Iterator Concepts

An Iterator is a restricted pointer-like object pointing into a vector or matrix container.

Indexed Bidirectional Iterator

Description

An Indexed Bidirectional Iterator is an iterator of a container that can be dereferenced, incremented, decremented and carries index information.

Refinement of

Assignable, Equality Comparable, Default Constructible.

Associated types

Value type The type of the value obtained by dereferencing a Indexed Bidirectional Iterator
Container type The type of the container a Indexed Bidirectional Iterator points into.

Notation

I A type that is a model of Indexed Bidirectional Iterator
T The value type of I
C The container type of I
it, itt, it1, it2 Objects of type I
t Object of type T
c Object of type C

Definitions

A Indexed Bidirectional Iterator may be mutable, meaning that the values referred to by objects of that type may be modified, or constant , meaning that they may not. If an iterator type is mutable, this implies that its value type is a model of Assignable; the converse, though, is not necessarily true.

A Indexed Bidirectional Iterator may have a singular value, meaning that the results of most operations, including comparison for equality, are undefined. The only operation that is guaranteed to be supported is assigning a nonsingular iterator to a singular iterator.

A Indexed Bidirectional Iterator may have a dereferenceable value, meaning that dereferencing it yields a well-defined value. Dereferenceable iterators are always nonsingular, but the converse is not true.

An Indexed Bidirectional Iterator is past-the-end if it points beyond the last element of a container. Past-the-end values are nonsingular and nondereferenceable.

Valid expressions

In addition to the expressions defined for Assignable, Equality Comparable and Default Constructible, the following expressions must be valid.

Name Expression Type requirements Return type
Default constructor I it    
Dereference *it   Convertible to T.
Dereference assignment *it = t I is mutable.  
Member access it->m T is a type for which t.m is defined.  
Preincrement ++ it   I &
Postincrement it ++   I
Predecrement -- it   I &
Postdecrement it --   I
Index it.index ()   C::size_type

Expression Semantics

Semantics of an expression is defined only where it differs from, or is not defined in, Assignable, Equality Comparable and Default Constructible.

Name Expression Precondition Semantics Postcondition
Default constructor I it     it is singular.
Dereference *it it is dereferenceable.    
Dereference assignment *it = t Same as for *it.   *it is a copy of t.
Member access it->m it is dereferenceable. Equivalent to (*it).m  
Preincrement ++ it it is dereferenceable. it is modified to point to the next element. it is dereferenceable or past-the-end.
&it == &++ it.
If it1 == it2,
then ++ it1 == ++ it2.
Postincrement it ++ Same as for ++ it. Equivalent to
{
 I itt = it;
 ++ it;
 return itt;
}		 it is dereferenceable or past-the-end.
Predecrement -- it it is dereferenceable or past-the-end.
There exists a dereferenceable iterator itt such that it == ++ itt.		 it is modified to point to the previous element. it is dereferenceable.
&it = &-- it.
If it1 == it2,
then -- it1 == -- it2.
If it2 is dereferenceable and it1 == ++it2,
then --it1 == it2.
Postdecrement it -- Same as for -- it. Equivalent to
{
 I itt = it;
 -- it;
 return itt;
}		 it is dereferenceable. 
Index it.index () it is dereferenceable. it.index () >= 0
and
it.index () < it ().size ()		 If it1 == it2,
then it1.index () == it2.index ().
If it1 == it2,
then it1.index () < (++ it2).index ().
If it1 == it2,
then it1.index () > (-- it2).index ().

Complexity guarantees

The complexity of operations on indexed bidirectional iterators is guaranteed to be amortized constant time.

Invariants

Identity it1 == it2 if and only if &*it1 == &*it2.
Symmetry of increment and decrement If it is dereferenceable, then ++ it; --it; is a null operation. Similarly, -- it; ++ it; is a null operation.
Relation between iterator index and container element operator If it is dereferenceable, *it == it () (it.index ()).

Models

Indexed Random Access Iterator

Description

An Indexed Random Access Iterator is an iterator of a container that can be dereferenced, moved forward, moved backward and carries index information.

Refinement of

LessThanComparable, Indexed Bidirectional Iterator .

Associated types

Value type The type of the value obtained by dereferencing a Indexed Random Access Iterator
Container type The type of the container a Indexed Random Access Iterator points into.

Notation

I A type that is a model of Indexed Random Access Iterator
T The value type of I
C The container type of I
it, itt, it1, it2 Objects of type I
t Object of type T
n Object of type C::difference_type

Definitions

An Indexed Random Access Iterator it1 is reachable from an Indexed Random Access Iterator it2 if, after applying operator ++ to it2 a finite number of times, it1 == it2.

Valid expressions

In addition to the expressions defined for Indexed Bidirectional Iterator , the following expressions must be valid.

Name Expression Type requirements Return type
Forward motion it += n   I &
Iterator addition it + n   I
Backward motion i -= n   I &
Iterator subtraction it - n   I 
Difference it1 - it2   C::difference_type
Element operator it [n]   Convertible to T.
Element assignment it [n] = t I is mutable Convertible to T.

Expression Semantics

Semantics of an expression is defined only where it differs from, or is not defined in, Indexed Bidirectional Iterator .

Name Expression Precondition Semantics Postcondition
Forward motion it += n Including it itself, there must be n dereferenceable or past-the-end iterators following or preceding it, depending on whether n is positive or negative. If n > 0, equivalent to executing ++ it n times. If n < 0, equivalent to executing -- it n times. If n == 0, this is a null operation. it is dereferenceable or past-the-end.
Iterator addition it + n Same as for i += n. Equivalent to
{
 I itt = it;
 return itt += n;
}		 Result is dereferenceable or past-the-end.
Backward motion it -= n Including it itself, there must be n dereferenceable or past-the-end iterators preceding or following it, depending on whether n is positive or negative. Equivalent to it += (-n). it is dereferenceable or past-the-end.
Iterator subtraction it - n Same as for i -= n. Equivalent to
{
 I itt = it;
 return itt -= n;
}		 Result is dereferenceable or past-the-end.
Difference it1 - it2 Either it1 is reachable from it2 or it2 is reachable from it1, or both. Returns a number n such that it1 == it2 + n  
Element operator it [n] it + n exists and is dereferenceable. Equivalent to *(it + n)  
Element assignment i[n] = t Same as for it [n]. Equivalent to *(it + n) = t  

Complexity guarantees

The complexity of operations on indexed random access iterators is guaranteed to be amortized constant time.

Invariants

Symmetry of addition and subtraction If it + n is well-defined, then it += n; it -= n; and (it + n) - n are null operations. Similarly, if it - n is well-defined, then it -= n; it += n; and (it - n) + n are null operations.
Relation between distance and addition If it1 - it2 is well-defined, then it1 == it2 + (it1 - it2).
Reachability and distance If it1 is reachable from it2, then it1 - it2 >= 0.

Models

Indexed Bidirectional Column/Row Iterator

Description

An Indexed Bidirectional Column/Row Iterator is an iterator of a container that can be dereferenced, incremented, decremented and carries index information.

Refinement of

Assignable, Equality Comparable, Default Constructible.

Associated types

Value type The type of the value obtained by dereferencing a Indexed Bidirectional Column/Row Iterator
Container type The type of the container a Indexed Bidirectional Column/Row Iterator points into.

Notation

I1 A type that is a model of Indexed Bidirectional Column/Row Iterator
I2 A type that is a model of Indexed Bidirectional Row/Column Iterator
T The value type of I1 and I2
C The container type of I1 and I2
it1, it1t, it11, it12 Objects of type I1
it2, it2t Objects of type I2
t Object of type T
c Object of type C

Definitions

Valid expressions

In addition to the expressions defined for Assignable, Equality Comparable and Default Constructible, the following expressions must be valid.

Name Expression Type requirements Return type
Default constructor I1 it    
Dereference *it   Convertible to T.
Dereference assignment *it = t I1 is mutable.  
Member access it->m T is a type for which t.m is defined.  
Preincrement ++ it   I1 &
Postincrement it ++   I1
Predecrement -- it   I1 &
Postdecrement it --   I1
Row Index it.index1 ()   C::size_type
Column Index it.index2 ()   C::size_type
Row/Column Begin it.begin ()   I2
Row/Column End it.end ()   I2
Reverse Row/Column Begin it.rbegin ()   reverse_iterator<I2>
Reverse Row/Column End it.rend ()   reverse_iterator<I2>

Expression Semantics

Semantics of an expression is defined only where it differs from, or is not defined in, Assignable, Equality Comparable and Default Constructible.

Name Expression Precondition Semantics Postcondition
Default constructor I1 it     it is singular.
Dereference *it it is dereferenceable.    
Dereference assignment *it = t Same as for *it.   *it is a copy of t.
Member access it->m it is dereferenceable. Equivalent to (*it).m  
Preincrement ++ it it is dereferenceable. it is modified to point to the next element of the column/row, i.e. for column iterators holds
it.index1 () < (++ it).index1 () and
it.index2 () == (++ it).index2 (),
for row iterators holds
it.index1 () == (++ it).index1 () and
it.index2 () < (++ it).index2 ().
 it is dereferenceable or past-the-end.
&it == &++ it.
If it1 == it2,
then ++ it1 == ++ it2.
Postincrement it ++ Same as for ++ it. Equivalent to
{
 I1 itt = it;
 ++ it;
 return itt;
}		 it is dereferenceable or past-the-end.
Predecrement -- it it is dereferenceable or past-the-end.
There exists a dereferenceable iterator itt such that it == ++ itt.		 it is modified to point to the previous  element of the column/row, i.e. for column iterators holds
it.index1 () > (-- it).index1 () and
it.index2 () == (-- it).index2 (),
for row iterators holds
it.index1 () == (-- it).index1 () and
it.index2 () > (-- it).index2 ().		 it is dereferenceable.
&it = &-- it.
If it1 == it2,
then -- it1 == -- it2.
Postdecrement it -- Same as for -- it. Equivalent to
{
 I1 itt = it;
 -- it;
 return itt;
}		 it is dereferenceable. 
Row Index it.index1 () If it is a Row iterator then it must be dereferenceable. it.index1 () >= 0 and
it.index1 () < it () .size1 ()		 If it1 == it2,
then it1.index1 () == 12.index1 ().
If it1, it2 are Row Iterators with it1 == it2,
then it1.index1 () < (++ it2).index1 ().
and it1.index1 () > (-- it2).index1 ().
Column Index it.index2 () If it is a Column iterator then it must be dereferenceable. it.index2 () >= 0 and
it.index2 () < it () .size2 ()		 If it1 == it2,
then it1.index2 () == it2.index2 () .
If it1, it2 are Column Iterators with it1 == i12,
then it1.index2 () < (++ it2).index2 ().
end it1.index2 () > (-- it2).index2 ().
Row/Column Begin it.begin () it is dereferenceable. If it is a Column Iterator,
then it2 = it.begin () is a Row Iterator
with it2.index1 () == it.index1 ().

If it is a Row Iterator,
then it2 = it.begin () is a Column Iterator
with it2.index2 () == it.index2 ().

  
Row/Column End it.end () it is dereferenceable. If it is a Column Iterator,
then it2 = it.end () is a Row Iterator
with it2.index1 () == it.index1 ().

If it is a Row Iterator,
then it2 = it.end () is a Column Iterator
with it2.index2 () == it.index2 ().

  
Reverse Row/Column Begin it.rbegin () it is dereferenceable. Equivalent to reverse_iterator<I2> (it.end ()).  
Reverse Row/Column End it.rend () it is dereferenceable. Equivalent to reverse_iterator<I2> (it.begin ()).  

Complexity guarantees

The complexity of operations on indexed bidirectional column/row iterators is guaranteed to be logarithmic depending on the size of the container. The complexity of one iterator (depending on the storage layout) can be lifted to be amortized constant time. The complexity of the other iterator (depending on the storage layout and the container) can be lifted to be amortized constant time for the first row/first column respectively.

Invariants

Identity it1 == it2 if and only if &*it1 == &*it2.
Symmetry of increment and decrement If it is dereferenceable, then ++ it; --it; is a null operation. Similarly, -- it; ++ it; is a null operation.
Relation between iterator index and container element operator If it is dereferenceable, *it == it () (it.index1 (), it.index2 ())
Relation between iterator column/row begin and iterator index If it is a Column Iterator and it2 = it.begin () then it2.index2 () < it2t.index2 () for all it2t with it2t () == it2 () and it2t ().index1 () == it2 ().index1 ().

If it is a Row Iterator and it2 = it.begin () then it2.index1 () < it2t.index1 () for all it2t with it2t () == it2 () and it2t ().index2 () == it2 ().index2 ().
Relation between iterator column/row end and iterator index If it is a Column Iterator and it2 = it.end () then it2.index2 () > it2t.index2 () for all it2t with it2t () == it2 () and it2t ().index1 () == it2 ().index1 ().

If it is a Row Iterator and it2 = it.end () then it2.index1 () > it2t.index1 () for all it2t with it2t () == it2 () and it2t ().index2 () == it2 ().index2 ().

Models

Indexed Random Access Column/Row Iterator

Description

An Indexed Random Access Column/Row Iterator is an iterator of a container that can be dereferenced, incremented, decremented and carries index information.

Refinement of

Indexed Bidirectional Column/Row Iterator .

Associated types

Value type The type of the value obtained by dereferencing a Indexed Random Access Column/Row Iterator
Container type The type of the container a Indexed Random Access Column/Row Iterator points into.

Notation

I A type that is a model of Indexed Random Access Column/Row Iterator
T The value type of I
C The container type of I
it, itt, it1, it2 Objects of type I
t Object of type T
c Object of type C

Definitions

Valid expressions

In addition to the expressions defined for Indexed Bidirectional Column/Row Iterator , the following expressions must be valid.

Name Expression Type requirements Return type
Forward motion it += n   I &
Iterator addition it + n   I
Backward motion i -= n   I &
Iterator subtraction it - n   I 
Difference it1 - it2   C::difference_type
Element operator it [n]   Convertible to T.
Element assignment it [n] = t I is mutable Convertible to T.

Expression Semantics

Semantics of an expression is defined only where it differs from, or is not defined in, Indexed Bidirectional Column/Row Iterator .

Name Expression Precondition Semantics Postcondition
Forward motion it += n Including it itself, there must be n dereferenceable or past-the-end iterators following or preceding it, depending on whether n is positive or negative. If n > 0, equivalent to executing ++ it n times. If n < 0, equivalent to executing -- it n times. If n == 0, this is a null operation. it is dereferenceable or past-the-end.
Iterator addition it + n Same as for i += n. Equivalent to
{
 I itt = it;
 return itt += n;
}		 Result is dereferenceable or past-the-end.
Backward motion it -= n Including it itself, there must be n dereferenceable or past-the-end iterators preceding or following it, depending on whether n is positive or negative. Equivalent to it += (-n). it is dereferenceable or past-the-end.
Iterator subtraction it - n Same as for i -= n. Equivalent to
{
 I itt = it;
 return itt -= n;
}		 Result is dereferenceable or past-the-end.
Difference it1 - it2 Either it1 is reachable from it2 or it2 is reachable from it1, or both. Returns a number n such that it1 == it2 + n  
Element operator it [n] it + n exists and is dereferenceable. Equivalent to *(it + n)  
Element assignment i[n] = t Same as for it [n]. Equivalent to *(it + n) = t  

Complexity guarantees

The complexity of operations on indexed random access Column/Row iterators is guaranteed to be amortized constant time.

Invariants

Symmetry of addition and subtraction If it + n is well-defined, then it += n; it -= n; and (it + n) - n are null operations. Similarly, if it - n is well-defined, then it -= n; it += n; and (it - n) + n are null operations.
Relation between distance and addition If it1 - it2 is well-defined, then it1 == it2 + (it1 - it2).
Reachability and distance If it1 is reachable from it2, then it1 - it2 >= 0.

Models

Copyright (©) 2000-2002 Joerg Walter, Mathias Koch
Permission to copy, use, modify, sell and distribute this document is granted provided this copyright notice appears in all copies. This document is provided ``as is'' without express or implied warranty, and with no claim as to its suitability for any purpose.