Introduction

This package provides sorted drop-in versions of Python’s set and dict (with optional augmentation). Being tree based, they are not as efficient as hash-based containers (such as Python’s builtins) for simple lookup and modification. Conversely:

• (Common Case:) They are far more efficient than them for the case where modifications and lookups are interleaved with sorted iterations.
• (Less Common Case:) Through optional tree augmentation, they are far more efficient than them for some other kinds of useful queries exploiting the underlying tree structure (e.g., what is the ordinal position of this item in the set? which geometric intervals overlap this interval?).

Features

• Supports high-performance algorithms for different use-cases:

  • Red-black trees for normal cases
  • Splay trees for temporal locality cases (i.e., when only a small subset of items will actually be accessed in any time period)
  • Sorted lists for infrequent-update cases

• Provides Pythonic interfaces:

  • Collections are almost entirely drop-in sorted replacements for Python’s set and dict
  • User defined key functions (or older style compare functions) are supported
  • Methods take slices and ranges where applicable
  • Pickle is supported
  • Reverse-order views are provided

• Allows optional tree augmentation with additional node metadata and tree methods:

  • Dynamic order statistics allow queries for the k-th item
  • Interval trees allow geometric querying
  • Any user-defined algorithm can be easily plugged in

  Note

  This feature can be almost entirely ignored if all that is needed are efficient sorted drop-in replacemnt containers for Python’s sets and dicts.

• Optimized implementation (see the Performance section in the online documentation):

  • C++ templated backend drives the implementation. C++ template metaprogramming is used to avoid run-time queries along the search path
  • Homogeneous-key trees optimization

A Few Quick Examples

Note

The following examples assume first typing:

>>> from banyan import *

• Choose an algorithm suiting the settings, and obtain a drop-in sorted replacement for Python’s builtins:

  • A (red-black tree) general drop-in replacement for Python’s set:

    >>> t = SortedSet([2, 3, 1])
    >>> t
    SortedSet([1, 2, 3])
    >>> assert 2 in t
    >>> t.add(4)
    >>> len(t)
    4
    >>> t.add(4)
    >>> len(t)
    4
    >>> t.remove(4)
    >>> len(t)
    3
    >>> t.remove(4)
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
      File "banyan/__init__.py", line 299, in remove
        self._tree.erase(item)
    KeyError: 4
    

  • A splay-based sorted drop-in replacement for Python’s dict, optimized for temporal-locality accesses:

    >>> t = SortedDict([(2, 'b'), (3, 'c'), (1, 'a')], alg = SPLAY_TREE)
    >>> print(list(t))
    [1, 2, 3]
    >>> assert 1 in t
    >>> assert 4 not in t
    >>> # Now access the key 2 for awhile
    >>> t[2] = 'e'
    >>> t[2] = 'f'
    >>> t[2] = 'g'
    >>> t[2] = 'a'
    >>> t[2] = 'b'
    >>> t[2] = 'c'
    >>> t[2] = 'd'
    >>> t[2] = 'e'
    

  • A (sorted-list based) sorted memory-efficient drop in for Python’s frozenset:

    >>> t = FrozenSortedSet(['hao', 'jiu', 'mei', 'jian'])
    >>> assert 'hao' in t
    >>> assert 'zaijian' not in t
    >>> t.add('zaijian')
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    AttributeError: 'FrozenSortedSet' object has no attribute 'add'
    

• Specify the comparison criteria - e.g., use a string dictionary with lowercase comparison:

  • Using the newer-style key parameter:

  >>> t = SortedDict(key = str.lower)
  >>> t['hao'] = 3
  >>> t['Hao'] = 4
  >>> t
  SortedDict({'Hao': 4})
  

  • Using the older-style (pre-Py3K) compare parameter:

  >>> t = SortedDict(compare = lambda x, y: cmp(str.lower(x), str.lower(y)))
  >>> t['hao'] = 3
  >>> t['Hao'] = 4
  >>> t
  SortedDict({'Hao': 4})
  

• Work with ranges and slices:

  >>> import string
  >>>
  >>> t = SortedDict(zip(string.ascii_lowercase, string.ascii_uppercase))
  >>>
  >>> # Erase everything starting at 'e'
  >>> del t['e': ]
  >>> t
  SortedDict({'a': 'A', 'b': 'B', 'c': 'C', 'd': 'D'})
  >>>
  >>> # View the items between 'b' and 'd'
  >>> t.items('b', 'd')
  ItemsView([('b', 'B'), ('c', 'C')])
  >>>
  >>> # View the values of the keys between 'a' and 'c', in reverse order
  >>> t.values('a', 'c', reverse = True)
  ValuesView(['B', 'A'])
  >>>
  >>> # Set the three values of the keys between 'a' and 'd' to 2
  >>> t['a': 'd'] = [2, 2, 2]
  >>> t
  SortedDict({'a': 2, 'b': 2, 'c': 2, 'd': 'D'})
  

• Easily use homogeneous-keys optimization:

  >>> # Simply specify the key type as key_type - no other changes are needed.
  >>> t = SortedSet([1, 2, 3], key_type = int)
  >>> assert 2 in t
  >>> t = SortedSet(['hao', 'jiu', 'mei', 'jian'], key_type = str)
  >>> assert 'hola' not in t
  

• Use Pythonic versions of C++/STL’s lower_bound/upper_bound:

  >>> from itertools import *
  >>>
  >>> t = SortedSet(['hao', 'jiu', 'mei', 'jian'])
  >>> t
  SortedSet(['hao', 'jian', 'jiu', 'mei'])
  >>> assert 'hao' in t
  >>>
  >>> # Find the key after 'hao'
  >>> keys = t.keys('hao', None)
  >>> next(islice(keys, 1, None))
  'jian'
  

• Exploit the tree structure for additional efficient functionality:

  • Use an overlapping-interval updator for creating a data structure that can efficiently answer overlapping queries:

  >>> t = SortedSet([(1, 3), (2, 4), (-2, 9)], updator = OverlappingIntervalsUpdator)
  >>>
  >>> print(t.overlap_point(-5))
  []
  >>> print(t.overlap_point(5))
  [(-2, 9)]
  >>> print(t.overlap_point(3.5))
  [(-2, 9), (2, 4)]
  >>>
  >>> print(t.overlap((-10, 10)))
  [(-2, 9), (1, 3), (2, 4)]
  

  For high performance, combine this with homogeneous-keys optimization:

  >>> t = SortedSet(key_type = (int, int), updator = OverlappingIntervalsUpdator)
  >>> t.add((1, 3))
  >>> t.overlap_point(2)
  [(1, 3)]
  >>>
  >>> t = SortedSet(key_type = (float, float), updator = OverlappingIntervalsUpdator)
  >>> t.add((1.0, 3.0))
  >>> t.overlap_point(2.5)
  [(1.0, 3.0)]
  

  • Use a rank updator for creating a data structure that can efficiently answer order queries:

  >>> t = SortedSet(['hao', 'jiu', 'mei', 'jian'], updator = RankUpdator)
  >>> t
  SortedSet(['hao', 'jian', 'jiu', 'mei'])
  >>>
  >>> # 'hao' is item no. 0
  >>> t.kth(0)
  'hao'
  >>> t.order('hao')
  0
  >>>
  >>> # 'mei' is item no. 3
  >>> t.kth(3)
  'mei'
  >>> t.order('mei')
  3
  

  • Use a min-gap updator for creating a data structur that can efficiently answer smallest-gap queries:

  >>> t = SortedSet([1, 3, 2], updator = MinGapUpdator)
  >>> t
  SortedSet([1, 2, 3])
  >>> t.min_gap()
  1
  >>> t.remove(2)
  >>> t
  SortedSet([1, 3])
  >>> t.min_gap()
  2
  

Download, Installation, Documentation, And Bugtracking

• The package is at PyPI.

• The usual setup for Python libraries is used. Type:

  $ pip install banyan

  or

  $ sudo pip install banyan

  Note

  To install this package from the source distribution, the system must have a C++ compiler installed. The setup script will invoke this compiler.

  Using Python 2.x on Windows will attempt to invoke Visual Studio 2008. If you are using a later version, download and extract the archive; then, from within the Banyan directory, use

  > SET VS90COMNTOOLS=%VS100COMNTOOLS%

  or

  > SET VS90COMNTOOLS=%VS110COMNTOOLS%

  (for Visual Studio 2010 and 2012, respectively), followed by

  > python setup.py install

• The documentation is hosted at PyPI Docs and can also be found in the ‘docs’ directory of the distribution.

• Bugtracking is on Google Code.

Changes

Changes

Version	Date	Description
0.1.5	05/04/2013	Faster red-black tree iteration; minor documentation bugfixes
0.1.4	01/04/2013	User key-function specification optimization; performance tests for dictionary types; better warnings for user mismatched policies
0.1.3.5	30/3/2013	OverlappingIntervalsUpdator: more regression tests + performance improvements + performance comparison tests
0.1.3	28/03/2013	OverlappingIntervalsUpdator implemented; minor documentation bugfixes
0.1.2	26/03/2013	Efficient C++ RankUpdator and MinGapUpdator; MinMaxUpdator out; major internal simplification
0.1.0	17/03/2013	Initial release

Planned Features

• Improve documentation and performance documentation w.r.t. key-type and policy specification.
• Give better yet warnings for user mismatched policies
• Implement priority search-tree updators