SortedListWithKey
=================

:doc:`SortedContainers<index>` is an Apache2 licensed Python sorted collections
library, written in pure-Python, and fast as C-extensions. SortedListWithKey
API documentation is detailed below. The :doc:`introduction<introduction>` is
the best way to get started.

.. currentmodule:: sortedcontainers

.. class:: SortedListWithKey(iterable=None, key=identity, load=1000)

   A :class:`SortedListWithKey` provides most of the same methods as a
   :class:`list`, but keeps the items in sorted order.  To add an element to the
   SortedListWithKey, use :ref:`add <SortedListWithKey.add>`.  To add several
   elements, use :ref:`update <SortedListWithKey.update>`.  To remove an
   element, use :ref:`discard <SortedListWithKey.discard>`, :ref:`remove
   <SortedListWithKey.remove>`, or :ref:`del L[i]
   <SortedListWithKey.__delitem__>`.

   An optional *iterable* provides an initial series of items to
   populate the :class:`SortedListWithKey`.

   An optional *key* argument defines a callable that, like the `key`
   argument to Python's `sorted` function, extracts a comparison key from
   each element. The default is the identity function.

   An optional *load* specifies the load-factor of the list. The default load
   factor of '1000' works well for lists from tens to tens of millions of
   elements.  Good practice is to use a value that is the square or cube root of
   the list size.  With billions of elements, the best load factor depends on
   your usage.  It's best to leave the load factor at the default until you
   start benchmarking. See :doc:`implementation details <implementation>` for
   more information.

   :class:`SortedListWithKey` implements the MutableSequence Abstract Base Class type.

   .. _SortedListWithKey.__contains__:
   .. method:: x in L

      Return True if and only if *x* is an element in the list.

      :rtype: :class:`bool`

   .. _SortedListWithKey.__delitem__:
   .. method:: del L[i]

      Remove the element located at index *i* from the list.

   .. method:: del L[i:j]

      Remove the elements from *i* to *j* from the list. Also note that *step*
      is supported in slice syntax.

   .. _SortedListWithKey.__eq__:
   .. method:: L == L2, L != L2, L < L2, L <= L2, L > L2, L >= L2

      Compare two lists. For full details see `Comparisons
      <http://docs.python.org/reference/expressions.html>`_ in
      the Python language reference.

      :rtype: :class:`bool`

   .. _SortedListWithKey.__getitem__:
   .. method:: L[i]

      Return the element at position *i*.

      :rtype: item

   .. method:: L[i:j]

      Return a new :class:`list` containing the elements from *i* to *j*. Also
      note that *step* is supported in slice syntax.

      :rtype: :class:`list`

   .. method:: L *= k

      Increase the length of the list by a factor of *k*, by inserting
      *k-1* additional shallow copies of each item in the list.

   .. _SortedListWithKey.__iter__:
   .. method:: iter(L)

      Return an iterator over the Sequence.

      Iterating the Sequence while adding or deleting values may raise a
      `RuntimeError` or fail to iterate over all entries.

      :rtype: iterator

   .. method:: len(L)

      Return the number of elements in the list.

      :rtype: :class:`int`

   .. _SortedListWithKey.__mul__:
   .. method:: L * k or k * L

      Return a new sorted list containing *k* shallow copies of each
      item in *L*.

      :rtype: :class:`SortedListWithKey`

   .. _SortedListWithKey.__imul__:
   .. method:: L *= k

      Update *L* to include *k* shallow copies of each item in *L*.

      :rtype: :class:`SortedListWithKey`

   .. _SortedListWithKey.__add__:
   .. method:: L + k

      Return a new sorted list containing all the elements in *L* and
      *k*. Elements in *k* do not need to be properly ordered with respect to
      *L*.

      :rtype: :class:`SortedListWithKey`

   .. _SortedListWithKey.__iadd__:
   .. method:: L += k

      Update *L* to include all values in *k*. Elements in *k* do not
      need to be properly ordered with respect to *L*.

   .. method:: reversed(L)

      Return an iterator to traverse the Sequence in reverse.

      Iterating the Sequence while adding or deleting values may raise a
      `RuntimeError` or fail to iterate over all entries.

      :rtype: iterator

   .. _SortedListWithKey.__setitem__:
   .. method:: L[i] = x

      Replace the item at position *i* of *L* with *x*. Supports slice
      notation. Raises a :exc:`ValueError` if the sort order would be violated.

   .. method:: L[i:j] = iterable

      Replace the items at positions *i* through *j* with the contents of
      *iterable*. Also note that *step* is supported in slice syntax.

   .. _SortedListWithKey.add:
   .. method:: L.add(value)

      Add the element *value* to the list.

   .. _SortedListWithKey.bisect_left:
   .. method:: L.bisect_left(value)

      Similar to the ``bisect`` module in the standard library, this
      returns an appropriate index to insert *value* in *L*. If *value* is
      already present in *L*, the insertion point will be before (to the
      left of) any existing entries.

      :rtype: :class:`int`

   .. _SortedListWithKey.bisect:
   .. method:: L.bisect(value)

      Same as :ref:`bisect_right <SortedListWithKey.bisect_right>`.

      :rtype: :class:`int`

   .. _SortedListWithKey.bisect_right:
   .. method:: L.bisect_right(value)

      Same as :ref:`bisect_left <SortedListWithKey.bisect_left>`, but if
      *value* is already present in *L*, the insertion point will be after
      (to the right of) any existing entries.

      :rtype: :class:`int`

   .. _SortedListWithKey.bisect_key_left:
   .. method:: L.bisect_key_left(key)

      Similar to the ``bisect`` module in the standard library, this returns an
      appropriate index to insert a value with a given *key*. If values with
      *key* are already present, the insertion point will be before (to the
      left of) any existing entries.

      :rtype: :class:`int`

   .. method:: L.bisect_key(key)

      Same as :ref:`bisect_key_right <SortedListWithKey.bisect_key_right>`.

      :rtype: :class:`int`

   .. _SortedListWithKey.bisect_key_right:
   .. method:: L.bisect_key_right(key)

      Same as :ref:`bisect_key_left <SortedListWithKey.bisect_key_left>`, but
      if *key* is already present, the insertion point will be after (to the
      right of) any existing entries.

      :rtype: :class:`int`

   .. _SortedListWithKey.count:
   .. method:: L.count(value)

      Return the number of occurrences of *value* in the list.

      :rtype: :class:`int`

   .. _SortedListWithKey.copy:
   .. method:: L.copy()

      Return a shallow copy of the sorted list with key.

      :rtype: :class:`SortedListWithKey`

   .. _SortedListWithKey.discard:
   .. method:: L.discard(value)

      Remove the first occurrence of *value*.  If *value* is not a
      member, does nothing.

   .. _SortedListWithKey.index:
   .. method:: L.index(value, [start, [stop]])

      Return the smallest *k* such that :math:`L[k] == x` and
      :math:`i <= k < j`.  Raises ValueError if *value* is not
      present.  *stop* defaults to the end of the list.  *start*
      defaults to the beginning.  Negative indexes are supported, as
      for slice indices.

      :rtype: :class:`int`

   .. _SortedListWithKey.pop:
   .. method:: L.pop([index])

      Remove and return item at index (default last).  Raises :exc:`IndexError`
      if list is empty or index is out of range.  Negative indexes are
      supported, as for slice indices.

      :rtype: item

   .. _SortedListWithKey.remove:
   .. method:: L.remove(value)

      Remove first occurrence of *value*.  Raises :exc:`ValueError` if
      *value* is not present.

   .. _SortedListWithKey.update:
   .. method:: L.update(iterable)

      Grow the list by inserting all elements from the *iterable*.

   .. method:: L.clear()

      Remove all the elements from the list.

   .. _SortedListWithKey.append:
   .. method:: L.append(value)

      Append the element *value* to the list. Raises a :exc:`ValueError` if the
      *value* would violate the sort order.

   .. _SortedListWithKey.extend:
   .. method:: L.extend(iterable)

      Extend the list by appending all elements from the *iterable*. Raises a
      :exc:`ValueError` if the sort order would be violated.

   .. _SortedListWithKey.insert:
   .. method:: L.insert(index, value)

      Insert the element *value* into the list at *index*. Raises a
      :exc:`ValueError` if the *value* at *index* would violate the sort order.

   .. method:: L.islice(start=None, stop=None, reverse=False)

      Returns an iterator that slices `self` from `start` to `stop` index,
      inclusive and exclusive respectively.

      When `reverse` is `True`, values are yielded from the iterator in
      reverse order.

      Both `start` and `stop` default to `None` which is automatically
      inclusive of the beginning and end.

      :rtype: iterator

   .. method:: L.irange(minimum=None, maximum=None, inclusive=(True, True), reverse=False)

      Create an iterator of values between `minimum` and `maximum`.

      `inclusive` is a pair of booleans that indicates whether the minimum
      and maximum ought to be included in the range, respectively. The
      default is (True, True) such that the range is inclusive of both
      minimum and maximum.

      Both `minimum` and `maximum` default to `None` which is automatically
      inclusive of the start and end of the list, respectively.

      When `reverse` is `True` the values are yielded from the iterator in
      reverse order; `reverse` defaults to `False`.

      :rtype: iterator

   .. _SortedListWithKey.irange_key:
   .. method:: L.irange_key(min_key=None, max_key=None, inclusive=(True, True), reverse=False)

      Create an iterator of values between `min_key` and `max_key`.

      `inclusive` is a pair of booleans that indicates whether the minimum
      and maximum ought to be included in the range, respectively. The
      default is (True, True) such that the range is inclusive of both
      minimum and maximum.

      Both `min_key` and `max_key` default to `None` which is automatically
      inclusive of the start and end of the list, respectively.

      When `reverse` is `True` the values are yielded from the iterator in
      reverse order; `reverse` defaults to `False`.

      :rtype: iterator
