Package provides Binary-, RedBlack- and AVL-Trees in Python and Cython.

## Binary Tree Package

## Bintrees Development Stopped

Use `sortedcontainers` instead: https://pypi.python.org/pypi/sortedcontainers

see also PyCon 2016 presentation: https://www.youtube.com/watch?v=7z2Ki44Vs4E

Advantages:

- pure Python no Cython/C dependencies
- faster
- active development
- more & better testing/profiling

## Abstract

This package provides Binary- RedBlack- and AVL-Trees written in Python and Cython/C.

This Classes are much slower than the built-in *dict* class, but all
iterators/generators yielding data in sorted key order. Trees can be
uses as drop in replacement for *dicts* in most cases.

### Source of Algorithms

AVL- and RBTree algorithms taken from Julienne Walker: http://eternallyconfuzzled.com/jsw_home.aspx

### Trees written in Python

BinaryTree– unbalanced binary treeAVLTree– balanced AVL-TreeRBTree– balanced Red-Black-Tree

### Trees written with C-Functions and Cython as wrapper

FastBinaryTree– unbalanced binary treeFastAVLTree– balanced AVL-TreeFastRBTree– balanced Red-Black-Tree

All trees provides the same API, the pickle protocol is supported.

Cython-Trees have C-structs as tree-nodes and C-functions for low level operations:

- insert
- remove
- get_value
- min_item
- max_item
- prev_item
- succ_item
- floor_item
- ceiling_item

#### Constructor

- Tree() -> new empty tree;
- Tree(mapping) -> new tree initialized from a mapping (requires only an items() method)
- Tree(seq) -> new tree initialized from seq [(k1, v1), (k2, v2), … (kn, vn)]

#### Methods

- __contains__(k) -> True if T has a key k, else False, O(log(n))
- __delitem__(y) <==> del T[y], del[s:e], O(log(n))
- __getitem__(y) <==> T[y], T[s:e], O(log(n))
- __iter__() <==> iter(T)
- __len__() <==> len(T), O(1)
- __max__() <==> max(T), get max item (k,v) of T, O(log(n))
- __min__() <==> min(T), get min item (k,v) of T, O(log(n))
- __and__(other) <==> T & other, intersection
- __or__(other) <==> T | other, union
- __sub__(other) <==> T - other, difference
- __xor__(other) <==> T ^ other, symmetric_difference
- __repr__() <==> repr(T)
- __setitem__(k, v) <==> T[k] = v, O(log(n))
- __copy__() -> shallow copy support, copy.copy(T)
- __deepcopy__() -> deep copy support, copy.deepcopy(T)
- clear() -> None, remove all items from T, O(n)
- copy() -> a shallow copy of T, O(n*log(n))
- discard(k) -> None, remove k from T, if k is present, O(log(n))
- get(k[,d]) -> T[k] if k in T, else d, O(log(n))
- is_empty() -> True if len(T) == 0, O(1)
- items([reverse]) -> generator for (k, v) items of T, O(n)
- keys([reverse]) -> generator for keys of T, O(n)
- values([reverse]) -> generator for values of T, O(n)
- pop(k[,d]) -> v, remove specified key and return the corresponding value, O(log(n))
- pop_item() -> (k, v), remove and return some (key, value) pair as a 2-tuple, O(log(n)) (synonym popitem() exist)
- set_default(k[,d]) -> value, T.get(k, d), also set T[k]=d if k not in T, O(log(n)) (synonym setdefault() exist)
- update(E) -> None. Update T from dict/iterable E, O(E*log(n))
- foreach(f, [order]) -> visit all nodes of tree (0 = ‘inorder’, -1 = ‘preorder’ or +1 = ‘postorder’) and call f(k, v) for each node, O(n)
- iter_items(s, e[, reverse]) -> generator for (k, v) items of T for s <= key < e, O(n)
- remove_items(keys) -> None, remove items by keys, O(n)

#### slicing by keys

- item_slice(s, e[, reverse]) -> generator for (k, v) items of T for s <= key < e, O(n), synonym for iter_items(…)
- key_slice(s, e[, reverse]) -> generator for keys of T for s <= key < e, O(n)
- value_slice(s, e[, reverse]) -> generator for values of T for s <= key < e, O(n)
- T[s:e] -> TreeSlice object, with keys in range s <= key < e, O(n)
- del T[s:e] -> remove items by key slicing, for s <= key < e, O(n)
start/end parameter:

- if ‘s’ is None or T[:e] TreeSlice/iterator starts with value of min_key();
- if ‘e’ is None or T[s:] TreeSlice/iterator ends with value of max_key();
- T[:] is a TreeSlice which represents the whole tree;
The step argument of the regular slicing syntax T[s:e:step] will silently ignored.

TreeSlice is a tree wrapper with range check and contains no references to objects, deleting objects in the associated tree also deletes the object in the TreeSlice.

- TreeSlice[k] -> get value for key k, raises KeyError if k not exists in range s:e

- TreeSlice[s1:e1] -> TreeSlice object, with keys in range s1 <= key < e1

- new lower bound is max(s, s1)
- new upper bound is min(e, e1)
TreeSlice methods:

- items() -> generator for (k, v) items of T, O(n)
- keys() -> generator for keys of T, O(n)
- values() -> generator for values of T, O(n)
- __iter__ <==> keys()
- __repr__ <==> repr(T)
- __contains__(key)-> True if TreeSlice has a key k, else False, O(log(n))

#### prev/succ operations

- prev_item(key) -> get (k, v) pair, where k is predecessor to key, O(log(n))
- prev_key(key) -> k, get the predecessor of key, O(log(n))
- succ_item(key) -> get (k,v) pair as a 2-tuple, where k is successor to key, O(log(n))
- succ_key(key) -> k, get the successor of key, O(log(n))
- floor_item(key) -> get (k, v) pair, where k is the greatest key less than or equal to key, O(log(n))
- floor_key(key) -> k, get the greatest key less than or equal to key, O(log(n))
- ceiling_item(key) -> get (k, v) pair, where k is the smallest key greater than or equal to key, O(log(n))
- ceiling_key(key) -> k, get the smallest key greater than or equal to key, O(log(n))

#### Heap methods

- max_item() -> get largest (key, value) pair of T, O(log(n))
- max_key() -> get largest key of T, O(log(n))
- min_item() -> get smallest (key, value) pair of T, O(log(n))
- min_key() -> get smallest key of T, O(log(n))
- pop_min() -> (k, v), remove item with minimum key, O(log(n))
- pop_max() -> (k, v), remove item with maximum key, O(log(n))
- nlargest(i[,pop]) -> get list of i largest items (k, v), O(i*log(n))
- nsmallest(i[,pop]) -> get list of i smallest items (k, v), O(i*log(n))

#### Set methods (using frozenset)

- intersection(t1, t2, …) -> Tree with keys
commonto all trees- union(t1, t2, …) -> Tree with keys from
eithertrees- difference(t1, t2, …) -> Tree with keys in T but not any of t1, t2, …
- symmetric_difference(t1) -> Tree with keys in either T and t1 but not both
- is_subset(S) -> True if every element in T is in S (synonym issubset() exist)
- is_superset(S) -> True if every element in S is in T (synonym issuperset() exist)
- is_disjoint(S) -> True if T has a null intersection with S (synonym isdisjoint() exist)

#### Classmethods

- from_keys(S[,v]) -> New tree with keys from S and values equal to v. (synonym fromkeys() exist)

#### Helper functions

- bintrees.has_fast_tree_support() -> True if Cython extension is working else False (False = using pure Python implementation)

## Installation

from source:

python setup.py install

or from PyPI:

pip install bintrees

Compiling the fast Trees requires Cython and on Windows is a C-Compiler necessary.

## Download Binaries for Windows

## Documentation

this README.rst

bintrees can be found on GitHub.com at:

## NEWS

Version 2.0.7 - 2017-04-28

- BUGFIX: foreach (pure Python implementation) works with empty trees
- acquire GIL for PyMem_Malloc() and PyMem_Free() calls

Version 2.0.6 - 2017-02-04

- BUGFIX: correct deepcopy() for tree in tree

Version 2.0.5 - 2017-02-04

- support for copy.deepcopy()
- changed status back to
Mature, there will be: bugfixes, compatibility checks and simple additions like this deep copy support, because I got feedback, that there are some special cases in whichbintreescan be useful.- switched development to 64bit only & MS compilers - on Windows 7 everything works fine now with CPython 2.7/3.5/3.6

Repository moved to GitHub: https://github.com/mozman/bintrees.git

Version 2.0.4 - 2016-01-09

- removed logging statements on import
- added helper function bintrees.has_fast_tree_support()
- HINT: pypy runs faster than CPython with Cython extension

Version 2.0.3 - 2016-01-06

- replaced print function by logging.warning for import warning messages
- KNOWN ISSUE: unable to build Cython extension with MingW32 and CPython 3.5 & CPython 2.7.10

Version 2.0.2 - 2015-02-12

- fixed foreach cython-function by Sam Yaple

Version 2.0.1 - 2013-10-01

- removed __del__() method to avoid problems with garbage collection

Version 2.0.0 - 2013-06-01

- API change: consistent method naming with synonyms for dict/set compatibility
- code base refactoring
- removed tree walkers
- removed low level node stack implementation -> caused crashes
- optimizations for pypy: iter_items(), succ_item(), prev_item()
- tested with CPython2.7, CPython3.3, pypy-2.0 on Win7 and Linux Mint 15 x64 (pypy-1.9)

Version 1.0.3 - 2013-05-01

- extended iter_items(startkey=None, endkey=None, reverse=reverse) -> better performance for slicing
- Cython implementation of iter_items() for Fast_X_Trees()
- added key parameter
reverseto itemslice(), keyslice(), valueslice()- tested with CPython2.7, CPython3.3, pypy-2.0

Version 1.0.2 - 2013-04-01

- bug fix: FastRBTree data corruption on inserting existing keys
- bug fix: union & symmetric_difference - copy all values to result tree

Version 1.0.1 - 2013-02-01

- bug fixes
- refactorings by graingert
- skip useless tests for pypy
- new license: MIT License
- tested with CPython2.7, CPython3.2, CPython3.3, pypy-1.9, pypy-2.0-beta1
- unified line endings to LF
- PEP8 refactorings
- added floor_item/key, ceiling_item/key methods, thanks to Dai Mikurube

Version 1.0.0 - 2011-12-29

- bug fixes
- status: 5 - Production/Stable
- removed useless TreeIterator() class and T.treeiter() method.
- patch from Max Motovilov to use Visual Studio 2008 for building C-extensions

Version 0.4.0 - 2011-04-14

- API change!!!
- full Python 3 support, also for Cython implementations
- removed user defined compare() function - keys have to be comparable!
- removed T.has_key(), use ‘key in T’
- keys(), items(), values() generating ‘views’
- removed iterkeys(), itervalues(), iteritems() methods
- replaced index slicing by key slicing
- removed index() and item_at()
- repr() produces a correct representation
- installs on systems without cython (tested with pypy)
- new license: GNU Library or Lesser General Public License (LGPL)

Version 0.3.2 - 2011-04-09

- added itemslice(startkey, endkey), keyslice(startkey, endkey), valueslice(startkey, endkey) - slicing by keys
- tested with pypy 1.4.1, damn fast
- Pure Python trees are working with Python 3
- No Cython implementation for Python 3

Version 0.3.1 - 2010-09-10

- runs with Python 2.7

Version 0.3.0 - 2010-05-11

- low level functions written as c-module only interface to python is a cython module
- support for the pickle protocol

Version 0.2.1 - 2010-05-06

- added delslice del T[0:3] -> remove treenodes 0, 1, 2
- added discard -> remove key without KeyError if not found
- added heap methods: min, max, nlarges, nsmallest …
- added Set methods -> intersection, differnce, union, …

- added slicing: T[5:10] get items with position (not key!) 5, 6, 7, 8, 9
- T[5] get item with key! 5
- added index: T.index(key) -> get position of item <key>

- added item_at: T.item_at(0) -> get item at position (not key!) 0
- T.item_at(0) O(n)! <==> T.min_item() O(log(n))

Version 0.2.0 - 2010-05-03

- TreeMixin Class as base for Python-Trees and as Mixin for Cython-Trees

Version 0.1.0 - 2010-04-27

- Alpha status
- Initial release

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