source: trunk/doc/src/frameworks-technologies/containers.qdoc

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/*!
    \group tools
    \title Non-GUI Classes
    \ingroup groups

    \brief Collection classes such as list, queue, stack and string, along
    with other classes that can be used without needing QApplication.

    The non-GUI classes are general-purpose collection and string classes
    that may be used independently of the GUI classes.

    In particular, these classes do not depend on QApplication at all,
    and so can be used in non-GUI programs.

*/

/*!
    \page containers.html
    \title Container Classes
    \ingroup technology-apis
    \ingroup groups
    \ingroup qt-basic-concepts
    \keyword container class
    \keyword container classes

    \brief Qt's template-based container classes.

    \tableofcontents

    \section1 Introduction

    The Qt library provides a set of general purpose template-based
    container classes. These classes can be used to store items of a
    specified type. For example, if you need a resizable array of
    \l{QString}s, use QVector<QString>.

    These container classes are designed to be lighter, safer, and
    easier to use than the STL containers. If you are unfamiliar with
    the STL, or prefer to do things the "Qt way", you can use these
    classes instead of the STL classes.

    The container classes are \l{implicitly shared}, they are
    \l{reentrant}, and they are optimized for speed, low memory
    consumption, and minimal inline code expansion, resulting in
    smaller executables. In addition, they are \l{thread-safe}
    in situations where they are used as read-only containers
    by all threads used to access them.

    For traversing the items stored in a container, you can use one
    of two types of iterators: \l{Java-style iterators} and
    \l{STL-style iterators}. The Java-style iterators are easier to
    use and provide high-level functionality, whereas the STL-style
    iterators are slightly more efficient and can be used together
    with Qt's and STL's \l{generic algorithms}.

    Qt also offers a \l{foreach} keyword that make it very
    easy to iterate over all the items stored in a container.

    \section1 The Container Classes

    Qt provides the following sequential containers: QList,
    QLinkedList, QVector, QStack, and QQueue. For most
    applications, QList is the best type to use. Although it is
    implemented as an array-list, it provides very fast prepends and
    appends. If you really need a linked-list, use QLinkedList; if you
    want your items to occupy consecutive memory locations, use QVector.
    QStack and QQueue are convenience classes that provide LIFO and
    FIFO semantics.

    Qt also provides these associative containers: QMap,
    QMultiMap, QHash, QMultiHash, and QSet. The "Multi" containers
    conveniently support multiple values associated with a single
    key. The "Hash" containers provide faster lookup by using a hash
    function instead of a binary search on a sorted set.

    As special cases, the QCache and QContiguousCache classes provide
    efficient hash-lookup of objects in a limited cache storage.

    \table
    \header \o Class \o Summary

    \row \o \l{QList}<T>
    \o This is by far the most commonly used container class. It
    stores a list of values of a given type (T) that can be accessed
    by index. Internally, the QList is implemented using an array,
    ensuring that index-based access is very fast.

    Items can be added at either end of the list using
    QList::append() and QList::prepend(), or they can be inserted in
    the middle using QList::insert(). More than any other container
    class, QList is highly optimized to expand to as little code as
    possible in the executable. QStringList inherits from
    QList<QString>.

    \row \o \l{QLinkedList}<T>
    \o This is similar to QList, except that it uses
    iterators rather than integer indexes to access items. It also
    provides better performance than QList when inserting in the
    middle of a huge list, and it has nicer iterator semantics.
    (Iterators pointing to an item in a QLinkedList remain valid as
    long as the item exists, whereas iterators to a QList can become
    invalid after any insertion or removal.)

    \row \o \l{QVector}<T>
    \o This stores an array of values of a given type at adjacent
    positions in memory. Inserting at the front or in the middle of
    a vector can be quite slow, because it can lead to large numbers
    of items having to be moved by one position in memory.

    \row \o \l{QStack}<T>
    \o This is a convenience subclass of QVector that provides
    "last in, first out" (LIFO) semantics. It adds the following
    functions to those already present in QVector:
    \l{QStack::push()}{push()}, \l{QStack::pop()}{pop()},
    and \l{QStack::top()}{top()}.

    \row \o \l{QQueue}<T>
    \o This is a convenience subclass of QList that provides
    "first in, first out" (FIFO) semantics. It adds the following
    functions to those already present in QList:
    \l{QQueue::enqueue()}{enqueue()},
    \l{QQueue::dequeue()}{dequeue()}, and \l{QQueue::head()}{head()}.

    \row \o \l{QSet}<T>
    \o This provides a single-valued mathematical set with fast
    lookups.

    \row \o \l{QMap}<Key, T>
    \o This provides a dictionary (associative array) that maps keys
    of type Key to values of type T. Normally each key is associated
    with a single value. QMap stores its data in Key order; if order
    doesn't matter QHash is a faster alternative.

    \row \o \l{QMultiMap}<Key, T>
    \o This is a convenience subclass of QMap that provides a nice
    interface for multi-valued maps, i.e. maps where one key can be
    associated with multiple values.

    \row \o \l{QHash}<Key, T>
    \o This has almost the same API as QMap, but provides
    significantly faster lookups. QHash stores its data in an
    arbitrary order.

    \row \o \l{QMultiHash}<Key, T>
    \o This is a convenience subclass of QHash that
    provides a nice interface for multi-valued hashes.

    \endtable

    Containers can be nested. For example, it is perfectly possible
    to use a QMap<QString, QList<int> >, where the key type is
    QString and the value type QList<int>. The only pitfall is that
    you must insert a space between the closing angle brackets (>);
    otherwise the C++ compiler will misinterpret the two >'s as a
    right-shift operator (>>) and report a syntax error.

    The containers are defined in individual header files with the
    same name as the container (e.g., \c <QLinkedList>). For
    convenience, the containers are forward declared in \c
    <QtContainerFwd>.

    \keyword assignable data type
    \keyword assignable data types

    The values stored in the various containers can be of any
    \e{assignable data type}. To qualify, a type must provide a
    default constructor, a copy constructor, and an assignment
    operator. This covers most data types you are likely to want to
    store in a container, including basic types such as \c int and \c
    double, pointer types, and Qt data types such as QString, QDate,
    and QTime, but it doesn't cover QObject or any QObject subclass
    (QWidget, QDialog, QTimer, etc.). If you attempt to instantiate a
    QList<QWidget>, the compiler will complain that QWidget's copy
    constructor and assignment operators are disabled. If you want to
    store these kinds of objects in a container, store them as
    pointers, for example as QList<QWidget *>.

    Here's an example custom data type that meets the requirement of
    an assignable data type:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 0

    If we don't provide a copy constructor or an assignment operator,
    C++ provides a default implementation that performs a
    member-by-member copy. In the example above, that would have been
    sufficient. Also, if you don't provide any constructors, C++
    provides a default constructor that initializes its member using
    default constructors. Although it doesn't provide any
    explicit constructors or assignment operator, the following data
    type can be stored in a container:

    \snippet doc/src/snippets/streaming/main.cpp 0

    Some containers have additional requirements for the data types
    they can store. For example, the Key type of a QMap<Key, T> must
    provide \c operator<(). Such special requirements are documented
    in a class's detailed description. In some cases, specific
    functions have special requirements; these are described on a
    per-function basis. The compiler will always emit an error if a
    requirement isn't met.

    Qt's containers provide operator<<() and operator>>() so that they
    can easily be read and written using a QDataStream. This means
    that the data types stored in the container must also support
    operator<<() and operator>>(). Providing such support is
    straightforward; here's how we could do it for the Movie struct
    above:

    \snippet doc/src/snippets/streaming/main.cpp 1
    \codeline
    \snippet doc/src/snippets/streaming/main.cpp 2

    \keyword default-constructed values

    The documentation of certain container class functions refer to
    \e{default-constructed values}; for example, QVector
    automatically initializes its items with default-constructed
    values, and QMap::value() returns a default-constructed value if
    the specified key isn't in the map. For most value types, this
    simply means that a value is created using the default
    constructor (e.g. an empty string for QString). But for primitive
    types like \c{int} and \c{double}, as well as for pointer types,
    the C++ language doesn't specify any initialization; in those
    cases, Qt's containers automatically initialize the value to 0.

    \section1 The Iterator Classes

    Iterators provide a uniform means to access items in a container.
    Qt's container classes provide two types of iterators: Java-style
    iterators and STL-style iterators. Iterators of both types are
    invalidated when the data in the container is modified or detached
    from \l{Implicit Sharing}{implicitly shared copies} due to a call
    to a non-const member function.

    \section2 Java-Style Iterators

    The Java-style iterators are new in Qt 4 and are the standard
    ones used in Qt applications. They are more convenient to use than
    the STL-style iterators, at the price of being slightly less
    efficient. Their API is modelled on Java's iterator classes.

    For each container class, there are two Java-style iterator data
    types: one that provides read-only access and one that provides
    read-write access.

    \table
    \header \o Containers                         \o Read-only iterator
                                                  \o Read-write iterator
    \row    \o QList<T>, QQueue<T>                \o QListIterator<T>
                                                  \o QMutableListIterator<T>
    \row    \o QLinkedList<T>                     \o QLinkedListIterator<T>
                                                  \o QMutableLinkedListIterator<T>
    \row    \o QVector<T>, QStack<T>              \o QVectorIterator<T>
                                                  \o QMutableVectorIterator<T>
    \row    \o QSet<T>                            \o QSetIterator<T>
                                                  \o QMutableSetIterator<T>
    \row    \o QMap<Key, T>, QMultiMap<Key, T>    \o QMapIterator<Key, T>
                                                  \o QMutableMapIterator<Key, T>
    \row    \o QHash<Key, T>, QMultiHash<Key, T>  \o QHashIterator<Key, T>
                                                  \o QMutableHashIterator<Key, T>
    \endtable

    In this discussion, we will concentrate on QList and QMap. The
    iterator types for QLinkedList, QVector, and QSet have exactly
    the same interface as QList's iterators; similarly, the iterator
    types for QHash have the same interface as QMap's iterators.

    Unlike STL-style iterators (covered \l{STL-style
    iterators}{below}), Java-style iterators point \e between items
    rather than directly \e at items. For this reason, they are
    either pointing to the very beginning of the container (before
    the first item), at the very end of the container (after the last
    item), or between two items. The diagram below shows the valid
    iterator positions as red arrows for a list containing four
    items:

    \img javaiterators1.png

    Here's a typical loop for iterating through all the elements of a
    QList<QString> in order and printing them to the console:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 1

    It works as follows: The QList to iterate over is passed to the
    QListIterator constructor. At that point, the iterator is located
    just in front of the first item in the list (before item "A").
    Then we call \l{QListIterator::hasNext()}{hasNext()} to
    check whether there is an item after the iterator. If there is, we
    call \l{QListIterator::next()}{next()} to jump over that
    item. The next() function returns the item that it jumps over. For
    a QList<QString>, that item is of type QString.

    Here's how to iterate backward in a QList:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 2

    The code is symmetric with iterating forward, except that we
    start by calling \l{QListIterator::toBack()}{toBack()}
    to move the iterator after the last item in the list.

    The diagram below illustrates the effect of calling
    \l{QListIterator::next()}{next()} and
    \l{QListIterator::previous()}{previous()} on an iterator:

    \img javaiterators2.png

    The following table summarizes the QListIterator API:

    \table
    \header \o Function \o Behavior
    \row    \o \l{QListIterator::toFront()}{toFront()}
            \o Moves the iterator to the front of the list (before the first item)
    \row    \o \l{QListIterator::toBack()}{toBack()}
            \o Moves the iterator to the back of the list (after the last item)
    \row    \o \l{QListIterator::hasNext()}{hasNext()}
            \o Returns true if the iterator isn't at the back of the list
    \row    \o \l{QListIterator::next()}{next()}
            \o Returns the next item and advances the iterator by one position
    \row    \o \l{QListIterator::peekNext()}{peekNext()}
            \o Returns the next item without moving the iterator
    \row    \o \l{QListIterator::hasPrevious()}{hasPrevious()}
            \o Returns true if the iterator isn't at the front of the list
    \row    \o \l{QListIterator::previous()}{previous()}
            \o Returns the previous item and moves the iterator back by one position
    \row    \o \l{QListIterator::peekPrevious()}{peekPrevious()}
            \o Returns the previous item without moving the iterator
    \endtable

    QListIterator provides no functions to insert or remove items
    from the list as we iterate. To accomplish this, you must use
    QMutableListIterator. Here's an example where we remove all
    odd numbers from a QList<int> using QMutableListIterator:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 3

    The next() call in the loop is made every time. It jumps over the
    next item in the list. The
    \l{QMutableListIterator::remove()}{remove()} function removes the
    last item that we jumped over from the list. The call to
    \l{QMutableListIterator::remove()}{remove()} does not invalidate
    the iterator, so it is safe to continue using it. This works just
    as well when iterating backward:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 4

    If we just want to modify the value of an existing item, we can
    use \l{QMutableListIterator::setValue()}{setValue()}. In the code
    below, we replace any value larger than 128 with 128:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 5

    Just like \l{QMutableListIterator::remove()}{remove()},
    \l{QMutableListIterator::setValue()}{setValue()} operates on the
    last item that we jumped over. If we iterate forward, this is the
    item just before the iterator; if we iterate backward, this is
    the item just after the iterator.

    The \l{QMutableListIterator::next()}{next()} function returns a
    non-const reference to the item in the list. For simple
    operations, we don't even need
    \l{QMutableListIterator::setValue()}{setValue()}:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 6

    As mentioned above, QLinkedList's, QVector's, and QSet's iterator
    classes have exactly the same API as QList's. We will now turn to
    QMapIterator, which is somewhat different because it iterates on
    (key, value) pairs.

    Like QListIterator, QMapIterator provides 
    \l{QMapIterator::toFront()}{toFront()}, 
    \l{QMapIterator::toBack()}{toBack()}, 
    \l{QMapIterator::hasNext()}{hasNext()}, 
    \l{QMapIterator::next()}{next()}, 
    \l{QMapIterator::peekNext()}{peekNext()}, 
    \l{QMapIterator::hasPrevious()}{hasPrevious()}, 
    \l{QMapIterator::previous()}{previous()}, and
    \l{QMapIterator::peekPrevious()}{peekPrevious()}. The key and
    value components are extracted by calling key() and value() on
    the object returned by next(), peekNext(), previous(), or
    peekPrevious().

    The following example removes all (capital, country) pairs where
    the capital's name ends with "City":

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 7

    QMapIterator also provides a key() and a value() function that
    operate directly on the iterator and that return the key and
    value of the last item that the iterator jumped above. For
    example, the following code copies the contents of a QMap into a
    QHash:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 8

    If we want to iterate through all the items with the same
    value, we can use \l{QMapIterator::findNext()}{findNext()}
    or \l{QMapIterator::findPrevious()}{findPrevious()}.
    Here's an example where we remove all the items with a particular
    value:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 9

    \section2 STL-Style Iterators

    STL-style iterators have been available since the release of Qt
    2.0. They are compatible with Qt's and STL's \l{generic
    algorithms} and are optimized for speed.

    For each container class, there are two STL-style iterator types:
    one that provides read-only access and one that provides
    read-write access. Read-only iterators should be used wherever
    possible because they are faster than read-write iterators.

    \table
    \header \o Containers                         \o Read-only iterator
                                                  \o Read-write iterator
    \row    \o QList<T>, QQueue<T>                \o QList<T>::const_iterator
                                                  \o QList<T>::iterator
    \row    \o QLinkedList<T>                     \o QLinkedList<T>::const_iterator
                                                  \o QLinkedList<T>::iterator
    \row    \o QVector<T>, QStack<T>              \o QVector<T>::const_iterator
                                                  \o QVector<T>::iterator
    \row    \o QSet<T>                            \o QSet<T>::const_iterator
                                                  \o QSet<T>::iterator
    \row    \o QMap<Key, T>, QMultiMap<Key, T>    \o QMap<Key, T>::const_iterator
                                                  \o QMap<Key, T>::iterator
    \row    \o QHash<Key, T>, QMultiHash<Key, T>  \o QHash<Key, T>::const_iterator
                                                  \o QHash<Key, T>::iterator
    \endtable

    The API of the STL iterators is modelled on pointers in an array.
    For example, the \c ++ operator advances the iterator to the next
    item, and the \c * operator returns the item that the iterator
    points to. In fact, for QVector and QStack, which store their
    items at adjacent memory positions, the
    \l{QVector::iterator}{iterator} type is just a typedef for \c{T *},
    and the \l{QVector::iterator}{const_iterator} type is
    just a typedef for \c{const T *}.

    In this discussion, we will concentrate on QList and QMap. The
    iterator types for QLinkedList, QVector, and QSet have exactly
    the same interface as QList's iterators; similarly, the iterator
    types for QHash have the same interface as QMap's iterators.

    Here's a typical loop for iterating through all the elements of a
    QList<QString> in order and converting them to lowercase:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 10

    Unlike \l{Java-style iterators}, STL-style iterators point
    directly at items. The begin() function of a container returns an
    iterator that points to the first item in the container. The
    end() function of a container returns an iterator to the
    imaginary item one position past the last item in the container.
    end() marks an invalid position; it must never be dereferenced.
    It is typically used in a loop's break condition. If the list is
    empty, begin() equals end(), so we never execute the loop.

    The diagram below shows the valid iterator positions as red
    arrows for a vector containing four items:

    \img stliterators1.png

    Iterating backward with an STL-style iterator requires us to
    decrement the iterator \e before we access the item. This
    requires a \c while loop:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 11

    In the code snippets so far, we used the unary \c * operator to
    retrieve the item (of type QString) stored at a certain iterator
    position, and we then called QString::toLower() on it. Most C++
    compilers also allow us to write \c{i->toLower()}, but some
    don't.

    For read-only access, you can use const_iterator, constBegin(),
    and constEnd(). For example:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 12

    The following table summarizes the STL-style iterators' API:

    \table
    \header \o Expression \o Behavior
    \row    \o \c{*i}     \o Returns the current item
    \row    \o \c{++i}    \o Advances the iterator to the next item
    \row    \o \c{i += n} \o Advances the iterator by \c n items
    \row    \o \c{--i}    \o Moves the iterator back by one item
    \row    \o \c{i -= n} \o Moves the iterator back by \c n items
    \row    \o \c{i - j}  \o Returns the number of items between iterators \c i and \c j
    \endtable

    The \c{++} and \c{--} operators are available both as prefix
    (\c{++i}, \c{--i}) and postfix (\c{i++}, \c{i--}) operators. The
    prefix versions modify the iterators and return a reference to
    the modified iterator; the postfix versions take a copy of the
    iterator before they modify it, and return that copy. In
    expressions where the return value is ignored, we recommend that
    you use the prefix operators (\c{++i}, \c{--i}), as these are
    slightly faster.

    For non-const iterator types, the return value of the unary \c{*}
    operator can be used on the left side of the assignment operator.

    For QMap and QHash, the \c{*} operator returns the value
    component of an item. If you want to retrieve the key, call key()
    on the iterator. For symmetry, the iterator types also provide a
    value() function to retrieve the value. For example, here's how
    we would print all items in a QMap to the console:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 13

    Thanks to \l{implicit sharing}, it is very inexpensive for a
    function to return a container per value. The Qt API contains
    dozens of functions that return a QList or QStringList per value
    (e.g., QSplitter::sizes()). If you want to iterate over these
    using an STL iterator, you should always take a copy of the
    container and iterate over the copy. For example:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 14

    This problem doesn't occur with functions that return a const or
    non-const reference to a container.

    \l{Implicit sharing} has another consequence on STL-style
    iterators: You must not take a copy of a container while
    non-const iterators are active on that container. Java-style
    iterators don't suffer from that limitation.

    \keyword foreach
    \section1 The foreach Keyword

    If you just want to iterate over all the items in a container
    in order, you can use Qt's \c foreach keyword. The keyword is a
    Qt-specific addition to the C++ language, and is implemented
    using the preprocessor.

    Its syntax is: \c foreach (\e variable, \e container) \e
    statement. For example, here's how to use \c foreach to iterate
    over a QLinkedList<QString>:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 15

    The \c foreach code is significantly shorter than the equivalent
    code that uses iterators:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 16

    Unless the data type contains a comma (e.g., \c{QPair<int,
    int>}), the variable used for iteration can be defined within the
    \c foreach statement:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 17

    And like any other C++ loop construct, you can use braces around
    the body of a \c foreach loop, and you can use \c break to leave
    the loop:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 18

    With QMap and QHash, \c foreach accesses the value component of
    the (key, value) pairs. If you want to iterate over both the keys
    and the values, you can use iterators (which are fastest), or you
    can write code like this:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 19

    For a multi-valued map:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 20

    Qt automatically takes a copy of the container when it enters a
    \c foreach loop. If you modify the container as you are
    iterating, that won't affect the loop. (If you do not modify the
    container, the copy still takes place, but thanks to \l{implicit
    sharing} copying a container is very fast.)

    Since foreach creates a copy of the container, using a non-const
    reference for the variable does not allow you to modify the original
    container. It only affects the copy, which is probably not what you
    want.

    In addition to \c foreach, Qt also provides a \c forever
    pseudo-keyword for infinite loops:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 21

    If you're worried about namespace pollution, you can disable
    these macros by adding the following line to your \c .pro file:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 22

    \section1 Other Container-Like Classes

    Qt includes three template classes that resemble containers in
    some respects. These classes don't provide iterators and cannot
    be used with the \c foreach keyword.

    \list
    \o QVarLengthArray<T, Prealloc> provides a low-level
       variable-length array. It can be used instead of QVector in
       places where speed is particularly important.

    \o QCache<Key, T> provides a cache to store objects of a certain
       type T associated with keys of type Key.

    \o QContiguousCache<T> provides an efficient way of caching data
    that is typically accessed in a contiguous way.

    \o QPair<T1, T2> stores a pair of elements.
    \endlist

    Additional non-template types that compete with Qt's template
    containers are QBitArray, QByteArray, QString, and QStringList.

    \section1 Algorithmic Complexity

    Algorithmic complexity is concerned about how fast (or slow) each
    function is as the number of items in the container grow. For
    example, inserting an item in the middle of a QLinkedList is an
    extremely fast operation, irrespective of the number of items
    stored in the QLinkedList. On the other hand, inserting an item
    in the middle of a QVector is potentially very expensive if the
    QVector contains many items, since half of the items must be
    moved one position in memory.

    To describe algorithmic complexity, we use the following
    terminology, based on the "big Oh" notation:

    \keyword constant time
    \keyword logarithmic time
    \keyword linear time
    \keyword linear-logarithmic time
    \keyword quadratic time

    \list
    \o \bold{Constant time:} O(1). A function is said to run in constant
       time if it requires the same amount of time no matter how many
       items are present in the container. One example is
       QLinkedList::insert().

    \o \bold{Logarithmic time:} O(log \e n). A function that runs in
       logarithmic time is a function whose running time is
       proportional to the logarithm of the number of items in the
       container. One example is qBinaryFind().

    \o \bold{Linear time:} O(\e n). A function that runs in linear time
       will execute in a time directly proportional to the number of
       items stored in the container. One example is
       QVector::insert().

    \o \bold{Linear-logarithmic time:} O(\e{n} log \e n). A function
       that runs in linear-logarithmic time is asymptotically slower
       than a linear-time function, but faster than a quadratic-time
       function.

    \o \bold{Quadratic time:} O(\e{n}\unicode{178}). A quadratic-time function
       executes in a time that is proportional to the square of the
       number of items stored in the container.
    \endlist

    The following table summarizes the algorithmic complexity of Qt's
    sequential container classes:

    \table
    \header \o                \o Index lookup \o Insertion \o Prepending         \o Appending
    \row    \o QLinkedList<T> \o O(\e n)      \o O(1)      \o O(1)               \o O(1)
    \row    \o QList<T>       \o O(1)         \o O(n)      \o Amort. O(1)        \o Amort. O(1)
    \row    \o QVector<T>     \o O(1)         \o O(n)      \o O(n)               \o Amort. O(1)
    \endtable

    In the table, "Amort." stands for "amortized behavior". For
    example, "Amort. O(1)" means that if you call the function
    only once, you might get O(\e n) behavior, but if you call it
    multiple times (e.g., \e n times), the average behavior will be
    O(1).

    The following table summarizes the algorithmic complexity of Qt's
    associative containers and sets:

    \table
    \header \o{1,2}          \o{2,1} Key lookup            \o{2,1} Insertion
    \header                  \o Average     \o Worst case  \o Average            \o Worst case
    \row    \o QMap<Key, T>  \o O(log \e n) \o O(log \e n) \o O(log \e n)        \o O(log \e n)
    \row    \o QMultiMap<Key, T>  \o O(log \e n) \o O(log \e n) \o O(log \e n)   \o O(log \e n)
    \row    \o QHash<Key, T> \o Amort. O(1) \o O(\e n)     \o Amort. O(1)        \o O(\e n)
    \row    \o QSet<Key>     \o Amort. O(1) \o O(\e n)     \o Amort. O(1)        \o O(\e n)
    \endtable

    With QVector, QHash, and QSet, the performance of appending items
    is amortized O(log \e n). It can be brought down to O(1) by
    calling QVector::reserve(), QHash::reserve(), or QSet::reserve()
    with the expected number of items before you insert the items.
    The next section discusses this topic in more depth.

    \section1 Growth Strategies

    QVector<T>, QString, and QByteArray store their items
    contiguously in memory; QList<T> maintains an array of pointers
    to the items it stores to provide fast index-based access (unless
    T is a pointer type or a basic type of the size of a pointer, in
    which case the value itself is stored in the array); QHash<Key,
    T> keeps a hash table whose size is proportional to the number
    of items in the hash. To avoid reallocating the data every single
    time an item is added at the end of the container, these classes
    typically allocate more memory than necessary.

    Consider the following code, which builds a QString from another
    QString:

    \snippet doc/src/snippets/code/doc_src_containers.qdoc 23

    We build the string \c out dynamically by appending one character
    to it at a time. Let's assume that we append 15000 characters to
    the QString string. Then the following 18 reallocations (out of a
    possible 15000) occur when QString runs out of space: 4, 8, 12,
    16, 20, 52, 116, 244, 500, 1012, 2036, 4084, 6132, 8180, 10228,
    12276, 14324, 16372. At the end, the QString has 16372 Unicode
    characters allocated, 15000 of which are occupied.

    The values above may seem a bit strange, but here are the guiding
    principles:
    \list
    \o QString allocates 4 characters at a time until it reaches size 20.
    \o From 20 to 4084, it advances by doubling the size each time.
       More precisely, it advances to the next power of two, minus
       12. (Some memory allocators perform worst when requested exact
       powers of two, because they use a few bytes per block for
       book-keeping.)
    \o From 4084 on, it advances by blocks of 2048 characters (4096
       bytes). This makes sense because modern operating systems
       don't copy the entire data when reallocating a buffer; the
       physical memory pages are simply reordered, and only the data
       on the first and last pages actually needs to be copied.
    \endlist

    QByteArray and QList<T> use more or less the same algorithm as
    QString.

    QVector<T> also uses that algorithm for data types that can be
    moved around in memory using memcpy() (including the basic C++
    types, the pointer types, and Qt's \l{shared classes}) but uses a
    different algorithm for data types that can only be moved by
    calling the copy constructor and a destructor. Since the cost of
    reallocating is higher in that case, QVector<T> reduces the
    number of reallocations by always doubling the memory when
    running out of space.

    QHash<Key, T> is a totally different case. QHash's internal hash
    table grows by powers of two, and each time it grows, the items
    are relocated in a new bucket, computed as qHash(\e key) %
    QHash::capacity() (the number of buckets). This remark applies to
    QSet<T> and QCache<Key, T> as well.

    For most applications, the default growing algorithm provided by
    Qt does the trick. If you need more control, QVector<T>,
    QHash<Key, T>, QSet<T>, QString, and QByteArray provide a trio of
    functions that allow you to check and specify how much memory to
    use to store the items:

    \list
    \o \l{QString::capacity()}{capacity()} returns the
       number of items for which memory is allocated (for QHash and
       QSet, the number of buckets in the hash table).
    \o \l{QString::reserve()}{reserve}(\e size) explicitly
       preallocates memory for \e size items.
    \o \l{QString::squeeze()}{squeeze()} frees any memory
       not required to store the items.
    \endlist

    If you know approximately how many items you will store in a
    container, you can start by calling reserve(), and when you are
    done populating the container, you can call squeeze() to release
    the extra preallocated memory.
*/