C++ named requirements: UnorderedAssociativeContainer (since C++11)

Unordered associative containers are Containers that provide fast lookup of objects based on keys. Worst case complexity is linear but on average much faster for most of the operations.

Unordered associative containers are parametrized by Key; Hash, a Hash function object which acts as hash function on Key; and Pred, a BinaryPredicate evaluating equivalence between Keys. std::unordered_map and std::unordered_multimap also have a mapped type T associated with the Key.

If two Keys are equal according to Pred, Hash must return the same value for both keys.

 
If both Hash::is_transparent and Pred::is_transparent exist and each names a type, member functions find, contains, count, and equal_range accept arguments of types other than Key and expect that Hash is callable with values of those types, and that Pred is a transparent comparison function such as std::equal_to<>. (since C++20)  

std::unordered_map and std::unordered_set can contain at most one element with a given key, std::unordered_multiset and std::unordered_multimap instead can have multiple elements with the same key (which must always be adjacent on iterations).

For std::unordered_set and std::unordered_multiset the value type is the same as the key type and both iterator and const_iterator are constant iterators. For std::unordered_map and std::unordered_multimap the value type is std::pair<const Key, T>.

Elements in an unordered associative container are organized into buckets, keys with the same hash will end up in the same bucket. The number of buckets is increased when the size of the container increases to keep the average number of elements in each bucket under a certain value.

Rehashing invalidates iterator and might cause the elements to be re-arranged in different buckets but it doesn't invalidate references to the elements.

Unordered associative containers meet the requirements of AllocatorAwareContainer. For std::unordered_map and std::unordered_multimap the requirements of value_type in AllocatorAwareContainer apply to key_type and mapped_type (not to value_type).

Requirements

Legend

X Container type
a Object of type X
b const Object of type X
a_uniq Object in X when X supports unique keys
a_eq Object in X when X supports multiple equivalent keys
i, j LegacyInputIterators denoting a valid range
p, q2 valid const_iterator to a
q, q1 dereferenceable const_iterator to a denoting a valid range
il Object of std::initializer_list<X::value_type>
t Object of type X::value_type
k Object of type X::key_type
hf const Object of type X::hasher
eq const Object of type X::key_equal
n Value of type X::size_type
z Value of type float

Expression	Return type	Pre/Requirements	Post/Effects	Complexity
X::key_type	Key			compile time
X::mapped_type	T	std::unordered_map and std::unordered_multimap only		compile time
X::value_type	Key	std::unordered_set and std::unordered_multiset only. Erasable in X		compile time
X::value_type	std::pair<const Key, T>	std::unordered_map and std::unordered_multimap only. Erasable in X		compile time
X::hasher	Hash	Hash		compile time
X::key_equal	Pred	BinaryPredicate taking two arguments of type Key and expressing an equivalence relation.		compile time
X::local_iterator	An LegacyIterator whose category and types are the same as X::iterator		Can be used to iterate through a single bucket	compile time
X::const_local_iterator	An LegacyIterator whose category and types are the same as X::const_iterator		Can be used to iterate through a single bucket	compile time
X(n,hf,eq)	X	hasher and key_equal CopyConstructible	Constructs an empty container with at least n buckets, using the given hash function and equality predicate	linear in n
X(n,hf)	X	hasher CopyConstructible , key_equal DefaultConstructible	Constructs an empty container with at least n buckets, using the given hash function and key_equal() as equality predicate	linear in n
X(n)	X	hasher and key_equal DefaultConstructible	Constructs an empty container with at least n buckets, using hasher() as hash function and key_equal() as equality predicate	linear in n
X()	X	hasher and key_equal DefaultConstructible	Constructs an empty container with an unspecified number of buckets, using hasher() as hash function and key_equal() as equality predicate	constant
X(i,j,n,hf,eq)	X	hasher and key_equal CopyConstructible, value_type EmplaceConstructible into X from *i	Constructs an empty container with at least n buckets, using the given hash function and equality predicate, and inserts elements from [i,j) into it.	average linear, worst quadratin (on the distance between i and j)
X(i,j,n,hf)	X	key_equal DefaultConstructible	As above, with eq=key_equal()	see above
X(i,j,n)	X	hasher DefaultConstructible	As above, with hf=hasher()	see above
X(i,j)	X		As above, with an unspecified number of buckets	see above
X(il)	X		X(il.begin(),il.end()	see above
X(il,n)	X		X(il.begin(),il.end(),n	see above
X(il,n,hf)	X		X(il.begin(),il.end(),n,hf	see above
X(il,n,hf,eq)	X		X(il.begin(),il.end(),n,hf,eq	see above
X(b)	X		Copy constructors, also copies the hash function, predicate and maximum load factor	average linear, worst quadratic (in b.size())
a = b	X&		Copy assignment, also copies the hash function, predicate and maximum load factor	average linear, worst quadratic (in b.size())
a = il	X&	value_type CopyAssignable andCopyInsertable into X	a = X(il)	see above

caution

This section is incomplete
Reason: Unfinished requirements regarding member functions

Unordered associative containers in the standard library

pub	std::unordered_set(C++11)	collection of unique keys, hashed by keys
pub	std::unordered_multiset(C++11)	collection of keys, hashed by keys
pub	std::unordered_map(C++11)	collection of key-value pairs, hashed by keys, keys are unique
pub	std::unordered_multimap(C++11)	collection of key-value pairs, hashed by keys