[#buckets]
:idprefix: buckets_
:imagesdir: ../diagrams

= Basics of Hash Tables

The containers are made up of a number of _buckets_, each of which can contain
any number of elements. For example, the following diagram shows a <<unordered_set,`boost::unordered_set`>> with 7 buckets containing 5 elements, `A`,
`B`, `C`, `D` and `E` (this is just for illustration, containers will typically
have more buckets).

image::buckets.png[]

In order to decide which bucket to place an element in, the container applies
the hash function, `Hash`, to the element's key (for sets the key is the whole element, but is referred to as the key
so that the same terminology can be used for sets and maps). This returns a
value of type `std::size_t`. `std::size_t` has a much greater range of values
then the number of buckets, so the container applies another transformation to
that value to choose a bucket to place the element in.

Retrieving the elements for a given key is simple. The same process is applied
to the key to find the correct bucket. Then the key is compared with the
elements in the bucket to find any elements that match (using the equality
predicate `Pred`). If the hash function has worked well the elements will be
evenly distributed amongst the buckets so only a small number of elements will
need to be examined.

There is <<hash_equality, more information on hash functions and
equality predicates in the next section>>.

You can see in the diagram that `A` & `D` have been placed in the same bucket.
When looking for elements in this bucket up to 2 comparisons are made, making
the search slower. This is known as a *collision*. To keep things fast we try to
keep collisions to a minimum.

If instead of `boost::unordered_set` we had used <<unordered_flat_set,`boost::unordered_flat_set`>>, the
diagram would look as follows:

image::buckets-oa.png[]

In open-addressing containers, buckets can hold at most one element; if a collision happens
(like is the case of `D` in the example), the element uses some other available bucket in
the vicinity of the original position. Given this simpler scenario, Boost.Unordered
open-addressing containers offer a very limited API for accessing buckets.

[caption=, title='Table {counter:table-counter}. Methods for Accessing Buckets']
[cols="1,.^1", frame=all, grid=rows]
|===
2+^h| *All containers*
h|*Method* h|*Description*

|`size_type bucket_count() const` 
|The number of buckets.

2+^h| *Closed-addressing containers only*
h|*Method* h|*Description*

|`size_type max_bucket_count() const` 
|An upper bound on the number of buckets.
|`size_type bucket_size(size_type n) const` 
|The number of elements in bucket `n`.

|`size_type bucket(key_type const& k) const`
|Returns the index of the bucket which would contain `k`.

|`local_iterator begin(size_type n)`
1.6+|Return begin and end iterators for bucket `n`.

|`local_iterator end(size_type n)`

|`const_local_iterator begin(size_type n) const`

|`const_local_iterator end(size_type n) const`

|`const_local_iterator cbegin(size_type n) const`

|`const_local_iterator cend(size_type n) const`

|===

== Controlling the Number of Buckets

As more elements are added to an unordered associative container, the number
of collisions will increase causing performance to degrade.
To combat this the containers increase the bucket count as elements are inserted.
You can also tell the container to change the bucket count (if required) by
calling `rehash`.

The standard leaves a lot of freedom to the implementer to decide how the
number of buckets is chosen, but it does make some requirements based on the
container's _load factor_, the number of elements divided by the number of buckets.
Containers also have a _maximum load factor_ which they should try to keep the
load factor below.

You can't control the bucket count directly but there are two ways to
influence it:

* Specify the minimum number of buckets when constructing a container or when calling `rehash`.
* Suggest a maximum load factor by calling `max_load_factor`.

`max_load_factor` doesn't let you set the maximum load factor yourself, it just
lets you give a _hint_. And even then, the standard doesn't actually
require the container to pay much attention to this value. The only time the
load factor is _required_ to be less than the maximum is following a call to
`rehash`. But most implementations will try to keep the number of elements
below the max load factor, and set the maximum load factor to be the same as
or close to the hint - unless your hint is unreasonably small or large.

[caption=, title='Table {counter:table-counter}. Methods for Controlling Bucket Size']
[cols="1,.^1", frame=all, grid=rows]
|===
2+^h| *All containers*
h|*Method* h|*Description*

|`X(size_type n)` 
|Construct an empty container with at least `n` buckets (`X` is the container type).

|`X(InputIterator i, InputIterator j, size_type n)` 
|Construct an empty container with at least `n` buckets and insert elements from the range `[i, j)` (`X` is the container type).

|`float load_factor() const` 
|The average number of elements per bucket.

|`float max_load_factor() const`
|Returns the current maximum load factor.

|`float max_load_factor(float z)`
|Changes the container's maximum load factor, using `z` as a hint. +
**Open-addressing and concurrent containers:** this function does nothing: users are not allowed to change the maximum load factor.

|`void rehash(size_type n)`
|Changes the number of buckets so that there at least `n` buckets, and so that the load factor is less than the maximum load factor.

2+^h| *Open-addressing and concurrent containers only*
h|*Method* h|*Description*

|`size_type max_load() const`
|Returns the maximum number of allowed elements in the container before rehash.

|===

A note on `max_load` for open-addressing and concurrent containers: the maximum load will be 
(`max_load_factor() * bucket_count()`) right after `rehash` or on container creation, but may
slightly decrease when erasing elements in high-load situations. For instance, if we
have a <<unordered_flat_map,`boost::unordered_flat_map`>> with `size()` almost
at `max_load()` level and then erase 1,000 elements, `max_load()` may decrease by around a
few dozen elements. This is done internally by Boost.Unordered in order
to keep its performance stable, and must be taken into account when planning for rehash-free insertions.


