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 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))
• __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 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)

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

https://github.com/mozman/bintrees/releases

Documentation

this README.rst

bintrees can be found on GitHub.com at:

https://github.com/mozman/bintrees.git