# C++ concepts: RandomAccessIterator

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A `RandomAccessIterator` is a `BidirectionalIterator` that can be moved to point to any element in constant time.

A pointer to an element of an array satisfies all requirements of `RandomAccessIterator`

### Requirements

The type `It` satisfies `RandomAccessIterator` if

- The type `It` satisfies `BidirectionalIterator`

And, given

- `value_type`, the type denoted by std::iterator_traits<It>::value_type
- `difference_type`, the type denoted by std::iterator_traits<It>::difference_type
- `reference`, the type denoted by std::iterator_traits<It>::reference
- `i`, `a`, `b`, objects of type `It` or `const It`
- `r`, a value of type `It&`
- `n`, an integer of type `difference_type`

The following expressions must be valid and have their specified effects

Expression | Return type | Operational semantics | Notes
--- | --- | --- | ---

r += n

It&

difference_type m = n;

if (m >= 0) while (m--) ++r;
else while (m++) --r;
return r;

- `n` can be both positive or negative
- The complexity is constant (that is, the implementation cannot actually execute the while loop shown in operational semantics)

a + n

n + a

It

It temp = a;

return temp += n;

- `n` can be both positive or negative
- a + n == n + a

r -= n | It& | return r += -n; | The absolute value of `n` must be within the range of representable values of `difference_type`. |
i - n | It | It temp = i; return temp -= n; |

b - a

`difference_type`

return n;

Precondition:

- there exists a value `n` of type `difference_type` such that a+n==b

Postcondition:

- b == a + (b - a).

i[n] | convertible to `reference` | *(i + n) |

a < b

contextually convertible to bool

b - a > 0

Strict total ordering relation:

- `!(a < a)`
- if `a < b` then `!(b < a)`
- if `a < b` and `b < c` then `a < c`
- `a < b` or `b < a` or `a == b`
  (exactly one of the expressions is true)

a > b | contextually convertible to bool | b < a | Total ordering relation opposite to a < b
a >= b | contextually convertible to bool | !(a < b) |
a <= b | contextually convertible to bool | !(a > b) |

The above rules imply that `RandomAccessIterator` also implements `LessThanComparable`.

A `mutable RandomAccessIterator` is a `RandomAccessIterator` that additionally satisfies the `OutputIterator` requirements.

### See also

- Iterator library

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