[Note: this document is formatted similarly to the SGI STL implementation documentation pages, and refers to concepts and classes defined there. However, neither this document nor the code it describes is associated with SGI, nor is it necessary to have SGI's STL implementation installed in order to use this class.]

# dense_hash_map<Key, Data, HashFcn, EqualKey, Alloc>

`dense_hash_map` is a Hashed Associative Container that associates objects of type `Key` with objects of type `Data`. `dense_hash_map` is a Pair Associative Container, meaning that its value type is `pair<const Key, Data>`. It is also a Unique Associative Container, meaning that no two elements have keys that compare equal using `EqualKey`.

Looking up an element in a `dense_hash_map` by its key is efficient, so `dense_hash_map` is useful for "dictionaries" where the order of elements is irrelevant. If it is important for the elements to be in a particular order, however, then `map` is more appropriate.

`dense_hash_map` is distinguished from other hash-map implementations by its speed and by the ability to save and restore contents to disk. On the other hand, this hash-map implementation can use significantly more space than other hash-map implementations, and it also has requirements -- for instance, for a distinguished "empty key" -- that may not be easy for all applications to satisfy.

This class is appropriate for applications that need speedy access to relatively small "dictionaries" stored in memory, or for applications that need these dictionaries to be persistent. [implementation note])

### Example

(Note: this example uses SGI semantics for `hash<>` -- the kind used by gcc and most Unix compiler suites -- and not Dinkumware semantics -- the kind used by Microsoft Visual Studio. If you are using MSVC, this example will not compile as-is: you'll need to change `hash` to `hash_compare`, and you won't use `eqstr` at all. See the MSVC documentation for `hash_map` and `hash_compare`, for more details.)

    #include <iostream>
    #include <sparsehash/dense_hash_map>

    using google::dense_hash_map;      // namespace where class lives by default
    using std::cout;
    using std::endl;
    using ext::hash;  // or __gnu_cxx::hash, or maybe tr1::hash, depending on your OS

    struct eqstr
    {
      bool operator()(const char* s1, const char* s2) const
      {
        return (s1 == s2) || (s1 && s2 && strcmp(s1, s2) == 0);
      }
    };

    int main()
    {
      dense_hash_map<const char*, int, hash<const char*>, eqstr> months;

      months.set_empty_key(NULL);
      months["january"] = 31;
      months["february"] = 28;
      months["march"] = 31;
      months["april"] = 30;
      months["may"] = 31;
      months["june"] = 30;
      months["july"] = 31;
      months["august"] = 31;
      months["september"] = 30;
      months["october"] = 31;
      months["november"] = 30;
      months["december"] = 31;

      cout << "september -> " << months["september"] << endl;
      cout << "april     -> " << months["april"] << endl;
      cout << "june      -> " << months["june"] << endl;
      cout << "november  -> " << months["november"] << endl;
    }

### Definition

Defined in the header dense_hash_map. This class is not part of the C++ standard, though it is mostly compatible with the tr1 class `unordered_map`.

### Template parameters

Parameter | Description | Default
--- | --- | ---
`Key` | The hash_map's key type. This is also defined as `dense_hash_map::key_type`. |
`Data` | The hash_map's data type. This is also defined as `dense_hash_map::data_type`. [7] |
`HashFcn` | The hash function used by the hash_map. This is also defined as `dense_hash_map::hasher`. Note: Hashtable performance depends heavily on the choice of hash function. See the performance page for more information. | `hash<Key>`
`EqualKey` | The hash_map key equality function: a binary predicate that determines whether two keys are equal. This is also defined as `dense_hash_map::key_equal`. | `equal_to<Key>`
`Alloc` | The STL allocator to use. By default, uses the provided allocator `libc_allocator_with_realloc`, which likely gives better performance than other STL allocators due to its built-in support for `realloc`, which this container takes advantage of. If you use an allocator other than the default, note that this container imposes an additional requirement on the STL allocator type beyond those in [lib.allocator.requirements]: it does not support allocators that define alternate memory models. That is, it assumes that `pointer`, `const_pointer`, `size_type`, and `difference_type` are just `T*`, `const T*`, `size_t`, and `ptrdiff_t`, respectively. This is also defined as `dense_hash_map::allocator_type`. |

### Model of

Unique Hashed Associative Container, Pair Associative Container

### Type requirements

- `Key` is Assignable.
- `EqualKey` is a Binary Predicate whose argument type is Key.
- `EqualKey` is an equivalence relation.
- `Alloc` is an Allocator.

### Public base classes

None.

### Members

Member | Where defined | Description
--- | --- | ---
`key_type` | Associative Container | The `dense_hash_map`'s key type, `Key`.
`data_type` | Pair Associative Container | The type of object associated with the keys.
`value_type` | Pair Associative Container | The type of object, `pair<const key_type, data_type>`, stored in the hash_map.
`hasher` | Hashed Associative Container | The `dense_hash_map`'s hash function.
`key_equal` | Hashed Associative Container | Function object that compares keys for equality.
`allocator_type` | `Unordered Associative Container` (tr1) | The type of the Allocator given as a template parameter.
`pointer` | Container | Pointer to `T`.
`reference` | Container | Reference to `T`
`const_reference` | Container | Const reference to `T`
`size_type` | Container | An unsigned integral type.
`difference_type` | Container | A signed integral type.
`iterator` | Container | Iterator used to iterate through a `dense_hash_map`. [1]
`const_iterator` | Container | Const iterator used to iterate through a `dense_hash_map`.
`local_iterator` | `Unordered Associative Container` (tr1) | Iterator used to iterate through a subset of `dense_hash_map`. [1]
`const_local_iterator` | `Unordered Associative Container` (tr1) | Const iterator used to iterate through a subset of `dense_hash_map`.
`iterator begin()` | Container | Returns an `iterator` pointing to the beginning of the `dense_hash_map`.
`iterator end()` | Container | Returns an `iterator` pointing to the end of the `dense_hash_map`.
`const_iterator begin() const` | Container | Returns an `const_iterator` pointing to the beginning of the `dense_hash_map`.
`const_iterator end() const` | Container | Returns an `const_iterator` pointing to the end of the `dense_hash_map`.
`local_iterator begin(size_type i)` | `Unordered Associative Container` (tr1) | Returns a `local_iterator` pointing to the beginning of bucket `i` in the `dense_hash_map`.
`local_iterator end(size_type i)` | `Unordered Associative Container` (tr1) | Returns a `local_iterator` pointing to the end of bucket `i` in the `dense_hash_map`. For `dense_hash_map`, each bucket contains either 0 or 1 item.
`const_local_iterator begin(size_type i) const` | `Unordered Associative Container` (tr1) | Returns a `const_local_iterator` pointing to the beginning of bucket `i` in the `dense_hash_map`.
`const_local_iterator end(size_type i) const` | `Unordered Associative Container` (tr1) | Returns a `const_local_iterator` pointing to the end of bucket `i` in the `dense_hash_map`. For `dense_hash_map`, each bucket contains either 0 or 1 item.
`size_type size() const` | Container | Returns the size of the `dense_hash_map`.
`size_type max_size() const` | Container | Returns the largest possible size of the `dense_hash_map`.
`bool empty() const` | Container | `true` if the `dense_hash_map`'s size is `0`.
`size_type bucket_count() const` | Hashed Associative Container | Returns the number of buckets used by the `dense_hash_map`.
`size_type max_bucket_count() const` | Hashed Associative Container | Returns the largest possible number of buckets used by the `dense_hash_map`.
`size_type bucket_size(size_type i) const` | `Unordered Associative Container` (tr1) | Returns the number of elements in bucket `i`. For `dense_hash_map`, this will be either 0 or 1.
`size_type bucket(const key_type& key) const` | `Unordered Associative Container` (tr1) | If the key exists in the map, returns the index of the bucket containing the given key, otherwise, return the bucket the key would be inserted into. This value may be passed to `begin(size_type)` and `end(size_type)`.
`float load_factor() const` | `Unordered Associative Container` (tr1) | The number of elements in the `dense_hash_map` divided by the number of buckets.
`float max_load_factor() const` | `Unordered Associative Container` (tr1) | The maximum load factor before increasing the number of buckets in the `dense_hash_map`.
`void max_load_factor(float new_grow)` | `Unordered Associative Container` (tr1) | Sets the maximum load factor before increasing the number of buckets in the `dense_hash_map`.
`float min_load_factor() const` | `dense_hash_map` | The minimum load factor before decreasing the number of buckets in the `dense_hash_map`.
`void min_load_factor(float new_grow)` | `dense_hash_map` | Sets the minimum load factor before decreasing the number of buckets in the `dense_hash_map`.
`void set_resizing_parameters(float shrink, float grow)` | `dense_hash_map` | DEPRECATED. See below.
`void resize(size_type n)` | Hashed Associative Container | Increases the bucket count to hold at least `n` items. [4] [5]
`void rehash(size_type n)` | `Unordered Associative Container` (tr1) | Increases the bucket count to hold at least `n` items. This is identical to `resize`. [4] [5]
`hasher hash_funct() const` | Hashed Associative Container | Returns the `hasher` object used by the `dense_hash_map`.
`hasher hash_function() const` | `Unordered Associative Container` (tr1) | Returns the `hasher` object used by the `dense_hash_map`. This is idential to `hash_funct`.
`key_equal key_eq() const` | Hashed Associative Container | Returns the `key_equal` object used by the `dense_hash_map`.
`allocator_type get_allocator() const` | `Unordered Associative Container` (tr1) | Returns the `allocator_type` object used by the `dense_hash_map`: either the one passed in to the constructor, or a default `Alloc` instance.
`dense_hash_map()` | Container | Creates an empty `dense_hash_map`.
`dense_hash_map(size_type n)` | Hashed Associative Container | Creates an empty `dense_hash_map` that's optimized for holding up to `n` items. [5]
`dense_hash_map(size_type n, const hasher& h)` | Hashed Associative Container | Creates an empty `dense_hash_map` that's optimized for up to `n` items, using `h` as the hash function.
`dense_hash_map(size_type n, const hasher& h, const key_equal& k)` | Hashed Associative Container | Creates an empty `dense_hash_map` that's optimized for up to `n` items, using `h` as the hash function and `k` as the key equal function.
`dense_hash_map(size_type n, const hasher& h, const key_equal& k, const allocator_type& a)` | `Unordered Associative Container` (tr1) | Creates an empty `dense_hash_map` that's optimized for up to `n` items, using `h` as the hash function, `k` as the key equal function, and `a` as the allocator object.
    template <class InputIterator>
    dense_hash_map(InputIterator f, InputIterator l)
[2] | Unique Hashed Associative Container | Creates a dense_hash_map with a copy of a range.
    template <class InputIterator>
    dense_hash_map(InputIterator f, InputIterator l, size_type n)
[2] | Unique Hashed Associative Container | Creates a hash_map with a copy of a range that's optimized to hold up to `n` items.
    template <class InputIterator>
    dense_hash_map(InputIterator f, InputIterator l, size_type n, const
    hasher& h)
[2] | Unique Hashed Associative Container | Creates a hash_map with a copy of a range that's optimized to hold up to `n` items, using `h` as the hash function.
    template <class InputIterator>
    dense_hash_map(InputIterator f, InputIterator l, size_type n, const
    hasher& h, const key_equal& k)
[2] | Unique Hashed Associative Container | Creates a hash_map with a copy of a range that's optimized for holding up to `n` items, using `h` as the hash function and `k` as the key equal function.
    template <class InputIterator>
    dense_hash_map(InputIterator f, InputIterator l, size_type n, const
    hasher& h, const key_equal& k, const allocator_type& a)
[2] | `Unordered Associative Container` (tr1) | Creates a hash_map with a copy of a range that's optimized for holding up to `n` items, using `h` as the hash function, `k` as the key equal function, and `a` as the allocator object.
`dense_hash_map(const hash_map&)` | Container | The copy constructor.
`dense_hash_map& operator=(const hash_map&)` | Container | The assignment operator
`void swap(hash_map&)` | Container | Swaps the contents of two hash_maps.
    pair<iterator, bool> insert(const value_type& x)
| Unique Associative Container | Inserts `x` into the `dense_hash_map`.
    template <class InputIterator>
    void insert(InputIterator f, InputIterator l)
[2] | Unique Associative Container | Inserts a range into the `dense_hash_map`.
`void set_empty_key(const key_type& key)` [6] | `dense_hash_map` | See below.
`void set_deleted_key(const key_type& key)` [6] | `dense_hash_map` | See below.
`void clear_deleted_key()` [6] | `dense_hash_map` | See below.
`void erase(iterator pos)` | Associative Container | Erases the element pointed to by `pos`. [6]
`size_type erase(const key_type& k)` | Associative Container | Erases the element whose key is `k`. [6]
`void erase(iterator first, iterator last)` | Associative Container | Erases all elements in a range. [6]
`void clear()` | Associative Container | Erases all of the elements.
`void clear_no_resize()` | `dense_hash_map` | See below.
`const_iterator find(const key_type& k) const` | Associative Container | Finds an element whose key is `k`.
`iterator find(const key_type& k)` | Associative Container | Finds an element whose key is `k`.
`size_type count(const key_type& k) const` | Unique Associative Container | Counts the number of elements whose key is `k`.
    pair<const_iterator, const_iterator> equal_range(const
    key_type& k) const
| Associative Container | Finds a range containing all elements whose key is `k`.
    pair<iterator, iterator> equal_range(const
    key_type& k)
| Associative Container | Finds a range containing all elements whose key is `k`.
    data_type& operator[](const key_type& k) [3]
| `dense_hash_map` | See below.
`template <ValueSerializer, OUTPUT> bool serialize(ValueSerializer serializer, OUTPUT *fp)` | `dense_hash_map` | See below.
`template <ValueSerializer, INPUT> bool unserialize(ValueSerializer serializer, INPUT *fp)` | `dense_hash_map` | See below.
`NopointerSerializer` | `dense_hash_map` | See below.
`bool write_metadata(FILE *fp)` | `dense_hash_map` | DEPRECATED. See below.
`bool read_metadata(FILE *fp)` | `dense_hash_map` | DEPRECATED. See below.
`bool write_nopointer_data(FILE *fp)` | `dense_hash_map` | DEPRECATED. See below.
`bool read_nopointer_data(FILE *fp)` | `dense_hash_map` | DEPRECATED. See below.
    bool operator==(const hash_map&, const hash_map&)
| Hashed Associative Container | Tests two hash_maps for equality. This is a global function, not a member function.

### New members

These members are not defined in the Unique Hashed Associative Container, Pair Associative Container, or tr1's +`Unordered Associative Container` requirements, but are specific to `dense_hash_map`.

Member | Description
--- | ---
`void set_empty_key(const key_type& key)` | Sets the distinguished "empty" key to `key`. This must be called immediately after construct time, before calls to another other `dense_hash_map` operation. [6]
`void set_deleted_key(const key_type& key)` | Sets the distinguished "deleted" key to `key`. This must be called before any calls to `erase()`. [6]
`void clear_deleted_key()` | Clears the distinguished "deleted" key. After this is called, calls to `erase()` are not valid on this object. [6]
`void clear_no_resize()` | Clears the hashtable like `clear()` does, but does not recover the memory used for hashtable buckets. (The memory used by the items in the hashtable is still recovered.) This can save time for applications that want to reuse a `dense_hash_map` many times, each time with a similar number of objects.
    data_type&
    operator[](const key_type& k) [3]
| Returns a reference to the object that is associated with a particular key. If the `dense_hash_map` does not already contain such an object, `operator[]` inserts the default object `data_type()`. [3]
| `void set_resizing_parameters(float shrink, float grow)` | This function is DEPRECATED. It is equivalent to calling `min_load_factor(shrink); max_load_factor(grow)`.
`template <ValueSerializer, OUTPUT> bool serialize(ValueSerializer serializer, OUTPUT *fp)` | Emit a serialization of the hash_map to a stream. See below.
`template <ValueSerializer, INPUT> bool unserialize(ValueSerializer serializer, INPUT *fp)` | Read in a serialization of a hash_map from a stream, replacing the existing hash_map contents with the serialized contents. See below.
`bool write_metadata(FILE *fp)` | This function is DEPRECATED. See below.
`bool read_metadata(FILE *fp)` | This function is DEPRECATED. See below.
`bool write_nopointer_data(FILE *fp)` | This function is DEPRECATED. See below.
`bool read_nopointer_data(FILE *fp)` | This function is DEPRECATED. See below.

### Notes

[1] `dense_hash_map::iterator` is not a mutable iterator, because `dense_hash_map::value_type` is not Assignable. That is, if `i` is of type `dense_hash_map::iterator` and `p` is of type `dense_hash_map::value_type`, then `*i = p` is not a valid expression. However, `dense_hash_map::iterator` isn't a constant iterator either, because it can be used to modify the object that it points to. Using the same notation as above, `(*i).second = p` is a valid expression.

[2] This member function relies on member template functions, which may not be supported by all compilers. If your compiler supports member templates, you can call this function with any type of input iterator. If your compiler does not yet support member templates, though, then the arguments must either be of type `const value_type*` or of type `dense_hash_map::const_iterator`.

[3] Since `operator[]` might insert a new element into the `dense_hash_map`, it can't possibly be a `const` member function. Note that the definition of `operator[]` is extremely simple: `m[k]` is equivalent to `(*((m.insert(value_type(k, data_type()))).first)).second`. Strictly speaking, this member function is unnecessary: it exists only for convenience.

[4] In order to preserve iterators, erasing hashtable elements does not cause a hashtable to resize. This means that after a string of `erase()` calls, the hashtable will use more space than is required. At a cost of invalidating all current iterators, you can call `resize()` to manually compact the hashtable. The hashtable promotes too-small `resize()` arguments to the smallest legal value, so to compact a hashtable, it's sufficient to call `resize(0)`.

[5] Unlike some other hashtable implementations, the optional n in the calls to the constructor, `resize`, and `rehash` indicates not the desired number of buckets that should be allocated, but instead the expected number of items to be inserted. The class then sizes the hash-map appropriately for the number of items specified. It's not an error to actually insert more or fewer items into the hashtable, but the implementation is most efficient -- does the fewest hashtable resizes -- if the number of inserted items is n or slightly less.

[6] `dense_hash_map` requires you call `set_empty_key()` immediately after constructing the hash-map, and before calling any other `dense_hash_map` method. (This is the largest difference between the `dense_hash_map` API and other hash-map APIs. See implementation.html for why this is necessary.) The argument to `set_empty_key()` should be a key-value that is never used for legitimate hash-map entries. If you have no such key value, you will be unable to use `dense_hash_map`. It is an error to call `insert()` with an item whose key is the "empty key."

`dense_hash_map` also requires you call `set_deleted_key()` before calling `erase()`. The argument to `set_deleted_key()` should be a key-value that is never used for legitimate hash-map entries. It must be different from the key-value used for `set_empty_key()`. It is an error to call `erase()` without first calling `set_deleted_key()`, and it is also an error to call `insert()` with an item whose key is the "deleted key."

There is no need to call `set_deleted_key` if you do not wish to call `erase()` on the hash-map.

It is acceptable to change the deleted-key at any time by calling `set_deleted_key()` with a new argument. You can also call `clear_deleted_key()`, at which point all keys become valid for insertion but no hashtable entries can be deleted until `set_deleted_key()` is called again.

[7] `dense_hash_map` requires that `data_type` has a zero-argument default constructor. This is because `dense_hash_map` uses the special value `pair(empty_key, data_type())` to denote empty buckets, and thus needs to be able to create `data_type` using a zero-argument constructor.

If your `data_type` does not have a zero-argument default constructor, there are several workarounds:

- Store a pointer to `data_type` in the map, instead of `data_type` directly. This may yield faster code as well, since hashtable-resizes will just have to move pointers around, rather than copying the entire `data_type`.
- Add a zero-argument default constructor to `data_type`.
- Subclass `data_type` and add a zero-argument default constructor to the subclass.

### Input/Output

It is possible to save and restore `dense_hash_map` objects to an arbitrary stream (such as a disk file) using the `serialize()` and `unserialize()` methods.

Each of these methods takes two arguments: a serializer, which says how to write hashtable items to disk, and a stream, which can be a C++ stream (`istream` or its subclasses for input, `ostream` or its subclasses for output), a `FILE*`, or a user-defined type (as described below).

The serializer is a functor that takes a stream and a single hashtable element (a `value_type`, which is a pair of the key and data) and copies the hashtable element to the stream (for `serialize()`) or fills the hashtable element contents from the stream (for `unserialize()`), and returns true on success or false on error. The copy-in and copy-out functions can be provided in a single functor. Here is a sample serializer that read/writes a hashtable element for an int-to-string hash_map to a `FILE*`:

    struct StringToIntSerializer {
      bool operator()(FILE* fp, const std::pair<const int, std::string>& value) const {
        // Write the key.  We ignore endianness for this example.
        if (fwrite(&value.first, sizeof(value.first), 1, fp) != 1)
          return false;
        // Write the value.
        assert(value.second.length() <= 255);   // we only support writing small strings
        const unsigned char size = value.second.length();
        if (fwrite(&size, 1, 1, fp) != 1)
          return false;
        if (fwrite(value.second.data(), size, 1, fp) != 1)
          return false;
        return true;
      }
      bool operator()(FILE* fp, std::pair<const int, std::string>* value) const {
        // Read the key.  Note the need for const_cast to get around
        // the fact hash_map keys are always const.
        if (fread(const_cast<int*>(&value->first), sizeof(value->first), 1, fp) != 1)
          return false;
        // Read the value.
        unsigned char size;    // all strings are <= 255 chars long
        if (fread(&size, 1, 1, fp) != 1)
          return false;
        char* buf = new char[size];
        if (fread(buf, size, 1, fp) != 1) {
          delete[] buf;
          return false;
        }
        value->second.assign(buf, size);
        delete[] buf;
        return true;
      }
    };

Here is the functor being used in code (error checking omitted):

       dense_hash_map<string, int> mymap = CreateMap();
       FILE* fp = fopen("hashtable.data", "w");
       mymap.serialize(StringToIntSerializer(), fp);
       fclose(fp);

       dense_hash_map<string, int> mymap2;
       FILE* fp_in = fopen("hashtable.data", "r");
       mymap2.unserialize(StringToIntSerializer(), fp_in);
       fclose(fp_in);
       assert(mymap == mymap2);

Note that this example serializer can only serialize to a FILE*. If you want to also be able to use this serializer with C++ streams, you will need to write two more overloads of `operator()`'s, one that reads from an `istream`, and one that writes to an `ostream`. Likewise if you want to support serializing to a custom class.

If both the key and data are "simple" enough, you can use the pre-supplied functor `NopointerSerializer`. This copies the hashtable data using the equivalent of a `memcpy<>`. Native C data types can be serialized this way, as can structs of native C data types. Pointers and STL objects cannot.

Note that `NopointerSerializer()` does not do any endian conversion. Thus, it is only appropriate when you intend to read the data on the same endian architecture as you write the data.

If you wish to serialize to your own stream type, you can do so by creating an object which supports two methods:

       bool Write(const void* data, size_t length);
       bool Read(void* data, size_t length);

`Write()` writes `length` bytes of `data` to a stream (presumably a stream owned by the object), while `Read()` reads `data` bytes from the stream into `data`. Both return true on success or false on error.

To unserialize a hashtable from a stream, you wil typically create a new `dense_hash_map` object, then call `unserialize()` on it. `unserialize()` destroys the old contents of the object. You must pass in the appropriate `ValueSerializer` for the data being read in.

Both `serialize()` and `unserialize()` return `true` on success, or `false` if there was an error streaming the data.

Note that `serialize()` is not a const method, since it purges deleted elements before serializing. It is not safe to serialize from two threads at once, without synchronization.

NOTE: older versions of `dense_hash_map` provided a different API, consisting of `read_metadata()`, `read_nopointer_data()`, `write_metadata()`, `write_nopointer_data()`. These methods were never implemented and always did nothing but return `false`. You should exclusively use the new API for serialization.

### Validity of Iterators

`erase()` is guaranteed not to invalidate any iterators -- except for any iterators pointing to the item being erased, of course. `insert()` invalidates all iterators, as does `resize()`.

This is implemented by making `erase()` not resize the hashtable. If you desire maximum space efficiency, you can call `resize(0)` after a string of `erase()` calls, to force the hashtable to resize to the smallest possible size.

In addition to invalidating iterators, `insert()` and `resize()` invalidate all pointers into the hashtable. If you want to store a pointer to an object held in a dense_hash_map, either do so after finishing hashtable inserts, or store the object on the heap and a pointer to it in the dense_hash_map.

### See also

The following are SGI STL, and some Google STL, concepts and classes related to `dense_hash_map`.

`hash_map`, Associative Container, Hashed Associative Container, Pair Associative Container, Unique Hashed Associative Container, `set`, `map` `multiset`, `multimap`, `hash_set`, `hash_multiset`, `hash_multimap`, `sparse_hash_map`, `sparse_hash_set`, `dense_hash_set`