // There are 0 children for leaf nodes and kNodeSlots + 1 children for
   //   // internal nodes.
   //   btree_node *children[kNodeSlots + 1];
   //
   // This class is only constructed by EmptyNodeType. Normally, pointers to the
   // layout above are allocated, cast to btree_node*, and de-allocated within
   // the btree implementation.
   ~btree_node() = default;
   btree_node(btree_node const &) = delete;
   btree_node &operator=(btree_node const &) = delete;
 
  protected:
   btree_node() = default;
 
  private:
   using layout_type =
       absl::container_internal::Layout<btree_node *, uint32_t, field_type,
                                        slot_type, btree_node *>;
   using leaf_layout_type = typename layout_type::template WithStaticSizes<
       /*parent*/ 1,
       /*generation*/ BtreeGenerationsEnabled() ? 1 : 0,
       /*position, start, finish, max_count*/ 4>;
   constexpr static size_type SizeWithNSlots(size_type n) {
     return leaf_layout_type(/*slots*/ n, /*children*/ 0).AllocSize();
   }
   // A lower bound for the overhead of fields other than slots in a leaf node.
   constexpr static size_type MinimumOverhead() {
     return SizeWithNSlots(1) - sizeof(slot_type);
   }
 
   // Compute how many values we can fit onto a leaf node taking into account
   // padding.
   constexpr static size_type NodeTargetSlots(const size_type begin,
                                              const size_type end) {
     return begin == end ? begin
            : SizeWithNSlots((begin + end) / 2 + 1) >
                    params_type::kTargetNodeSize
                ? NodeTargetSlots(begin, (begin + end) / 2)
                : NodeTargetSlots((begin + end) / 2 + 1, end);
   }
 
   constexpr static size_type kTargetNodeSize = params_type::kTargetNodeSize;
   constexpr static size_type kNodeTargetSlots =
       NodeTargetSlots(0, kTargetNodeSize);
 
   // We need a minimum of 3 slots per internal node in order to perform
   // splitting (1 value for the two nodes involved in the split and 1 value
   // propagated to the parent as the delimiter for the split). For performance
   // reasons, we don't allow 3 slots-per-node due to bad worst case occupancy of
   // 1/3 (for a node, not a b-tree).
   constexpr static size_type kMinNodeSlots = 4;
 
   constexpr static size_type kNodeSlots =
       kNodeTargetSlots >= kMinNodeSlots ? kNodeTargetSlots : kMinNodeSlots;
 
   using internal_layout_type = typename layout_type::template WithStaticSizes<
       /*parent*/ 1,
       /*generation*/ BtreeGenerationsEnabled() ? 1 : 0,
       /*position, start, finish, max_count*/ 4, /*slots*/ kNodeSlots,
       /*children*/ kNodeSlots + 1>;
 
   // The node is internal (i.e. is not a leaf node) if and only if `max_count`
   // has this value.
   constexpr static field_type kInternalNodeMaxCount = 0;
 
   // Leaves can have less than kNodeSlots values.
   constexpr static leaf_layout_type LeafLayout(
       const size_type slot_count = kNodeSlots) {
     return leaf_layout_type(slot_count, 0);
   }
   constexpr static auto InternalLayout() { return internal_layout_type(); }
   constexpr static size_type LeafSize(const size_type slot_count = kNodeSlots) {
     return LeafLayout(slot_count).AllocSize();
   }
   constexpr static size_type InternalSize() {
     return InternalLayout().AllocSize();
   }
 
   constexpr static size_type Alignment() {
     static_assert(LeafLayout(1).Alignment() == InternalLayout().Alignment(),
                   "Alignment of all nodes must be equal.");
     return InternalLayout().Alignment();
   }
 
   // N is the index of the type in the Layout definition.
   // ElementType<N> is the Nth type in the Layout definition.
   template <size_type N>
   inline typename layout_type::template ElementType<N> *GetField() {
     // We assert that we don't read from values that aren't there.
     assert(N < 4 || is_internal());
     return InternalLayout().template Pointer<N>(reinterpret_cast<char *>(this));
   }
   template <size_type N>
   inline const typename layout_type::template ElementType<N> *GetField() const {
     assert(N < 4 || is_internal());
     return InternalLayout().template Pointer<N>(
         reinterpret_cast<const char *>(this));
   }
   void set_parent(btree_node *p) { *GetField<0>() = p; }
   field_type &mutable_finish() { return GetField<2>()[2]; }
   slot_type *slot(size_type i) { return &GetField<3>()[i]; }
   slot_type *start_slot() { return slot(start()); }
   slot_type *finish_slot() { return slot(finish()); }
   const slot_type *slot(size_type i) const { return &GetField<3>()[i]; }
   void set_position(field_type v) { GetField<2>()[0] = v; }
   void set_start(field_type v) { GetField<2>()[1] = v; }
   void set_finish(field_type v) { GetField<2>()[2] = v; }
   // This method is only called by the node init methods.
   void set_max_count(field_type v) { GetField<2>()[3] = v; }
 
  public:
   // Whether this is a leaf node or not. This value doesn't change after the
   // node is created.
   bool is_leaf() const { return GetField<2>()[3] != kInternalNodeMaxCount; }
   // Whether this is an internal node or not. This value doesn't change after
   // the node is created.
   bool is_internal() const { return !is_leaf(); }
 
   // Getter for the position of this node in its parent.
   field_type position() const { return GetField<2>()[0]; }
 
   // Getter for the offset of the first value in the `values` array.
   field_type start() const {
     // TODO(ezb): when floating storage is implemented, return GetField<2>()[1];
     assert(GetField<2>()[1] == 0);
     return 0;
   }
 
   // Getter for the offset after the last value in the `values` array.
   field_type finish() const { return GetField<2>()[2]; }
 
   // Getters for the number of values stored in this node.
   field_type count() const {
     assert(finish() >= start());
     return finish() - start();
   }
   field_type max_count() const {
     // Internal nodes have max_count==kInternalNodeMaxCount.
     // Leaf nodes have max_count in [1, kNodeSlots].
     const field_type max_count = GetField<2>()[3];
     return max_count == field_type{kInternalNodeMaxCount}
                ? field_type{kNodeSlots}
                : max_count;
   }
 
   // Getter for the parent of this node.
   btree_node *parent() const { return *GetField<0>(); }
   // Getter for whether the node is the root of the tree. The parent of the
   // root of the tree is the leftmost node in the tree which is guaranteed to
   // be a leaf.
   bool is_root() const { return parent()->is_leaf(); }
   void make_root() {
     assert(parent()->is_root());
     set_generation(parent()->generation());
     set_parent(parent()->parent());
   }
 
   // Gets the root node's generation integer, which is the one used by the tree.
   uint32_t *get_root_generation() const {
     assert(BtreeGenerationsEnabled());
     const btree_node *curr = this;
     for (; !curr->is_root(); curr = curr->parent()) continue;
     return const_cast<uint32_t *>(&curr->GetField<1>()[0]);
   }
 
   // Returns the generation for iterator validation.
   uint32_t generation() const {
     return BtreeGenerationsEnabled() ? *get_root_generation() : 0;
   }
   // Updates generation. Should only be called on a root node or during node
   // initialization.
   void set_generation(uint32_t generation) {
     if (BtreeGenerationsEnabled()) GetField<1>()[0] = generation;
   }
   // Updates the generation. We do this whenever the node is mutated.
   void next_generation() {
     if (BtreeGenerationsEnabled()) ++*get_root_generation();
   }
 
   // Getters for the key/value at position i in the node.
   const key_type &key(size_type i) const { return params_type::key(slot(i)); }
   reference value(size_type i) { return params_type::element(slot(i)); }
   const_reference value(size_type i) const {
     return params_type::element(slot(i));
   }
 
   // Getters/setter for the child at position i in the node.
   btree_node *child(field_type i) const { return GetField<4>()[i]; }
   btree_node *start_child() const { return child(start()); }
   btree_node *&mutable_child(field_type i) { return GetField<4>()[i]; }
   void clear_child(field_type i) {
     absl::container_internal::SanitizerPoisonObject(&mutable_child(i));
   }
   void set_child_noupdate_position(field_type i, btree_node *c) {
     absl::container_internal::SanitizerUnpoisonObject(&mutable_child(i));
     mutable_child(i) = c;
   }
   void set_child(field_type i, btree_node *c) {
     set_child_noupdate_position(i, c);
     c->set_position(i);
   }
   void init_child(field_type i, btree_node *c) {
     set_child(i, c);
     c->set_parent(this);
   }
 
   // Returns the position of the first value whose key is not less than k.
   template <typename K>
   SearchResult<size_type, is_key_compare_to::value> lower_bound(
       const K &k, const key_compare &comp) const {
     return use_linear_search::value ? linear_search(k, comp)
                                     : binary_search(k, comp);
   }
   // Returns the position of the first value whose key is greater than k.
   template <typename K>
   size_type upper_bound(const K &k, const key_compare &comp) const {
     auto upper_compare = upper_bound_adapter<key_compare>(comp);
     return use_linear_search::value ? linear_search(k, upper_compare).value
                                     : binary_search(k, upper_compare).value;
   }
 
   template <typename K, typename Compare>
   SearchResult<size_type, btree_is_key_compare_to<Compare, key_type>::value>
   linear_search(const K &k, const Compare &comp) const {
     return linear_search_impl(k, start(), finish(), comp,
                               btree_is_key_compare_to<Compare, key_type>());
   }
 
   template <typename K, typename Compare>
   SearchResult<size_type, btree_is_key_compare_to<Compare, key_type>::value>
   binary_search(const K &k, const Compare &comp) const {
     return binary_search_impl(k, start(), finish(), comp,
                               btree_is_key_compare_to<Compare, key_type>());
   }
 
   // Returns the position of the first value whose key is not less than k using
   // linear search performed using plain compare.
   template <typename K, typename Compare>
   SearchResult<size_type, false> linear_search_impl(
       const K &k, size_type s, const size_type e, const Compare &comp,
       std::false_type /* IsCompareTo */) const {
     while (s < e) {
       if (!comp(key(s), k)) {
         break;
       }
       ++s;
     }
     return SearchResult<size_type, false>{s};
   }
 
   // Returns the position of the first value whose key is not less than k using
   // linear search performed using compare-to.
   template <typename K, typename Compare>
   SearchResult<size_type, true> linear_search_impl(
       const K &k, size_type s, const size_type e, const Compare &comp,
       std::true_type /* IsCompareTo */) const {
     while (s < e) {
       const absl::weak_ordering c = comp(key(s), k);
       if (c == 0) {
         return {s, MatchKind::kEq};
       } else if (c > 0) {
         break;
       }
       ++s;
     }
     return {s, MatchKind::kNe};
   }
 
   // Returns the position of the first value whose key is not less than k using
   // binary search performed using plain compare.
   template <typename K, typename Compare>
   SearchResult<size_type, false> binary_search_impl(
       const K &k, size_type s, size_type e, const Compare &comp,
       std::false_type /* IsCompareTo */) const {
     while (s != e) {
       const size_type mid = (s + e) >> 1;
       if (comp(key(mid), k)) {
         s = mid + 1;
       } else {
         e = mid;
       }
     }
     return SearchResult<size_type, false>{s};
   }
 
   // Returns the position of the first value whose key is not less than k using
   // binary search performed using compare-to.
   template <typename K, typename CompareTo>
   SearchResult<size_type, true> binary_search_impl(
       const K &k, size_type s, size_type e, const CompareTo &comp,
       std::true_type /* IsCompareTo */) const {
     if (params_type::template can_have_multiple_equivalent_keys<K>()) {
       MatchKind exact_match = MatchKind::kNe;
       while (s != e) {
         const size_type mid = (s + e) >> 1;
         const absl::weak_ordering c = comp(key(mid), k);
         if (c < 0) {
           s = mid + 1;
         } else {
           e = mid;
           if (c == 0) {
             // Need to return the first value whose key is not less than k,
             // which requires continuing the binary search if there could be
             // multiple equivalent keys.
             exact_match = MatchKind::kEq;
           }
         }
       }
       return {s, exact_match};
     } else {  // Can't have multiple equivalent keys.
       while (s != e) {
         const size_type mid = (s + e) >> 1;
         const absl::weak_ordering c = comp(key(mid), k);
         if (c < 0) {
           s = mid + 1;
         } else if (c > 0) {
           e = mid;
         } else {
           return {mid, MatchKind::kEq};
         }
       }
       return {s, MatchKind::kNe};
     }
   }
 
   // Returns whether key i is ordered correctly with respect to the other keys
   // in the node. The motivation here is to detect comparators that violate
   // transitivity. Note: we only do comparisons of keys on this node rather than
   // the whole tree so that this is constant time.
   template <typename Compare>
   bool is_ordered_correctly(field_type i, const Compare &comp) const {
     if (std::is_base_of<BtreeTestOnlyCheckedCompareOptOutBase,
                         Compare>::value ||
         params_type::kIsKeyCompareStringAdapted) {
       return true;
     }
 
     const auto compare = [&](field_type a, field_type b) {
       const absl::weak_ordering cmp =
           compare_internal::do_three_way_comparison(comp, key(a), key(b));
       return cmp < 0 ? -1 : cmp > 0 ? 1 : 0;
     };
     int cmp = -1;
     constexpr bool kCanHaveEquivKeys =
         params_type::template can_have_multiple_equivalent_keys<key_type>();
     for (field_type j = start(); j < finish(); ++j) {
       if (j == i) {
         if (cmp > 0) return false;
         continue;
       }
       int new_cmp = compare(j, i);
       if (new_cmp < cmp || (!kCanHaveEquivKeys && new_cmp == 0)) return false;
       cmp = new_cmp;
     }
     return true;
   }
 
   // Emplaces a value at position i, shifting all existing values and
   // children at positions >= i to the right by 1.
   template <typename... Args>
   void emplace_value(field_type i, allocator_type *alloc, Args &&...args);
 
   // Removes the values at positions [i, i + to_erase), shifting all existing
   // values and children after that range to the left by to_erase. Clears all
   // children between [i, i + to_erase).
   void remove_values(field_type i, field_type to_erase, allocator_type *alloc);
 
   // Rebalances a node with its right sibling.
   void rebalance_right_to_left(field_type to_move, btree_node *right,
                                allocator_type *alloc);
   void rebalance_left_to_right(field_type to_move, btree_node *right,
                                allocator_type *alloc);
 
   // Splits a node, moving a portion of the node's values to its right sibling.
   void split(int insert_position, btree_node *dest, allocator_type *alloc);
 
   // Merges a node with its right sibling, moving all of the values and the
   // delimiting key in the parent node onto itself, and deleting the src node.
   void merge(btree_node *src, allocator_type *alloc);
 
   // Node allocation/deletion routines.
   void init_leaf(field_type position, field_type max_count,
                  btree_node *parent) {
     set_generation(0);
     set_parent(parent);
     set_position(position);
     set_start(0);
     set_finish(0);
     set_max_count(max_count);
     absl::container_internal::SanitizerPoisonMemoryRegion(
         start_slot(), max_count * sizeof(slot_type));
   }
   void init_internal(field_type position, btree_node *parent) {
     init_leaf(position, kNodeSlots, parent);
     // Set `max_count` to a sentinel value to indicate that this node is
     // internal.
     set_max_count(kInternalNodeMaxCount);
     absl::container_internal::SanitizerPoisonMemoryRegion(
         &mutable_child(start()), (kNodeSlots + 1) * sizeof(btree_node *));
   }
 
   static void deallocate(const size_type size, btree_node *node,
                          allocator_type *alloc) {
     absl::container_internal::SanitizerUnpoisonMemoryRegion(node, size);
     absl::container_internal::Deallocate<Alignment()>(alloc, node, size);
   }
 
   // Deletes a node and all of its children.
   static void clear_and_delete(btree_node *node, allocator_type *alloc);
 
  private:
   template <typename... Args>
   void value_init(const field_type i, allocator_type *alloc, Args &&...args) {
     next_generation();
     absl::container_internal::SanitizerUnpoisonObject(slot(i));
     params_type::construct(alloc, slot(i), std::forward<Args>(args)...);
   }
   void value_destroy(const field_type i, allocator_type *alloc) {
     next_generation();
     params_type::destroy(alloc, slot(i));
     absl::container_internal::SanitizerPoisonObject(slot(i));
   }
   void value_destroy_n(const field_type i, const field_type n,
                        allocator_type *alloc) {
     next_generation();
     for (slot_type *s = slot(i), *end = slot(i + n); s != end; ++s) {
       params_type::destroy(alloc, s);
       absl::container_internal::SanitizerPoisonObject(s);
     }
   }
 
   static void transfer(slot_type *dest, slot_type *src, allocator_type *alloc) {
     absl::container_internal::SanitizerUnpoisonObject(dest);
     params_type::transfer(alloc, dest, src);
     absl::container_internal::SanitizerPoisonObject(src);
   }
 
   // Transfers value from slot `src_i` in `src_node` to slot `dest_i` in `this`.
   void transfer(const size_type dest_i, const size_type src_i,
                 btree_node *src_node, allocator_type *alloc) {
     next_generation();
     transfer(slot(dest_i), src_node->slot(src_i), alloc);
   }
 
   // Transfers `n` values starting at value `src_i` in `src_node` into the
   // values starting at value `dest_i` in `this`.
   void transfer_n(const size_type n, const size_type dest_i,
                   const size_type src_i, btree_node *src_node,
                   allocator_type *alloc) {
     next_generation();
     for (slot_type *src = src_node->slot(src_i), *end = src + n,
                    *dest = slot(dest_i);
          src != end; ++src, ++dest) {
       transfer(dest, src, alloc);
     }
   }
 
   // Same as above, except that we start at the end and work our way to the
   // beginning.
   void transfer_n_backward(const size_type n, const size_type dest_i,
                            const size_type src_i, btree_node *src_node,
                            allocator_type *alloc) {
     next_generation();
     for (slot_type *src = src_node->slot(src_i + n), *end = src - n,
                    *dest = slot(dest_i + n);
          src != end; --src, --dest) {
       // If we modified the loop index calculations above to avoid the -1s here,
       // it would result in UB in the computation of `end` (and possibly `src`
       // as well, if n == 0), since slot() is effectively an array index and it
       // is UB to compute the address of any out-of-bounds array element except
       // for one-past-the-end.
       transfer(dest - 1, src - 1, alloc);
     }
   }
 
   template <typename P>
   friend class btree;
   template <typename N, typename R, typename P>
   friend class btree_iterator;
   friend class BtreeNodePeer;
   friend struct btree_access;
 };
 
 template <typename Node>
 bool AreNodesFromSameContainer(const Node *node_a, const Node *node_b) {
   // If either node is null, then give up on checking whether they're from the
   // same container. (If exactly one is null, then we'll trigger the
   // default-constructed assert in Equals.)
   if (node_a == nullptr || node_b == nullptr) return true;
   while (!node_a->is_root()) node_a = node_a->parent();
   while (!node_b->is_root()) node_b = node_b->parent();
   return node_a == node_b;
 }
 
 class btree_iterator_generation_info_enabled {
  public:
   explicit btree_iterator_generation_info_enabled(uint32_t g)
       : generation_(g) {}
 
   // Updates the generation. For use internally right before we return an
   // iterator to the user.
   template <typename Node>
   void update_generation(const Node *node) {
     if (node != nullptr) generation_ = node->generation();
   }
   uint32_t generation() const { return generation_; }
 
   template <typename Node>
   void assert_valid_generation(const Node *node) const {
     if (node != nullptr && node->generation() != generation_) {
       ABSL_INTERNAL_LOG(
           FATAL,
           "Attempting to use an invalidated iterator. The corresponding b-tree "
           "container has been mutated since this iterator was constructed.");
     }
   }
 
  private:
   // Used to check that the iterator hasn't been invalidated.
   uint32_t generation_;
 };
 
 class btree_iterator_generation_info_disabled {
  public:
   explicit btree_iterator_generation_info_disabled(uint32_t) {}
   static void update_generation(const void *) {}
   static uint32_t generation() { return 0; }
   static void assert_valid_generation(const void *) {}
 };
 
 #ifdef ABSL_BTREE_ENABLE_GENERATIONS
 using btree_iterator_generation_info = btree_iterator_generation_info_enabled;
 #else
 using btree_iterator_generation_info = btree_iterator_generation_info_disabled;
 #endif
 
 template <typename Node, typename Reference, typename Pointer>
 class btree_iterator : private btree_iterator_generation_info {
   using field_type = typename Node::field_type;
   using key_type = typename Node::key_type;
   using size_type = typename Node::size_type;
   using params_type = typename Node::params_type;
   using is_map_container = typename params_type::is_map_container;
 
   using node_type = Node;
   using normal_node = typename std::remove_const<Node>::type;
   using const_node = const Node;
   using normal_pointer = typename params_type::pointer;
   using normal_reference = typename params_type::reference;
   using const_pointer = typename params_type::const_pointer;
   using const_reference = typename params_type::const_reference;
   using slot_type = typename params_type::slot_type;
 
   // In sets, all iterators are const.
   using iterator = absl::conditional_t<
       is_map_container::value,
       btree_iterator<normal_node, normal_reference, normal_pointer>,
       btree_iterator<normal_node, const_reference, const_pointer>>;
   using const_iterator =
       btree_iterator<const_node, const_reference, const_pointer>;
 
  public:
   // These aliases are public for std::iterator_traits.
   using difference_type = typename Node::difference_type;
   using value_type = typename params_type::value_type;
   using pointer = Pointer;
   using reference = Reference;
   using iterator_category = std::bidirectional_iterator_tag;
 
   btree_iterator() : btree_iterator(nullptr, -1) {}
   explicit btree_iterator(Node *n) : btree_iterator(n, n->start()) {}
   btree_iterator(Node *n, int p)
       : btree_iterator_generation_info(n != nullptr ? n->generation()
                                                     : ~uint32_t{}),
         node_(n),
         position_(p) {}
 
   // NOTE: this SFINAE allows for implicit conversions from iterator to
   // const_iterator, but it specifically avoids hiding the copy constructor so
   // that the trivial one will be used when possible.
   template <typename N, typename R, typename P,
             absl::enable_if_t<
                 std::is_same<btree_iterator<N, R, P>, iterator>::value &&
                     std::is_same<btree_iterator, const_iterator>::value,
                 int> = 0>
   btree_iterator(const btree_iterator<N, R, P> other)  // NOLINT
       : btree_iterator_generation_info(other),
         node_(other.node_),
         position_(other.position_) {}
 
   bool operator==(const iterator &other) const {
     return Equals(other);
   }
   bool operator==(const const_iterator &other) const {
     return Equals(other);
   }
   bool operator!=(const iterator &other) const {
     return !Equals(other);
   }
   bool operator!=(const const_iterator &other) const {
     return !Equals(other);
   }
 
   // Returns n such that n calls to ++other yields *this.
   // Precondition: n exists.
   difference_type operator-(const_iterator other) const {
     if (node_ == other.node_) {
       if (node_->is_leaf()) return position_ - other.position_;
       if (position_ == other.position_) return 0;
     }
     return distance_slow(other);
   }
 
   // Accessors for the key/value the iterator is pointing at.
   reference operator*() const {
     ABSL_HARDENING_ASSERT(node_ != nullptr);
     assert_valid_generation(node_);
     ABSL_HARDENING_ASSERT(position_ >= node_->start());
     if (position_ >= node_->finish()) {
       ABSL_HARDENING_ASSERT(!IsEndIterator() && "Dereferencing end() iterator");
       ABSL_HARDENING_ASSERT(position_ < node_->finish());
     }
     return node_->value(static_cast<field_type>(position_));
   }
   pointer operator->() const { return &operator*(); }
 
   btree_iterator &operator++() {
     increment();
     return *this;
   }
   btree_iterator &operator--() {
     decrement();
     return *this;
   }
   btree_iterator operator++(int) {
     btree_iterator tmp = *this;
     ++*this;
     return tmp;
   }
   btree_iterator operator--(int) {
     btree_iterator tmp = *this;
     --*this;
     return tmp;
   }
 
  private:
   friend iterator;
   friend const_iterator;
   template <typename Params>
   friend class btree;
   template <typename Tree>
   friend class btree_container;
   template <typename Tree>
   friend class btree_set_container;
   template <typename Tree>
   friend class btree_map_container;
   template <typename Tree>
   friend class btree_multiset_container;
   template <typename TreeType, typename CheckerType>
   friend class base_checker;
   friend struct btree_access;
 
   // This SFINAE allows explicit conversions from const_iterator to
   // iterator, but also avoids hiding the copy constructor.
   // NOTE: the const_cast is safe because this constructor is only called by
   // non-const methods and the container owns the nodes.
   template <typename N, typename R, typename P,
             absl::enable_if_t<
                 std::is_same<btree_iterator<N, R, P>, const_iterator>::value &&
                     std::is_same<btree_iterator, iterator>::value,
                 int> = 0>
   explicit btree_iterator(const btree_iterator<N, R, P> other)
       : btree_iterator_generation_info(other.generation()),
         node_(const_cast<node_type *>(other.node_)),
         position_(other.position_) {}
 
   bool Equals(const const_iterator other) const {
     ABSL_HARDENING_ASSERT(((node_ == nullptr && other.node_ == nullptr) ||
                            (node_ != nullptr && other.node_ != nullptr)) &&
                           "Comparing default-constructed iterator with "
                           "non-default-constructed iterator.");
     // Note: we use assert instead of ABSL_HARDENING_ASSERT here because this
     // changes the complexity of Equals from O(1) to O(log(N) + log(M)) where
     // N/M are sizes of the containers containing node_/other.node_.
     assert(AreNodesFromSameContainer(node_, other.node_) &&
            "Comparing iterators from different containers.");
     assert_valid_generation(node_);
     other.assert_valid_generation(other.node_);
     return node_ == other.node_ && position_ == other.position_;
   }
 
   bool IsEndIterator() const {
     if (position_ != node_->finish()) return false;
     node_type *node = node_;
     while (!node->is_root()) {
       if (node->position() != node->parent()->finish()) return false;
       node = node->parent();
     }
     return true;
   }
 
   // Returns n such that n calls to ++other yields *this.
   // Precondition: n exists && (this->node_ != other.node_ ||
   // !this->node_->is_leaf() || this->position_ != other.position_).
   difference_type distance_slow(const_iterator other) const;
 
   // Increment/decrement the iterator.
   void increment() {
     assert_valid_generation(node_);
     if (node_->is_leaf() && ++position_ < node_->finish()) {
       return;
     }
     increment_slow();
   }
   void increment_slow();
 
   void decrement() {
     assert_valid_generation(node_);
     if (node_->is_leaf() && --position_ >= node_->start()) {
       return;
     }
     decrement_slow();
   }
   void decrement_slow();
 
   const key_type &key() const {
     return node_->key(static_cast<size_type>(position_));
   }
   decltype(std::declval<Node *>()->slot(0)) slot() {
     return node_->slot(static_cast<size_type>(position_));
   }
 
   void update_generation() {
     btree_iterator_generation_info::update_generation(node_);
   }
 
   // The node in the tree the iterator is pointing at.
   Node *node_;
   // The position within the node of the tree the iterator is pointing at.
   // NOTE: this is an int rather than a field_type because iterators can point
   // to invalid positions (such as -1) in certain circumstances.
   int position_;
 };
 
 template <typename Params>
 class btree {
   using node_type = btree_node<Params>;
   using is_key_compare_to = typename Params::is_key_compare_to;
   using field_type = typename node_type::field_type;
 
   // We use a static empty node for the root/leftmost/rightmost of empty btrees
   // in order to avoid branching in begin()/end().
   struct EmptyNodeType : node_type {
     using field_type = typename node_type::field_type;
     node_type *parent;
 #ifdef ABSL_BTREE_ENABLE_GENERATIONS
     uint32_t generation = 0;
 #endif
     field_type position = 0;
     field_type start = 0;
     field_type finish = 0;
     // max_count must be != kInternalNodeMaxCount (so that this node is regarded
     // as a leaf node). max_count() is never called when the tree is empty.
     field_type max_count = node_type::kInternalNodeMaxCount + 1;
 
     constexpr EmptyNodeType() : parent(this) {}
   };
 
   static node_type *EmptyNode() {
     alignas(node_type::Alignment()) static constexpr EmptyNodeType empty_node;
     return const_cast<EmptyNodeType *>(&empty_node);
   }
 
   enum : uint32_t {
     kNodeSlots = node_type::kNodeSlots,
     kMinNodeValues = kNodeSlots / 2,
   };
 
   struct node_stats {
     using size_type = typename Params::size_type;
 
     node_stats(size_type l, size_type i) : leaf_nodes(l), internal_nodes(i) {}
 
     node_stats &operator+=(const node_stats &other) {
       leaf_nodes += other.leaf_nodes;
       internal_nodes += other.internal_nodes;
       return *this;
     }
 
     size_type leaf_nodes;
     size_type internal_nodes;
   };
 
  public:
   using key_type = typename Params::key_type;
   using value_type = typename Params::value_type;
   using size_type = typename Params::size_type;
   using difference_type = typename Params::difference_type;
   using key_compare = typename Params::key_compare;
   using original_key_compare = typename Params::original_key_compare;
   using value_compare = typename Params::value_compare;
   using allocator_type = typename Params::allocator_type;
   using reference = typename Params::reference;
   using const_reference = typename Params::const_reference;
   using pointer = typename Params::pointer;
   using const_pointer = typename Params::const_pointer;
   using iterator =
       typename btree_iterator<node_type, reference, pointer>::iterator;
   using const_iterator = typename iterator::const_iterator;
   using reverse_iterator = std::reverse_iterator<iterator>;
   using const_reverse_iterator = std::reverse_iterator<const_iterator>;
   using node_handle_type = node_handle<Params, Params, allocator_type>;
 
   // Internal types made public for use by btree_container types.
   using params_type = Params;
   using slot_type = typename Params::slot_type;
 
  private:
   // Copies or moves (depending on the template parameter) the values in
   // other into this btree in their order in other. This btree must be empty
   // before this method is called. This method is used in copy construction,
   // copy assignment, and move assignment.
   template <typename Btree>
   void copy_or_move_values_in_order(Btree &other);
 
   // Validates that various assumptions/requirements are true at compile time.
   constexpr static bool static_assert_validation();
 
  public:
   btree(const key_compare &comp, const allocator_type &alloc)
       : root_(EmptyNode()), rightmost_(comp, alloc, EmptyNode()), size_(0) {}
 
   btree(const btree &other) : btree(other, other.allocator()) {}
   btree(const btree &other, const allocator_type &alloc)
       : btree(other.key_comp(), alloc) {
     copy_or_move_values_in_order(other);
   }
   btree(btree &&other) noexcept
       : root_(std::exchange(other.root_, EmptyNode())),
         rightmost_(std::move(other.rightmost_)),
         size_(std::exchange(other.size_, 0u)) {
     other.mutable_rightmost() = EmptyNode();
   }
   btree(btree &&other, const allocator_type &alloc)
       : btree(other.key_comp(), alloc) {
     if (alloc == other.allocator()) {
       swap(other);
     } else {
       // Move values from `other` one at a time when allocators are different.
       copy_or_move_values_in_order(other);
     }
   }
 
   ~btree() {
     // Put static_asserts in destructor to avoid triggering them before the type
     // is complete.
     static_assert(static_assert_validation(), "This call must be elided.");
     clear();
   }
 
   // Assign the contents of other to *this.
   btree &operator=(const btree &other);
   btree &operator=(btree &&other) noexcept;
 
   iterator begin() { return iterator(leftmost()); }
   const_iterator begin() const { return const_iterator(leftmost()); }
   iterator end() { return iterator(rightmost(), rightmost()->finish()); }
   const_iterator end() const {
     return const_iterator(rightmost(), rightmost()->finish());
   }
   reverse_iterator rbegin() { return reverse_iterator(end()); }
   const_reverse_iterator rbegin() const {
     return const_reverse_iterator(end());
   }
   reverse_iterator rend() { return reverse_iterator(begin()); }
   const_reverse_iterator rend() const {
     return const_reverse_iterator(begin());
   }
 
   // Finds the first element whose key is not less than `key`.
   template <typename K>
   iterator lower_bound(const K &key) {
     return internal_end(internal_lower_bound(key).value);
   }
   template <typename K>
   const_iterator lower_bound(const K &key) const {
     return internal_end(internal_lower_bound(key).value);
   }
 
   // Finds the first element whose key is not less than `key` and also returns
   // whether that element is equal to `key`.
   template <typename K>
   std::pair<iterator, bool> lower_bound_equal(const K &key) const;
 
   // Finds the first element whose key is greater than `key`.
   template <typename K>
   iterator upper_bound(const K &key) {
     return internal_end(internal_upper_bound(key));
   }
   template <typename K>
   const_iterator upper_bound(const K &key) const {
     return internal_end(internal_upper_bound(key));
   }
 
   // Finds the range of values which compare equal to key. The first member of
   // the returned pair is equal to lower_bound(key). The second member of the
   // pair is equal to upper_bound(key).
   template <typename K>
   std::pair<iterator, iterator> equal_range(const K &key);
   template <typename K>
   std::pair<const_iterator, const_iterator> equal_range(const K &key) const {
     return const_cast<btree *>(this)->equal_range(key);
   }
 
   // Inserts a value into the btree only if it does not already exist. The
   // boolean return value indicates whether insertion succeeded or failed.
   // Requirement: if `key` already exists in the btree, does not consume `args`.
   // Requirement: `key` is never referenced after consuming `args`.
   template <typename K, typename... Args>
   std::pair<iterator, bool> insert_unique(const K &key, Args &&...args);
 
   // Inserts with hint. Checks to see if the value should be placed immediately
   // before `position` in the tree. If so, then the insertion will take
   // amortized constant time. If not, the insertion will take amortized
   // logarithmic time as if a call to insert_unique() were made.
   // Requirement: if `key` already exists in the btree, does not consume `args`.
   // Requirement: `key` is never referenced after consuming `args`.
   template <typename K, typename... Args>
   std::pair<iterator, bool> insert_hint_unique(iterator position, const K &key,
                                                Args &&...args);
 
   // Insert a range of values into the btree.
   // Note: the first overload avoids constructing a value_type if the key
   // already exists in the btree.
   template <typename InputIterator,
             typename = decltype(std::declval<const key_compare &>()(
                 params_type::key(*std::declval<InputIterator>()),
                 std::declval<const key_type &>()))>
   void insert_iterator_unique(InputIterator b, InputIterator e, int);
   // We need the second overload for cases in which we need to construct a
   // value_type in order to compare it with the keys already in the btree.
   template <typename InputIterator>
   void insert_iterator_unique(InputIterator b, InputIterator e, char);
 
   // Inserts a value into the btree.
   template <typename ValueType>
   iterator insert_multi(const key_type &key, ValueType &&v);
 
   // Inserts a value into the btree.
   template <typename ValueType>
   iterator insert_multi(ValueType &&v) {
     return insert_multi(params_type::key(v), std::forward<ValueType>(v));
   }
 
   // Insert with hint. Check to see if the value should be placed immediately
   // before position in the tree. If it does, then the insertion will take
   // amortized constant time. If not, the insertion will take amortized
   // logarithmic time as if a call to insert_multi(v) were made.
   template <typename ValueType>
   iterator insert_hint_multi(iterator position, ValueType &&v);
 
   // Insert a range of values into the btree.
   template <typename InputIterator>
   void insert_iterator_multi(InputIterator b,
                              InputIterator e);
 
   // Erase the specified iterator from the btree. The iterator must be valid
   // (i.e. not equal to end()).  Return an iterator pointing to the node after
   // the one that was erased (or end() if none exists).
   // Requirement: does not read the value at `*iter`.
   iterator erase(iterator iter);
 
   // Erases range. Returns the number of keys erased and an iterator pointing
   // to the element after the last erased element.
   std::pair<size_type, iterator> erase_range(iterator begin, iterator end);
 
   // Finds an element with key equivalent to `key` or returns `end()` if `key`
   // is not present.
   template <typename K>
   iterator find(const K &key) {
     return internal_end(internal_find(key));
   }
   template <typename K>
   const_iterator find(const K &key) const {
     return internal_end(internal_find(key));
   }
 
   // Clear the btree, deleting all of the values it contains.
   void clear();
 
   // Swaps the contents of `this` and `other`.
   void swap(btree &other);
 
   const key_compare &key_comp() const noexcept {
     return rightmost_.template get<0>();
   }
   template <typename K1, typename K2>
   bool compare_keys(const K1 &a, const K2 &b) const {
     return compare_internal::compare_result_as_less_than(key_comp()(a, b));
   }
 
   value_compare value_comp() const {
     return value_compare(original_key_compare(key_comp()));
   }
 
   // Verifies the structure of the btree.
   void verify() const;
 
   // Size routines.
   size_type size() const { return size_; }
   size_type max_size() const { return (std::numeric_limits<size_type>::max)(); }
   bool empty() const { return size_ == 0; }
 
   // The height of the btree. An empty tree will have height 0.
   size_type height() const {
     size_type h = 0;
     if (!empty()) {
       // Count the length of the chain from the leftmost node up to the
       // root. We actually count from the root back around to the level below
       // the root, but the calculation is the same because of the circularity
       // of that traversal.
       const node_type *n = root();
       do {
         ++h;
         n = n->parent();
       } while (n != root());
     }
     return h;
   }
 
   // The number of internal, leaf and total nodes used by the btree.
   size_type leaf_nodes() const { return internal_stats(root()).leaf_nodes; }
   size_type internal_nodes() const {
     return internal_stats(root()).internal_nodes;
   }
   size_type nodes() const {
     node_stats stats = internal_stats(root());
     return stats.leaf_nodes + stats.internal_nodes;
   }
 
   // The total number of bytes used by the btree.
   // TODO(b/169338300): update to support node_btree_*.
   size_type bytes_used() const {
     node_stats stats = internal_stats(root());
     if (stats.leaf_nodes == 1 && stats.internal_nodes == 0) {
       return sizeof(*this) + node_type::LeafSize(root()->max_count());
     } else {
       return sizeof(*this) + stats.leaf_nodes * node_type::LeafSize() +
              stats.internal_nodes * node_type::InternalSize();
     }
   }
 
   // The average number of bytes used per value stored in the btree assuming
   // random insertion order.
   static double average_bytes_per_value() {
     // The expected number of values per node with random insertion order is the
     // average of the maximum and minimum numbers of values per node.
     const double expected_values_per_node = (kNodeSlots + kMinNodeValues) / 2.0;
     return node_type::LeafSize() / expected_values_per_node;
   }
 
   // The fullness of the btree. Computed as the number of elements in the btree
   // divided by the maximum number of elements a tree with the current number
   // of nodes could hold. A value of 1 indicates perfect space
   // utilization. Smaller values indicate space wastage.
   // Returns 0 for empty trees.
   double fullness() const {
     if (empty()) return 0.0;
     return static_cast<double>(size()) / (nodes() * kNodeSlots);
   }
   // The overhead of the btree structure in bytes per node. Computed as the
   // total number of bytes used by the btree minus the number of bytes used for
   // storing elements divided by the number of elements.
   // Returns 0 for empty trees.
   double overhead() const {
     if (empty()) return 0.0;
     return (bytes_used() - size() * sizeof(value_type)) /
            static_cast<double>(size());
   }
 
   // The allocator used by the btree.
   allocator_type get_allocator() const { return allocator(); }
 
  private:
   friend struct btree_access;
 
   // Internal accessor routines.
   node_type *root() { return root_; }
   const node_type *root() const { return root_; }
   node_type *&mutable_root() noexcept { return root_; }
   node_type *rightmost() { return rightmost_.template get<2>(); }
   const node_type *rightmost() const { return rightmost_.template get<2>(); }
   node_type *&mutable_rightmost() noexcept {
     return rightmost_.template get<2>();
   }
   key_compare *mutable_key_comp() noexcept {
     return &rightmost_.template get<0>();
   }
 
   // The leftmost node is stored as the parent of the root node.
   node_type *leftmost() { return root()->parent(); }
   const node_type *leftmost() const { return root()->parent(); }
 
   // Allocator routines.
   allocator_type *mutable_allocator() noexcept {
     return &rightmost_.template get<1>();
   }
   const allocator_type &allocator() const noexcept {
     return rightmost_.template get<1>();
   }
 
   // Allocates a correctly aligned node of at least size bytes using the
   // allocator.
   node_type *allocate(size_type size) {
     return reinterpret_cast<node_type *>(
         absl::container_internal::Allocate<node_type::Alignment()>(
             mutable_allocator(), size));
   }
 
   // Node creation/deletion routines.
   node_type *new_internal_node(field_type position, node_type *parent) {
     node_type *n = allocate(node_type::InternalSize());
     n->init_internal(position, parent);
     return n;
   }
   node_type *new_leaf_node(field_type position, node_type *parent) {
     node_type *n = allocate(node_type::LeafSize());
     n->init_leaf(position, kNodeSlots, parent);
     return n;
   }
   node_type *new_leaf_root_node(field_type max_count) {
     node_type *n = allocate(node_type::LeafSize(max_count));
     n->init_leaf(/*position=*/0, max_count, /*parent=*/n);
     return n;
   }
 
   // Deletion helper routines.
   iterator rebalance_after_delete(iterator iter);
 
   // Rebalances or splits the node iter points to.
   void rebalance_or_split(iterator *iter);
 
   // Merges the values of left, right and the delimiting key on their parent
   // onto left, removing the delimiting key and deleting right.
   void merge_nodes(node_type *left, node_type *right);
 
   // Tries to merge node with its left or right sibling, and failing that,
   // rebalance with its left or right sibling. Returns true if a merge
   // occurred, at which point it is no longer valid to access node. Returns
   // false if no merging took place.
   bool try_merge_or_rebalance(iterator *iter);
 
   // Tries to shrink the height of the tree by 1.
   void try_shrink();
 
   iterator internal_end(iterator iter) {
     return iter.node_ != nullptr ? iter : end();
   }
   const_iterator internal_end(const_iterator iter) const {
     return iter.node_ != nullptr ? iter : end();
   }
 
   // Emplaces a value into the btree immediately before iter. Requires that
   // key(v) <= iter.key() and (--iter).key() <= key(v).
   template <typename... Args>
   iterator internal_emplace(iterator iter, Args &&...args);
 
   // Returns an iterator pointing to the first value >= the value "iter" is
   // pointing at. Note that "iter" might be pointing to an invalid location such
   // as iter.position_ == iter.node_->finish(). This routine simply moves iter
   // up in the tree to a valid location. Requires: iter.node_ is non-null.
   template <typename IterType>
   static IterType internal_last(IterType iter);
 
   // Returns an iterator pointing to the leaf position at which key would
   // reside in the tree, unless there is an exact match - in which case, the
   // result may not be on a leaf. When there's a three-way comparator, we can
   // return whether there was an exact match. This allows the caller to avoid a
   // subsequent comparison to determine if an exact match was made, which is
   // important for keys with expensive comparison, such as strings.
   template <typename K>
   SearchResult<iterator, is_key_compare_to::value> internal_locate(
       const K &key) const;
 
   // Internal routine which implements lower_bound().
   template <typename K>
   SearchResult<iterator, is_key_compare_to::value> internal_lower_bound(
       const K &key) const;
 
   // Internal routine which implements upper_bound().
   template <typename K>
   iterator internal_upper_bound(const K &key) const;
 
   // Internal routine which implements find().
   template <typename K>
   iterator internal_find(const K &key) const;
 
   // Verifies the tree structure of node.
   size_type internal_verify(const node_type *node, const key_type *lo,
                             const key_type *hi) const;
 
   node_stats internal_stats(const node_type *node) const {
     // The root can be a static empty node.
     if (node == nullptr || (node == root() && empty())) {
       return node_stats(0, 0);
     }
     if (node->is_leaf()) {
       return node_stats(1, 0);
     }
     node_stats res(0, 1);
     for (int i = node->start(); i <= node->finish(); ++i) {
       res += internal_stats(node->child(i));
     }
     return res;
   }
 
   node_type *root_;
 
   // A pointer to the rightmost node. Note that the leftmost node is stored as
   // the root's parent. We use compressed tuple in order to save space because
   // key_compare and allocator_type are usually empty.
   absl::container_internal::CompressedTuple<key_compare, allocator_type,
                                             node_type *>
       rightmost_;
 
   // Number of values.
   size_type size_;
 };
 
 ////
 // btree_node methods
 template <typename P>
 template <typename... Args>
 inline void btree_node<P>::emplace_value(const field_type i,
                                          allocator_type *alloc,
                                          Args &&...args) {
   assert(i >= start());
   assert(i <= finish());
   // Shift old values to create space for new value and then construct it in
   // place.
   if (i < finish()) {
     transfer_n_backward(finish() - i, /*dest_i=*/i + 1, /*src_i=*/i, this,
                         alloc);
   }
   value_init(static_cast<field_type>(i), alloc, std::forward<Args>(args)...);
   set_finish(finish() + 1);
 
   if (is_internal() && finish() > i + 1) {
     for (field_type j = finish(); j > i + 1; --j) {
       set_child(j, child(j - 1));
     }
     clear_child(i + 1);
   }
 }
 
 template <typename P>
 inline void btree_node<P>::remove_values(const field_type i,
                                          const field_type to_erase,
                                          allocator_type *alloc) {
   // Transfer values after the removed range into their new places.
   value_destroy_n(i, to_erase, alloc);
   const field_type orig_finish = finish();
   const field_type src_i = i + to_erase;
   transfer_n(orig_finish - src_i, i, src_i, this, alloc);
 
   if (is_internal()) {
     // Delete all children between begin and end.
     for (field_type j = 0; j < to_erase; ++j) {
       clear_and_delete(child(i + j + 1), alloc);
     }
     // Rotate children after end into new positions.
     for (field_type j = i + to_erase + 1; j <= orig_finish; ++j) {
       set_child(j - to_erase, child(j));
       clear_child(j);
     }
   }
   set_finish(orig_finish - to_erase);
 }
 
 template <typename P>
 void btree_node<P>::rebalance_right_to_left(field_type to_move,
                                             btree_node *right,
                                             allocator_type *alloc) {
   assert(parent() == right->parent());
   assert(position() + 1 == right->position());
   assert(right->count() >= count());
   assert(to_move >= 1);
   assert(to_move <= right->count());
 
   // 1) Move the delimiting value in the parent to the left node.
   transfer(finish(), position(), parent(), alloc);
 
   // 2) Move the (to_move - 1) values from the right node to the left node.
   transfer_n(to_move - 1, finish() + 1, right->start(), right, alloc);
 
   // 3) Move the new delimiting value to the parent from the right node.
   parent()->transfer(position(), right->start() + to_move - 1, right, alloc);
 
   // 4) Shift the values in the right node to their correct positions.
   right->transfer_n(right->count() - to_move, right->start(),
                     right->start() + to_move, right, alloc);
 
   if (is_internal()) {
     // Move the child pointers from the right to the left node.
     for (field_type i = 0; i < to_move; ++i) {
       init_child(finish() + i + 1, right->child(i));
     }
     for (field_type i = right->start(); i <= right->finish() - to_move; ++i) {
       assert(i + to_move <= right->max_count());
       right->init_child(i, right->child(i + to_move));
       right->clear_child(i + to_move);
     }
   }
 
   // Fixup `finish` on the left and right nodes.
   set_finish(finish() + to_move);
   right->set_finish(right->finish() - to_move);
 }
 
 template <typename P>
 void btree_node<P>::rebalance_left_to_right(field_type to_move,
                                             btree_node *right,
                                             allocator_type *alloc) {
   assert(parent() == right->parent());
   assert(position() + 1 == right->position());
   assert(count() >= right->count());
   assert(to_move >= 1);
   assert(to_move <= count());
 
   // Values in the right node are shifted to the right to make room for the
   // new to_move values. Then, the delimiting value in the parent and the
   // other (to_move - 1) values in the left node are moved into the right node.
   // Lastly, a new delimiting value is moved from the left node into the
   // parent, and the remaining empty left node entries are destroyed.
 
   // 1) Shift existing values in the right node to their correct positions.
   right->transfer_n_backward(right->count(), right->start() + to_move,
                              right->start(), right, alloc);
 
   // 2) Move the delimiting value in the parent to the right node.
   right->transfer(right->start() + to_move - 1, position(), parent(), alloc);
 
   // 3) Move the (to_move - 1) values from the left node to the right node.
   right->transfer_n(to_move - 1, right->start(), finish() - (to_move - 1), this,
                     alloc);
 
   // 4) Move the new delimiting value to the parent from the left node.
   parent()->transfer(position(), finish() - to_move, this, alloc);
 
   if (is_internal()) {
     // Move the child pointers from the left to the right node.
     for (field_type i = right->finish() + 1; i > right->start(); --i) {
       right->init_child(i - 1 + to_move, right->child(i - 1));
       right->clear_child(i - 1);
     }
     for (field_type i = 1; i <= to_move; ++i) {
       right->init_child(i - 1, child(finish() - to_move + i));
       clear_child(finish() - to_move + i);
     }
   }
 
   // Fixup the counts on the left and right nodes.
   set_finish(finish() - to_move);
   right->set_finish(right->finish() + to_move);
 }
 
 template <typename P>
 void btree_node<P>::split(const int insert_position, btree_node *dest,
                           allocator_type *alloc) {
   assert(dest->count() == 0);
   assert(max_count() == kNodeSlots);
   assert(position() + 1 == dest->position());
   assert(parent() == dest->parent());
 
   // We bias the split based on the position being inserted. If we're
   // inserting at the beginning of the left node then bias the split to put
   // more values on the right node. If we're inserting at the end of the
   // right node then bias the split to put more values on the left node.
   if (insert_position == start()) {
     dest->set_finish(dest->start() + finish() - 1);
   } else if (insert_position == kNodeSlots) {
     dest->set_finish(dest->start());
   } else {
     dest->set_finish(dest->start() + count() / 2);
   }
   set_finish(finish() - dest->count());
   assert(count() >= 1);
 
   // Move values from the left sibling to the right sibling.
   dest->transfer_n(dest->count(), dest->start(), finish(), this, alloc);
 
   // The split key is the largest value in the left sibling.
   --mutable_finish();
   parent()->emplace_value(position(), alloc, finish_slot());
   value_destroy(finish(), alloc);
   parent()->set_child_noupdate_position(position() + 1, dest);
 
   if (is_internal()) {
     for (field_type i = dest->start(), j = finish() + 1; i <= dest->finish();
          ++i, ++j) {
       assert(child(j) != nullptr);
       dest->init_child(i, child(j));
       clear_child(j);
     }
   }
 }
 
 template <typename P>
 void btree_node<P>::merge(btree_node *src, allocator_type *alloc) {
   assert(parent() == src->parent());
   assert(position() + 1 == src->position());
 
   // Move the delimiting value to the left node.
   value_init(finish(), alloc, parent()->slot(position()));
 
   // Move the values from the right to the left node.
   transfer_n(src->count(), finish() + 1, src->start(), src, alloc);
 
   if (is_internal()) {
     // Move the child pointers from the right to the left node.
     for (field_type i = src->start(), j = finish() + 1; i <= src->finish();
          ++i, ++j) {
       init_child(j, src->child(i));
       src->clear_child(i);
     }
   }
 
   // Fixup `finish` on the src and dest nodes.
   set_finish(start() + 1 + count() + src->count());
   src->set_finish(src->start());
 
   // Remove the value on the parent node and delete the src node.
   parent()->remove_values(position(), /*to_erase=*/1, alloc);
 }
 
 template <typename P>
 void btree_node<P>::clear_and_delete(btree_node *node, allocator_type *alloc) {
   if (node->is_leaf()) {
     node->value_destroy_n(node->start(), node->count(), alloc);
     deallocate(LeafSize(node->max_count()), node, alloc);
     return;
   }
   if (node->count() == 0) {
     deallocate(InternalSize(), node, alloc);
     return;
   }
 
   // The parent of the root of the subtree we are deleting.
   btree_node *delete_root_parent = node->parent();
 
   // Navigate to the leftmost leaf under node, and then delete upwards.
   while (node->is_internal()) node = node->start_child();
 #ifdef ABSL_BTREE_ENABLE_GENERATIONS
   // When generations are enabled, we delete the leftmost leaf last in case it's
   // the parent of the root and we need to check whether it's a leaf before we
   // can update the root's generation.
   // TODO(ezb): if we change btree_node::is_root to check a bool inside the node
   // instead of checking whether the parent is a leaf, we can remove this logic.
   btree_node *leftmost_leaf = node;
 #endif
   // Use `size_type` because `pos` needs to be able to hold `kNodeSlots+1`,
   // which isn't guaranteed to be a valid `field_type`.
   size_type pos = node->position();
   btree_node *parent = node->parent();
   for (;;) {
     // In each iteration of the next loop, we delete one leaf node and go right.
     assert(pos <= parent->finish());
     do {
       node = parent->child(static_cast<field_type>(pos));
       if (node->is_internal()) {
         // Navigate to the leftmost leaf under node.
         while (node->is_internal()) node = node->start_child();
         pos = node->position();
         parent = node->parent();
       }
       node->value_destroy_n(node->start(), node->count(), alloc);
 #ifdef ABSL_BTREE_ENABLE_GENERATIONS
       if (leftmost_leaf != node)
 #endif
         deallocate(LeafSize(node->max_count()), node, alloc);
       ++pos;
     } while (pos <= parent->finish());
 
     // Once we've deleted all children of parent, delete parent and go up/right.
     assert(pos > parent->finish());
     do {
       node = parent;
       pos = node->position();
       parent = node->parent();
       node->value_destroy_n(node->start(), node->count(), alloc);
       deallocate(InternalSize(), node, alloc);
       if (parent == delete_root_parent) {
 #ifdef ABSL_BTREE_ENABLE_GENERATIONS
         deallocate(LeafSize(leftmost_leaf->max_count()), leftmost_leaf, alloc);
 #endif
         return;
       }
       ++pos;
     } while (pos > parent->finish());
   }
 }
 
 ////
 // btree_iterator methods
 
 // Note: the implementation here is based on btree_node::clear_and_delete.
 template <typename N, typename R, typename P>
 auto btree_iterator<N, R, P>::distance_slow(const_iterator other) const
     -> difference_type {
   const_iterator begin = other;
   const_iterator end = *this;
   assert(begin.node_ != end.node_ || !begin.node_->is_leaf() ||
          begin.position_ != end.position_);
 
   const node_type *node = begin.node_;
   // We need to compensate for double counting if begin.node_ is a leaf node.
   difference_type count = node->is_leaf() ? -begin.position_ : 0;
 
   // First navigate to the leftmost leaf node past begin.
   if (node->is_internal()) {
     ++count;
     node = node->child(begin.position_ + 1);
   }
   while (node->is_internal()) node = node->start_child();
 
   // Use `size_type` because `pos` needs to be able to hold `kNodeSlots+1`,
   // which isn't guaranteed to be a valid `field_type`.
   size_type pos = node->position();
   const node_type *parent = node->parent();
   for (;;) {
     // In each iteration of the next loop, we count one leaf node and go right.
     assert(pos <= parent->finish());
     do {
       node = parent->child(static_cast<field_type>(pos));
       if (node->is_internal()) {
         // Navigate to the leftmost leaf under node.
         while (node->is_internal()) node = node->start_child();
         pos = node->position();
         parent = node->parent();
       }
       if (node == end.node_) return count + end.position_;
       if (parent == end.node_ && pos == static_cast<size_type>(end.position_))
         return count + node->count();
       // +1 is for the next internal node value.
       count += node->count() + 1;
       ++pos;
     } while (pos <= parent->finish());
 
     // Once we've counted all children of parent, go up/right.
     assert(pos > parent->finish());
     do {
       node = parent;
       pos = node->position();
       parent = node->parent();
       // -1 because we counted the value at end and shouldn't.
       if (parent == end.node_ && pos == static_cast<size_type>(end.position_))
         return count - 1;
       ++pos;
     } while (pos > parent->finish());
   }
 }
 
 template <typename N, typename R, typename P>
 void btree_iterator<N, R, P>::increment_slow() {
   if (node_->is_leaf()) {
     assert(position_ >= node_->finish());
     btree_iterator save(*this);
     while (position_ == node_->finish() && !node_->is_root()) {
       assert(node_->parent()->child(node_->position()) == node_);
       position_ = node_->position();
       node_ = node_->parent();
     }
     // TODO(ezb): assert we aren't incrementing end() instead of handling.
     if (position_ == node_->finish()) {
       *this = save;
     }
   } else {
     assert(position_ < node_->finish());
     node_ = node_->child(static_cast<field_type>(position_ + 1));
     while (node_->is_internal()) {
       node_ = node_->start_child();
     }
     position_ = node_->start();
   }
 }
 
 template <typename N, typename R, typename P>
 void btree_iterator<N, R, P>::decrement_slow() {
   if (node_->is_leaf()) {
     assert(position_ <= -1);
     btree_iterator save(*this);
     while (position_ < node_->start() && !node_->is_root()) {
       assert(node_->parent()->child(node_->position()) == node_);
       position_ = node_->position() - 1;
       node_ = node_->parent();
     }
     // TODO(ezb): assert we aren't decrementing begin() instead of handling.
     if (position_ < node_->start()) {
       *this = save;
     }
   } else {
     assert(position_ >= node_->start());
     node_ = node_->child(static_cast<field_type>(position_));
     while (node_->is_internal()) {
       node_ = node_->child(node_->finish());
     }
     position_ = node_->finish() - 1;
   }
 }
 
 ////
 // btree methods
 template <typename P>
 template <typename Btree>
 void btree<P>::copy_or_move_values_in_order(Btree &other) {
   static_assert(std::is_same<btree, Btree>::value ||
                     std::is_same<const btree, Btree>::value,
                 "Btree type must be same or const.");
   assert(empty());
 
   // We can avoid key comparisons because we know the order of the
   // values is the same order we'll store them in.
   auto iter = other.begin();
   if (iter == other.end()) return;
   insert_multi(iter.slot());
   ++iter;
   for (; iter != other.end(); ++iter) {
     // If the btree is not empty, we can just insert the new value at the end
     // of the tree.
     internal_emplace(end(), iter.slot());
   }
 }
 
 template <typename P>
 constexpr bool btree<P>::static_assert_validation() {
   static_assert(std::is_nothrow_copy_constructible<key_compare>::value,
                 "Key comparison must be nothrow copy constructible");
   static_assert(std::is_nothrow_copy_constructible<allocator_type>::value,
                 "Allocator must be nothrow copy constructible");
   static_assert(std::is_trivially_copyable<iterator>::value,
                 "iterator not trivially copyable.");
 
   // Note: We assert that kTargetValues, which is computed from
   // Params::kTargetNodeSize, must fit the node_type::field_type.
   static_assert(
       kNodeSlots < (1 << (8 * sizeof(typename node_type::field_type))),
       "target node size too large");
 
   // Verify that key_compare returns an absl::{weak,strong}_ordering or bool.
   static_assert(
       compare_has_valid_result_type<key_compare, key_type>(),
       "key comparison function must return absl::{weak,strong}_ordering or "
       "bool.");
 
   // Test the assumption made in setting kNodeSlotSpace.
   static_assert(node_type::MinimumOverhead() >= sizeof(void *) + 4,
                 "node space assumption incorrect");
 
   return true;
 }
 
 template <typename P>
 template <typename K>
 auto btree<P>::lower_bound_equal(const K &key) const
     -> std::pair<iterator, bool> {
   const SearchResult<iterator, is_key_compare_to::value> res =
       internal_lower_bound(key);
   const iterator lower = iterator(internal_end(res.value));
   const bool equal = res.HasMatch()
                          ? res.IsEq()
                          : lower != end() && !compare_keys(key, lower.key());
   return {lower, equal};
 }
 
 template <typename P>
 template <typename K>
 auto btree<P>::equal_range(const K &key) -> std::pair<iterator, iterator> {
   const std::pair<iterator, bool> lower_and_equal = lower_bound_equal(key);
   const iterator lower = lower_and_equal.first;
   if (!lower_and_equal.second) {
     return {lower, lower};
   }
 
   const iterator next = std::next(lower);
   if (!params_type::template can_have_multiple_equivalent_keys<K>()) {
     // The next iterator after lower must point to a key greater than `key`.
     // Note: if this assert fails, then it may indicate that the comparator does
     // not meet the equivalence requirements for Compare
     // (see https://en.cppreference.com/w/cpp/named_req/Compare).
     assert(next == end() || compare_keys(key, next.key()));
     return {lower, next};
   }
   // Try once more to avoid the call to upper_bound() if there's only one
   // equivalent key. This should prevent all calls to upper_bound() in cases of
   // unique-containers with heterogeneous comparators in which all comparison
   // operators have the same equivalence classes.
   if (next == end() || compare_keys(key, next.key())) return {lower, next};
 
   // In this case, we need to call upper_bound() to avoid worst case O(N)
   // behavior if we were to iterate over equal keys.
   return {lower, upper_bound(key)};
 }
 
 template <typename P>
 template <typename K, typename... Args>
 auto btree<P>::insert_unique(const K &key, Args &&...args)
     -> std::pair<iterator, bool> {
   if (empty()) {
     mutable_root() = mutable_rightmost() = new_leaf_root_node(1);
   }
 
   SearchResult<iterator, is_key_compare_to::value> res = internal_locate(key);
   iterator iter = res.value;
 
   if (res.HasMatch()) {
     if (res.IsEq()) {
       // The key already exists in the tree, do nothing.
       return {iter, false};
     }
   } else {
     iterator last = internal_last(iter);
     if (last.node_ && !compare_keys(key, last.key())) {
       // The key already exists in the tree, do nothing.
       return {last, false};
     }
   }
   return {internal_emplace(iter, std::forward<Args>(args)...), true};
 }
 
 template <typename P>
 template <typename K, typename... Args>
 inline auto btree<P>::insert_hint_unique(iterator position, const K &key,
                                          Args &&...args)
     -> std::pair<iterator, bool> {
   if (!empty()) {
     if (position == end() || compare_keys(key, position.key())) {
       if (position == begin() || compare_keys(std::prev(position).key(), key)) {
         // prev.key() < key < position.key()
         return {internal_emplace(position, std::forward<Args>(args)...), true};
       }
     } else if (compare_keys(position.key(), key)) {
       ++position;
       if (position == end() || compare_keys(key, position.key())) {
         // {original `position`}.key() < key < {current `position`}.key()
         return {internal_emplace(position, std::forward<Args>(args)...), true};
       }
     } else {
       // position.key() == key
       return {position, false};
     }
   }
   return insert_unique(key, std::forward<Args>(args)...);
 }
 
 template <typename P>
 template <typename InputIterator, typename>
 void btree<P>::insert_iterator_unique(InputIterator b, InputIterator e, int) {
   for (; b != e; ++b) {
     insert_hint_unique(end(), params_type::key(*b), *b);
   }
 }
 
 template <typename P>
 template <typename InputIterator>
 void btree<P>::insert_iterator_unique(InputIterator b, InputIterator e, char) {
   for (; b != e; ++b) {
     // Use a node handle to manage a temp slot.
     auto node_handle =
         CommonAccess::Construct<node_handle_type>(get_allocator(), *b);
     slot_type *slot = CommonAccess::GetSlot(node_handle);
     insert_hint_unique(end(), params_type::key(slot), slot);
   }
 }
 
 template <typename P>
 template <typename ValueType>
 auto btree<P>::insert_multi(const key_type &key, ValueType &&v) -> iterator {
   if (empty()) {
     mutable_root() = mutable_rightmost() = new_leaf_root_node(1);
   }
 
   iterator iter = internal_upper_bound(key);
   if (iter.node_ == nullptr) {
     iter = end();
   }
   return internal_emplace(iter, std::forward<ValueType>(v));
 }
 
 template <typename P>
 template <typename ValueType>
 auto btree<P>::insert_hint_multi(iterator position, ValueType &&v) -> iterator {
   if (!empty()) {
     const key_type &key = params_type::key(v);
     if (position == end() || !compare_keys(position.key(), key)) {
       if (position == begin() ||
           !compare_keys(key, std::prev(position).key())) {
         // prev.key() <= key <= position.key()
         return internal_emplace(position, std::forward<ValueType>(v));
       }
     } else {
       ++position;
       if (position == end() || !compare_keys(position.key(), key)) {
         // {original `position`}.key() < key < {current `position`}.key()
         return internal_emplace(position, std::forward<ValueType>(v));
       }
     }
   }
   return insert_multi(std::forward<ValueType>(v));
 }
 
 template <typename P>
 template <typename InputIterator>
 void btree<P>::insert_iterator_multi(InputIterator b, InputIterator e) {
   for (; b != e; ++b) {
     insert_hint_multi(end(), *b);
   }
 }
 
 template <typename P>
 auto btree<P>::operator=(const btree &other) -> btree & {
   if (this != &other) {
     clear();
 
     *mutable_key_comp() = other.key_comp();
     if (absl::allocator_traits<
             allocator_type>::propagate_on_container_copy_assignment::value) {
       *mutable_allocator() = other.allocator();
     }
 
     copy_or_move_values_in_order(other);
   }
   return *this;
 }
 
 template <typename P>
 auto btree<P>::operator=(btree &&other) noexcept -> btree & {
   if (this != &other) {
     clear();
 
     using std::swap;
     if (absl::allocator_traits<
             allocator_type>::propagate_on_container_move_assignment::value) {
       swap(root_, other.root_);
       // Note: `rightmost_` also contains the allocator and the key comparator.
       swap(rightmost_, other.rightmost_);
       swap(size_, other.size_);
     } else {
       if (allocator() == other.allocator()) {
         swap(mutable_root(), other.mutable_root());
         swap(*mutable_key_comp(), *other.mutable_key_comp());
         swap(mutable_rightmost(), other.mutable_rightmost());
         swap(size_, other.size_);
       } else {
         // We aren't allowed to propagate the allocator and the allocator is
         // different so we can't take over its memory. We must move each element
         // individually. We need both `other` and `this` to have `other`s key
         // comparator while moving the values so we can't swap the key
         // comparators.
         *mutable_key_comp() = other.key_comp();
         copy_or_move_values_in_order(other);
       }
     }
   }
   return *this;
 }
 
 template <typename P>
 auto btree<P>::erase(iterator iter) -> iterator {
   iter.node_->value_destroy(static_cast<field_type>(iter.position_),
                             mutable_allocator());
   iter.update_generation();
 
   const bool internal_delete = iter.node_->is_internal();
   if (internal_delete) {
     // Deletion of a value on an internal node. First, transfer the largest
     // value from our left child here, then erase/rebalance from that position.
     // We can get to the largest value from our left child by decrementing iter.
     iterator internal_iter(iter);
     --iter;
     assert(iter.node_->is_leaf());
     internal_iter.node_->transfer(
         static_cast<size_type>(internal_iter.position_),
         static_cast<size_type>(iter.position_), iter.node_,
         mutable_allocator());
   } else {
     // Shift values after erased position in leaf. In the internal case, we
     // don't need to do this because the leaf position is the end of the node.
     const field_type transfer_from =
         static_cast<field_type>(iter.position_ + 1);
     const field_type num_to_transfer = iter.node_->finish() - transfer_from;
     iter.node_->transfer_n(num_to_transfer,
                            static_cast<size_type>(iter.position_),
                            transfer_from, iter.node_, mutable_allocator());
   }
   // Update node finish and container size.
   iter.node_->set_finish(iter.node_->finish() - 1);
   --size_;
 
   // We want to return the next value after the one we just erased. If we
   // erased from an internal node (internal_delete == true), then the next
   // value is ++(++iter). If we erased from a leaf node (internal_delete ==
   // false) then the next value is ++iter. Note that ++iter may point to an
   // internal node and the value in the internal node may move to a leaf node
   // (iter.node_) when rebalancing is performed at the leaf level.
 
   iterator res = rebalance_after_delete(iter);
 
   // If we erased from an internal node, advance the iterator.
   if (internal_delete) {
     ++res;
   }
   return res;
 }
 
 template <typename P>
 auto btree<P>::rebalance_after_delete(iterator iter) -> iterator {
   // Merge/rebalance as we walk back up the tree.
   iterator res(iter);
   bool first_iteration = true;
   for (;;) {
     if (iter.node_ == root()) {
       try_shrink();
       if (empty()) {
         return end();
       }
       break;
     }
     if (iter.node_->count() >= kMinNodeValues) {
       break;
     }
     bool merged = try_merge_or_rebalance(&iter);
     // On the first iteration, we should update `res` with `iter` because `res`
     // may have been invalidated.
     if (first_iteration) {
       res = iter;
       first_iteration = false;
     }
     if (!merged) {
       break;
     }
     iter.position_ = iter.node_->position();
     iter.node_ = iter.node_->parent();
   }
   res.update_generation();
 
   // Adjust our return value. If we're pointing at the end of a node, advance
   // the iterator.
   if (res.position_ == res.node_->finish()) {
     res.position_ = res.node_->finish() - 1;
     ++res;
   }
 
   return res;
 }
 
 // Note: we tried implementing this more efficiently by erasing all of the
 // elements in [begin, end) at once and then doing rebalancing once at the end
 // (rather than interleaving deletion and rebalancing), but that adds a lot of
 // complexity, which seems to outweigh the performance win.
 template <typename P>
 auto btree<P>::erase_range(iterator begin, iterator end)
     -> std::pair<size_type, iterator> {
   size_type count = static_cast<size_type>(end - begin);
   assert(count >= 0);
 
   if (count == 0) {
     return {0, begin};
   }
 
   if (static_cast<size_type>(count) == size_) {
     clear();
     return {count, this->end()};
   }
 
   if (begin.node_ == end.node_) {
     assert(end.position_ > begin.position_);
     begin.node_->remove_values(
         static_cast<field_type>(begin.position_),
         static_cast<field_type>(end.position_ - begin.position_),
         mutable_allocator());
     size_ -= count;
     return {count, rebalance_after_delete(begin)};
   }
 
   const size_type target_size = size_ - count;
   while (size_ > target_size) {
     if (begin.node_->is_leaf()) {
       const size_type remaining_to_erase = size_ - target_size;
       const size_type remaining_in_node =
           static_cast<size_type>(begin.node_->finish() - begin.position_);
       const field_type to_erase = static_cast<field_type>(
           (std::min)(remaining_to_erase, remaining_in_node));
       begin.node_->remove_values(static_cast<field_type>(begin.position_),
                                  to_erase, mutable_allocator());
       size_ -= to_erase;
       begin = rebalance_after_delete(begin);
     } else {
       begin = erase(begin);
     }
   }
   begin.update_generation();
   return {count, begin};
 }
 
 template <typename P>
 void btree<P>::clear() {
   if (!empty()) {
     node_type::clear_and_delete(root(), mutable_allocator());
   }
   mutable_root() = mutable_rightmost() = EmptyNode();
   size_ = 0;
 }
 
 template <typename P>
 void btree<P>::swap(btree &other) {
   using std::swap;
   if (absl::allocator_traits<
           allocator_type>::propagate_on_container_swap::value) {
     // Note: `rightmost_` also contains the allocator and the key comparator.
     swap(rightmost_, other.rightmost_);
   } else {
     // It's undefined behavior if the allocators are unequal here.
     assert(allocator() == other.allocator());
     swap(mutable_rightmost(), other.mutable_rightmost());
     swap(*mutable_key_comp(), *other.mutable_key_comp());
   }
   swap(mutable_root(), other.mutable_root());
   swap(size_, other.size_);
 }
 
 template <typename P>
 void btree<P>::verify() const {
   assert(root() != nullptr);
   assert(leftmost() != nullptr);
   assert(rightmost() != nullptr);
   assert(empty() || size() == internal_verify(root(), nullptr, nullptr));
   assert(leftmost() == (++const_iterator(root(), -1)).node_);
   assert(rightmost() == (--const_iterator(root(), root()->finish())).node_);
   assert(leftmost()->is_leaf());
   assert(rightmost()->is_leaf());
 }
 
 template <typename P>
 void btree<P>::rebalance_or_split(iterator *iter) {
   node_type *&node = iter->node_;
   int &insert_position = iter->position_;
   assert(node->count() == node->max_count());
   assert(kNodeSlots == node->max_count());
 
   // First try to make room on the node by rebalancing.
   node_type *parent = node->parent();
   if (node != root()) {
     if (node->position() > parent->start()) {
       // Try rebalancing with our left sibling.
       node_type *left = parent->child(node->position() - 1);
       assert(left->max_count() == kNodeSlots);
       if (left->count() < kNodeSlots) {
         // We bias rebalancing based on the position being inserted. If we're
         // inserting at the end of the right node then we bias rebalancing to
         // fill up the left node.
         field_type to_move =
             (kNodeSlots - left->count()) /
             (1 + (static_cast<field_type>(insert_position) < kNodeSlots));
         to_move = (std::max)(field_type{1}, to_move);
 
         if (static_cast<field_type>(insert_position) - to_move >=
                 node->start() ||
             left->count() + to_move < kNodeSlots) {
           left->rebalance_right_to_left(to_move, node, mutable_allocator());
 
           assert(node->max_count() - node->count() == to_move);
           insert_position = static_cast<int>(
               static_cast<field_type>(insert_position) - to_move);
           if (insert_position < node->start()) {
             insert_position = insert_position + left->count() + 1;
             node = left;
           }
 
           assert(node->count() < node->max_count());
           return;
         }
       }
     }
 
     if (node->position() < parent->finish()) {
       // Try rebalancing with our right sibling.
       node_type *right = parent->child(node->position() + 1);
       assert(right->max_count() == kNodeSlots);
       if (right->count() < kNodeSlots) {
         // We bias rebalancing based on the position being inserted. If we're
         // inserting at the beginning of the left node then we bias rebalancing
         // to fill up the right node.
         field_type to_move = (kNodeSlots - right->count()) /
                              (1 + (insert_position > node->start()));
         to_move = (std::max)(field_type{1}, to_move);
 
         if (static_cast<field_type>(insert_position) <=
                 node->finish() - to_move ||
             right->count() + to_move < kNodeSlots) {
           node->rebalance_left_to_right(to_move, right, mutable_allocator());
 
           if (insert_position > node->finish()) {
             insert_position = insert_position - node->count() - 1;
             node = right;
           }
 
           assert(node->count() < node->max_count());
           return;
         }
       }
     }
 
     // Rebalancing failed, make sure there is room on the parent node for a new
     // value.
     assert(parent->max_count() == kNodeSlots);
     if (parent->count() == kNodeSlots) {
       iterator parent_iter(parent, node->position());
       rebalance_or_split(&parent_iter);
       parent = node->parent();
     }
   } else {
     // Rebalancing not possible because this is the root node.
     // Create a new root node and set the current root node as the child of the
     // new root.
     parent = new_internal_node(/*position=*/0, parent);
     parent->set_generation(root()->generation());
     parent->init_child(parent->start(), node);
     mutable_root() = parent;
     // If the former root was a leaf node, then it's now the rightmost node.
     assert(parent->start_child()->is_internal() ||
            parent->start_child() == rightmost());
   }
 
   // Split the node.
   node_type *split_node;
   if (node->is_leaf()) {
     split_node = new_leaf_node(node->position() + 1, parent);
     node->split(insert_position, split_node, mutable_allocator());
     if (rightmost() == node) mutable_rightmost() = split_node;
   } else {
     split_node = new_internal_node(node->position() + 1, parent);
     node->split(insert_position, split_node, mutable_allocator());
   }
 
   if (insert_position > node->finish()) {
     insert_position = insert_position - node->count() - 1;
     node = split_node;
   }
 }
 
 template <typename P>
 void btree<P>::merge_nodes(node_type *left, node_type *right) {
   left->merge(right, mutable_allocator());
   if (rightmost() == right) mutable_rightmost() = left;
 }
 
 template <typename P>
 bool btree<P>::try_merge_or_rebalance(iterator *iter) {
   node_type *parent = iter->node_->parent();
   if (iter->node_->position() > parent->start()) {
     // Try merging with our left sibling.
     node_type *left = parent->child(iter->node_->position() - 1);
     assert(left->max_count() == kNodeSlots);
     if (1U + left->count() + iter->node_->count() <= kNodeSlots) {
       iter->position_ += 1 + left->count();
       merge_nodes(left, iter->node_);
       iter->node_ = left;
       return true;
     }
   }
   if (iter->node_->position() < parent->finish()) {
     // Try merging with our right sibling.
     node_type *right = parent->child(iter->node_->position() + 1);
     assert(right->max_count() == kNodeSlots);
     if (1U + iter->node_->count() + right->count() <= kNodeSlots) {
       merge_nodes(iter->node_, right);
       return true;
     }
     // Try rebalancing with our right sibling. We don't perform rebalancing if
     // we deleted the first element from iter->node_ and the node is not
     // empty. This is a small optimization for the common pattern of deleting
     // from the front of the tree.
     if (right->count() > kMinNodeValues &&
         (iter->node_->count() == 0 || iter->position_ > iter->node_->start())) {
       field_type to_move = (right->count() - iter->node_->count()) / 2;
       to_move =
           (std::min)(to_move, static_cast<field_type>(right->count() - 1));
       iter->node_->rebalance_right_to_left(to_move, right, mutable_allocator());
       return false;
     }
   }
   if (iter->node_->position() > parent->start()) {
     // Try rebalancing with our left sibling. We don't perform rebalancing if
     // we deleted the last element from iter->node_ and the node is not
     // empty. This is a small optimization for the common pattern of deleting
     // from the back of the tree.
     node_type *left = parent->child(iter->node_->position() - 1);
     if (left->count() > kMinNodeValues &&
         (iter->node_->count() == 0 ||
          iter->position_ < iter->node_->finish())) {
       field_type to_move = (left->count() - iter->node_->count()) / 2;
       to_move = (std::min)(to_move, static_cast<field_type>(left->count() - 1));
       left->rebalance_left_to_right(to_move, iter->node_, mutable_allocator());
       iter->position_ += to_move;
       return false;
     }
   }
   return false;
 }
 
 template <typename P>
 void btree<P>::try_shrink() {
   node_type *orig_root = root();
   if (orig_root->count() > 0) {
     return;
   }
   // Deleted the last item on the root node, shrink the height of the tree.
   if (orig_root->is_leaf()) {
     assert(size() == 0);
     mutable_root() = mutable_rightmost() = EmptyNode();
   } else {
     node_type *child = orig_root->start_child();
     child->make_root();
     mutable_root() = child;
   }
   node_type::clear_and_delete(orig_root, mutable_allocator());
 }
 
 template <typename P>
 template <typename IterType>
 inline IterType btree<P>::internal_last(IterType iter) {
   assert(iter.node_ != nullptr);
   while (iter.position_ == iter.node_->finish()) {
     iter.position_ = iter.node_->position();
     iter.node_ = iter.node_->parent();
     if (iter.node_->is_leaf()) {
       iter.node_ = nullptr;
       break;
     }
   }
   iter.update_generation();
   return iter;
 }
 
 template <typename P>
 template <typename... Args>
 inline auto btree<P>::internal_emplace(iterator iter, Args &&...args)
     -> iterator {
   if (iter.node_->is_internal()) {
     // We can't insert on an internal node. Instead, we'll insert after the
     // previous value which is guaranteed to be on a leaf node.
     --iter;
     ++iter.position_;
   }
   const field_type max_count = iter.node_->max_count();
   allocator_type *alloc = mutable_allocator();
 
   const auto transfer_and_delete = [&](node_type *old_node,
                                        node_type *new_node) {
     new_node->transfer_n(old_node->count(), new_node->start(),
                          old_node->start(), old_node, alloc);
     new_node->set_finish(old_node->finish());
     old_node->set_finish(old_node->start());
     new_node->set_generation(old_node->generation());
     node_type::clear_and_delete(old_node, alloc);
   };
   const auto replace_leaf_root_node = [&](field_type new_node_size) {
     assert(iter.node_ == root());
     node_type *old_root = iter.node_;
     node_type *new_root = iter.node_ = new_leaf_root_node(new_node_size);
     transfer_and_delete(old_root, new_root);
     mutable_root() = mutable_rightmost() = new_root;
   };
 
   bool replaced_node = false;
   if (iter.node_->count() == max_count) {
     // Make room in the leaf for the new item.
     if (max_count < kNodeSlots) {
       // Insertion into the root where the root is smaller than the full node
       // size. Simply grow the size of the root node.
       replace_leaf_root_node(static_cast<field_type>(
           (std::min)(static_cast<int>(kNodeSlots), 2 * max_count)));
       replaced_node = true;
     } else {
       rebalance_or_split(&iter);
     }
   }
   (void)replaced_node;
 #if defined(ABSL_HAVE_ADDRESS_SANITIZER) || \
     defined(ABSL_HAVE_HWADDRESS_SANITIZER)
   if (!replaced_node) {
     assert(iter.node_->is_leaf());
     if (iter.node_->is_root()) {
       replace_leaf_root_node(max_count);
     } else {
       node_type *old_node = iter.node_;
       const bool was_rightmost = rightmost() == old_node;
       const bool was_leftmost = leftmost() == old_node;
       node_type *parent = old_node->parent();
       const field_type position = old_node->position();
       node_type *new_node = iter.node_ = new_leaf_node(position, parent);
       parent->set_child_noupdate_position(position, new_node);
       transfer_and_delete(old_node, new_node);
       if (was_rightmost) mutable_rightmost() = new_node;
       // The leftmost node is stored as the parent of the root node.
       if (was_leftmost) root()->set_parent(new_node);
     }
   }
 #endif
   iter.node_->emplace_value(static_cast<field_type>(iter.position_), alloc,
                             std::forward<Args>(args)...);
   assert(
       iter.node_->is_ordered_correctly(static_cast<field_type>(iter.position_),
                                        original_key_compare(key_comp())) &&
       "If this assert fails, then either (1) the comparator may violate "
       "transitivity, i.e. comp(a,b) && comp(b,c) -> comp(a,c) (see "
       "https://en.cppreference.com/w/cpp/named_req/Compare), or (2) a "
       "key may have been mutated after it was inserted into the tree.");
   ++size_;
   iter.update_generation();
   return iter;
 }
 
 template <typename P>
 template <typename K>
 inline auto btree<P>::internal_locate(const K &key) const
     -> SearchResult<iterator, is_key_compare_to::value> {
   iterator iter(const_cast<node_type *>(root()));
   for (;;) {
     SearchResult<size_type, is_key_compare_to::value> res =
         iter.node_->lower_bound(key, key_comp());
     iter.position_ = static_cast<int>(res.value);
     if (res.IsEq()) {
       return {iter, MatchKind::kEq};
     }
     // Note: in the non-key-compare-to case, we don't need to walk all the way
     // down the tree if the keys are equal, but determining equality would
     // require doing an extra comparison on each node on the way down, and we
     // will need to go all the way to the leaf node in the expected case.
     if (iter.node_->is_leaf()) {
       break;
     }
     iter.node_ = iter.node_->child(static_cast<field_type>(iter.position_));
   }
   // Note: in the non-key-compare-to case, the key may actually be equivalent
   // here (and the MatchKind::kNe is ignored).
   return {iter, MatchKind::kNe};
 }
 
 template <typename P>
 template <typename K>
 auto btree<P>::internal_lower_bound(const K &key) const
     -> SearchResult<iterator, is_key_compare_to::value> {
   if (!params_type::template can_have_multiple_equivalent_keys<K>()) {
     SearchResult<iterator, is_key_compare_to::value> ret = internal_locate(key);
     ret.value = internal_last(ret.value);
     return ret;
   }
   iterator iter(const_cast<node_type *>(root()));
   SearchResult<size_type, is_key_compare_to::value> res;
   bool seen_eq = false;
   for (;;) {
     res = iter.node_->lower_bound(key, key_comp());
     iter.position_ = static_cast<int>(res.value);
     if (iter.node_->is_leaf()) {
       break;
     }
     seen_eq = seen_eq || res.IsEq();
     iter.node_ = iter.node_->child(static_cast<field_type>(iter.position_));
   }
   if (res.IsEq()) return {iter, MatchKind::kEq};
   return {internal_last(iter), seen_eq ? MatchKind::kEq : MatchKind::kNe};
 }
 
 template <typename P>
 template <typename K>
 auto btree<P>::internal_upper_bound(const K &key) const -> iterator {
   iterator iter(const_cast<node_type *>(root()));
   for (;;) {
     iter.position_ = static_cast<int>(iter.node_->upper_bound(key, key_comp()));
     if (iter.node_->is_leaf()) {
       break;
     }
     iter.node_ = iter.node_->child(static_cast<field_type>(iter.position_));
   }
   return internal_last(iter);
 }
 
 template <typename P>
 template <typename K>
 auto btree<P>::internal_find(const K &key) const -> iterator {
   SearchResult<iterator, is_key_compare_to::value> res = internal_locate(key);
   if (res.HasMatch()) {
     if (res.IsEq()) {
       return res.value;
     }
   } else {
     const iterator iter = internal_last(res.value);
     if (iter.node_ != nullptr && !compare_keys(key, iter.key())) {
       return iter;
     }
   }
   return {nullptr, 0};
 }
 
 template <typename P>
 typename btree<P>::size_type btree<P>::internal_verify(
     const node_type *node, const key_type *lo, const key_type *hi) const {
   assert(node->count() > 0);
   assert(node->count() <= node->max_count());
   if (lo) {
     assert(!compare_keys(node->key(node->start()), *lo));
   }
   if (hi) {
     assert(!compare_keys(*hi, node->key(node->finish() - 1)));
   }
   for (int i = node->start() + 1; i < node->finish(); ++i) {
     assert(!compare_keys(node->key(i), node->key(i - 1)));
   }
   size_type count = node->count();
   if (node->is_internal()) {
     for (field_type i = node->start(); i <= node->finish(); ++i) {
       assert(node->child(i) != nullptr);
       assert(node->child(i)->parent() == node);
       assert(node->child(i)->position() == i);
       count += internal_verify(node->child(i),
                                i == node->start() ? lo : &node->key(i - 1),
                                i == node->finish() ? hi : &node->key(i));
     }
   }
   return count;
 }
 
 struct btree_access {
   template <typename BtreeContainer, typename Pred>
   static auto erase_if(BtreeContainer &container, Pred pred) ->
       typename BtreeContainer::size_type {
     const auto initial_size = container.size();
     auto &tree = container.tree_;
     auto *alloc = tree.mutable_allocator();
     for (auto it = container.begin(); it != container.end();) {
       if (!pred(*it)) {
         ++it;
         continue;
       }
       auto *node = it.node_;
       if (node->is_internal()) {
         // Handle internal nodes normally.
         it = container.erase(it);
         continue;
       }
       // If this is a leaf node, then we do all the erases from this node
       // at once before doing rebalancing.
 
       // The current position to transfer slots to.
       int to_pos = it.position_;
       node->value_destroy(it.position_, alloc);
       while (++it.position_ < node->finish()) {
         it.update_generation();
         if (pred(*it)) {
           node->value_destroy(it.position_, alloc);
         } else {
           node->transfer(node->slot(to_pos++), node->slot(it.position_), alloc);
         }
       }
       const int num_deleted = node->finish() - to_pos;
       tree.size_ -= num_deleted;
       node->set_finish(to_pos);
       it.position_ = to_pos;
       it = tree.rebalance_after_delete(it);
     }
     return initial_size - container.size();
   }
 };
 
 #undef ABSL_BTREE_ENABLE_GENERATIONS
 
 }  // namespace container_internal
 ABSL_NAMESPACE_END
 }  // namespace absl
 
 #endif  // ABSL_CONTAINER_INTERNAL_BTREE_H_