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# Bidirectional Iterator

### Description

A Bidirectional Iterator is a Forward Iterator that provides a way to obtain an iterator to the previous element in a sequence.

### Refinement of

Forward Iterator

### Definitions

- a bidirectional iterator `i` is decrementable if there is a "previous" iterator, that is, if `prior<i>::type` expression is well-defined; iterators pointing to the first element of the sequence are not decrementable.

### Expression requirements

In addition to the requirements defined in Forward Iterator, the following requirements must be met.

Expression | Type | Complexity
--- | --- | ---
`next<i>::type` | Bidirectional Iterator | Amortized constant time
`prior<i>::type` | Bidirectional Iterator | Amortized constant time
`i::category` | Integral Constant, convertible to `bidirectional_iterator_tag` | Constant time

### Expression semantics

    typedef prior<i>::type j;

Precondition: | `i` is decrementable
Semantics: | `j` is an iterator pointing to the previous element of the sequence
Postcondition: | `j` is dereferenceable and incrementable

### Invariants

For any bidirectional iterators `i` and `j` the following invariants always hold:

- If `i` is incrementable, then `prior< next<i>::type >::type` is a null operation; similarly, if `i` is decrementable, `next< prior<i>::type >::type` is a null operation.

### See also

Iterators, Forward Iterator, Random Access Iterator, Bidirectional Sequence, `prior`