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Fast, pure Python indexable skip list

Project description

PySkipList is a fast, pure Python implementation of an indexable skiplist. It implements a SkipList data structure that provides an always sorted, list-like data structure for (key, value) pairs. It efficiently supports the following operations:

  • Insert a pair in the list, maintaining sorted order.
  • Find the value of a given key.
  • Remove a given pair based on a key.
  • Iterate over all pairs in sorted order.
  • Find the position of a given key.
  • Access a pair at a certain position.
  • Delete a pair at a certain position.

Since PySkipList is a pure Python implementation, it should work well on alternative Python implementations such as PyPy and Jython.


The following provides a few examples on how to use the SkipList API:

>>> from pyskiplist import SkipList
>>> sl = SkipList()
>>> sl.insert('foo', 'bar')
>>> sl.insert('baz', 'qux')
>>> sl
SkipList((('baz', 'qux'), ('foo', 'bar')))
>>> sl[0]
('baz', 'qux')
>>> sl.remove('foo')  # remove by key
>>> del sl[0]  # remove by position

Asymptotic Complexity

Below are the Big-O complexities of the various operations implemented by pyskiplist:

Operation Complexity
insertion O(log N)
search by key O(log N)
removal by key O(log N)
forward iteration O(1)
find by position O(log N)
access by position O(log N)
delete by position O(log N)


Below are the results of some performance tests. These are for Python 3.4.2 on my Linux laptop:

Test Operations / second
Insert @ 1k nodes 45,056
Insert @ 10k nodes 42,137
Insert @ 100k nodes 28,086
Remove @ 1k nodes 54,316
Remove @ 10k nodes 46,240
Remove @ 100k nodes 35,114
Search @ 1k nodes 137,248
Search @ 10k nodes 109,480
Search @ 100k nodes 77,939

Memory usage

PySkipList tries to be efficient with regards to memory usage. The numbers below are for Python 3.4.2 on my Linux laptop. This specific test stores pairs of integer keys and an integer values in a skiplist. The total size of the two integers on this Python version is 56 bytes.

Nodes Bytes / node Overhead (fixed)
1k 164 108
10k 162 106
100k 162 106

Implementation notes

Reference papers on skiplists:

This implementation uses a novel (as far as I know) technique where it stores just a single link width per node, and only in nodes with level > 0. The link corresponds to the number of nodes skipped by the highest incoming link. Other implementations that I’ve seen all store a width for every link. This approach saves a lot of memory. The overhead should just be 1/e (0.37) integers per node. It makes an indexable skiplist almost as memory efficient as its non-indexable cousin.

Duplicate keys are allowed in this implementation, and insertion order is maintained.

Skiplist nodes are implemented as plain lists instead of objects. This saves memory. Kudos to for the idea.

The built-in Mersenne Twister is used as the random source. This is preferable over SystemRandom since it doesn’t require a system call and there is no need for cryptographically secure numbers.

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