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