Red-black trees
Project description
Blackjack is a simple implementation of the classic red-black tree as a standard Python data structure. A set and a dictionary are included:
>>> from blackjack import BJ, Deck >>> bj = BJ() >>> bj BJ([]) >>> bj.add(42) >>> 42 in bj True >>> d = Deck() >>> d[1] = 2 >>> d[3] = 4 >>> d.keys() [1, 3] >>> d.values() [2, 4]
Usage
Blackjacks and decks behave just like normal Python sets and dictionaries, but have different performance characteristics and different requirements for keys. All keys must be comparable, but need not be hashable:
>>> bj = BJ() >>> bj.add([1]) >>> bj.add([1,2]) >>> bj.add([1,2,3]) >>> bj BJ([[1], [1, 2], [1, 2, 3]])
This does impact heterogeneity somewhat, but shouldn’t be a problem for most common uses. On the other hand, the average and worst-case times for access, membership testing, insertion, and deletion are all logarithmic, which makes blackjacks ideal for storing mappings of data with untrusted keys:
$ python -mtimeit \ > -s 'l = [(x*(2**64 - 1), hash(x*(2**64 - 1))) for x in xrange(10000)]' \ > 'dict(l)' 10 loops, best of 3: 4.11 sec per loop $ python -mtimeit \ -s 'l = [(x*(2**64 - 1), hash(x*(2**64 - 1))) for x in xrange(10000)] from blackjack import Deck' \ 'Deck(l)' 10 loops, best of 3: 2.07 sec per loop
Even on small- to medium-sized sets of data, blackjacks quickly become more effective than dictionaries in the face of untrusted input.
This package only contains the blackjack module; tests are in the module and may be run with any standard test runner:
$ trial blackjack | tail -n1 PASSED (successes=17)
Technical information
The specific trees used are left-leaning red-black trees. Red children are opportunistically reduced during balancing if nodes will be recreated anyway; this tends to shorten overall tree height by reducing the number of red children. Complexities are as follows:
Operation |
Time |
Space |
|---|---|---|
Lookup |
O(log n) |
O(1) |
Membership |
O(log n) |
O(1) |
Insertion |
O(log n) |
O(log n) |
Deletion |
O(log n) |
O(log n) |
Update |
O(log n) |
O(log n) |
Sort |
O(1) |
O(1) |
Length |
O(1) |
O(1) |
Sorting according to the provided key function is constant because the tree’s traversal order is presorted. Length is recorded and updated on mutation. Nodes are persistent and altering the tree generally requires a logarithmic space commitment to create new nodes.
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