bintrees 2.0.0

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

Binary Tree Package

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 tree

• AVLTree – balanced AVL-Tree

• RBTree – balanced Red-Black-Tree

Trees written with C-Functions and Cython as wrapper

• FastBinaryTree – unbalanced binary tree

• FastAVLTree – balanced AVL-Tree

• FastRBTree – 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))

• 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;

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 common to all trees

• union(t1, t2, …) -> Tree with keys from either trees

• 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)

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 (MingW works fine).

Download Binaries for Windows

http://bitbucket.org/mozman/bintrees/downloads

Documentation

this README.rst

bintrees can be found on bitbucket.org at:

http://bitbucket.org/mozman/bintrees

NEWS

Version 2.0.0 June 2013

• 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 May 2013

• 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 reverse to itemslice(), keyslice(), valueslice()

• tested with CPython2.7, CPython3.3, pypy-2.0

Version 1.0.2 April 2013

• bug fix: FastRBTree data corruption on inserting existing keys

• bug fix: union & symmetric_difference - copy all values to result tree

Version 1.0.1 February 2013

• 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 29.12.2011

• 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 14.04.2011

• 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 09.04.2011

• 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 10.09.2010

• runs with Python 2.7

Version 0.3.0 11.05.2010

• low level functions written as c-module only interface to python is a cython module

• support for the pickle protocol

Version 0.2.1 06.05.2010

• 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 - 03.05.2010

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

Version 0.1.0 - 27.04.2010

• Alpha status

• Initial release