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## Comparison with Associative Containers

Table 25.4. Interface differences.

Associative Containers | Unordered Associative Containers
--- | ---
Parameterized by an ordering relation `Compare` | Parameterized by a function object `Hash` and an equivalence relation `Pred`
Keys can be compared using `key_compare` which is accessed by member function `key_comp()`, values can be compared using `value_compare` which is accessed by member function `value_comp()`. | Keys can be hashed using `hasher` which is accessed by member function `hash_function()`, and checked for equality using `key_equal` which is accessed by member function `key_eq()`. There is no function object for compared or hashing values.
Constructors have optional extra parameters for the comparison object. | Constructors have optional extra parameters for the initial minimum number of buckets, a hash function and an equality object.
Keys `k1`, `k2` are considered equivalent if `!Compare(k1, k2) && !Compare(k2, k1)` | Keys `k1`, `k2` are considered equivalent if `Pred(k1, k2)`
Member function `lower_bound(k)` and `upper_bound(k)` | No equivalent. Since the elements aren't ordered `lower_bound` and `upper_bound` would be meaningless.
`equal_range(k)` returns an empty range at the position that k would be inserted if k isn't present in the container. | `equal_range(k)` returns a range at the end of the container if k isn't present in the container. It can't return a positioned range as k could be inserted into multiple place. To find out the bucket that k would be inserted into use `bucket(k)`. But remember that an insert can cause the container to rehash - meaning that the element can be inserted into a different bucket.
`iterator`, `const_iterator` are of the bidirectional category. | `iterator`, `const_iterator` are of at least the forward category.
Iterators, pointers and references to the container's elements are never invalidated. | Iterators can be invalidated by calls to insert or rehash. Pointers and references to the container's elements are never invalidated.
Iterators iterate through the container in the order defined by the comparison object. | Iterators iterate through the container in an arbitrary order, that can change as elements are inserted. Although, equivalent elements are always adjacent.
No equivalent | Local iterators can be used to iterate through individual buckets. (I don't think that the order of local iterators and iterators are required to have any correspondence.)
Can be compared using the `==`, `!=`, `<`, `<=`, `>`, `>=` operators. | No comparison operators are defined in the standard, although implementations might extend the containers to support `==` and `!=`.
| When inserting with a hint, implementations are permitted to ignore the hint.
`erase` never throws an exception | The containers' hash or predicate function can throw exceptions from `erase`

Table 25.5. Complexity Guarantees

Operation | Associative Containers | Unordered Associative Containers
--- | --- | ---
Construction of empty container | constant | O(n) where n is the minimum number of buckets.
Construction of container from a range of N elements | O(N log N), O(N) if the range is sorted with `value_comp()` | Average case O(N), worst case O(N2)
Insert a single element | logarithmic | Average case constant, worst case linear
Insert a single element with a hint | Amortized constant if t elements inserted right after hint, logarithmic otherwise | Average case constant, worst case linear (ie. the same as a normal insert).
Inserting a range of N elements | N log(`size()`+N) | Average case O(N), worst case O(N * `size()`)
Erase by key, `k` | O(log(`size()`) + `count(k)`) | Average case: O(`count(k)`), Worst case: O(`size()`)
Erase a single element by iterator | Amortized constant | Average case: O(1), Worst case: O(`size()`)
Erase a range of N elements | O(log(`size()`) + N) | Average case: O(N), Worst case: O(`size()`)
Clearing the container | O(`size()`) | O(`size()`)
Find | logarithmic | Average case: O(1), Worst case: O(`size()`)
Count | O(log(`size()`) + `count(k)`) | Average case: O(1), Worst case: O(`size()`)
`equal_range(k)` | logarithmic | Average case: O(`count(k)`), Worst case: O(`size()`)
`lower_bound`,`upper_bound` | logarithmic | n/a