Binary Tree Package
===================
Abstract
========
This package provides Binary- RedBlack- and AVL-Trees written in Python and Cython.
This Classes are much slower than the built-in dict class, but all
iterators/generators yielding data in sorted key order.
Source of Algorithms
--------------------
AVL- and RBTree algorithms taken from Julienne Walker: http://eternallyconfuzzled.com/jsw_home.aspx
Trees written in Python (only standard library)
-----------------------------------------------
- *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.
FastXTrees has C-structs as tree-node structure and C-implementation for low level
operations: insert, remove, get_value, max_item, min_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))
* popitem() -> (k, v), remove and return some (key, value) pair as a 2-tuple, O(log(n))
* setdefault(k[,d]) -> T.get(k, d), also set T[k]=d if k not in T, O(log(n))
* 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)
slicing by keys
~~~~~~~~~~~~~~~
* itemslice(s, e) -> generator for (k, v) items of T for s <= key < e, O(n)
* keyslice(s, e) -> generator for keys of T for s <= key < e, O(n)
* valueslice(s, e) -> 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
* issubset(S) -> True if every element in T is in S
* issuperset(S) -> True if every element in S is in T
* isdisjoint(S) -> True if T has a null intersection with S
Classmethods
~~~~~~~~~~~~
* fromkeys(S[,v]) -> New tree with keys from S and values equal to v.
Performance
===========
Profiling with timeit(): 5000 unique random int keys, time in seconds
======================== ============= ============== ============== ==============
unbalanced Trees CPython 2.7.2 FastBinaryTree ipy 2.7.0 pypy 1.7.0
======================== ============= ============== ============== ==============
build time 100x 7,55 0,60 2,51 0,29
build & delete time 100x 13,34 1,48 4,45 0,47
search 100x all keys 2,86 0,96 0,27 0,06
======================== ============= ============== ============== ==============
======================== ============= ============== ============== ==============
AVLTrees CPython 2.7.2 FastAVLTree ipy 2.7.0 pypy 1.7.0
======================== ============= ============== ============== ==============
build time 100x 22,66 0,65 10,45 1,29
build & delete time 100x 36,71 1,47 20,89 3,02
search 100x all keys 2,34 0,85 0,89 0,14
======================== ============= ============== ============== ==============
======================== ============= ============== ============== ==============
RBTrees CPython 2.7.2 FastRBTree ipy 2.7.0 pypy 1.7.0
======================== ============= ============== ============== ==============
build time 100x 14,78 0,65 4,43 0,49
build & delete time 100x 39,34 1,63 12,43 1,32
search 100x all keys 2,32 0,86 0,86 0,13
======================== ============= ============== ============== ==============
News
====
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
* 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
* 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)
Installation
============
from source::
python setup.py install
Download
========
http://bitbucket.org/mozman/bintrees/downloads
Documentation
=============
this README.txt
bintrees can be found on bitbucket.org at:
http://bitbucket.org/mozman/bintrees