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C++ named requirements: RandomAccessIterator

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.

The type It satisfies RandomAccessIterator if.

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.