treap.py is a python module (more than one actually) for implementing a "treap", which is a datastructure that is a hybrid of a binary heap and a binary tree.

It was originally GPLv3-licensed, but now it's Apache v2 licensed.

This treap module is designed to have a dictionary-like interface:

$ python Python 2.6.4 (r264:75706, Nov 2 2009, 14:38:03) [GCC 4.4.1] on linux2 Type "help", "copyright", "credits" or "license" for more information. >>> import treap >>> t = treap.treap() >>> for i in xrange(8): ... t[i] = 2**i ... >>> for i in t.keys(): ... print t[i] ... 1 2 4 8 16 32 64 128 >>>

However, it's also ordered:

>>> print list(t) [0, 1, 2, 3, 4, 5, 6, 7] >>> print t.find_min() 0 >>> print t.find_max() 7 >>>

It comes with a pure python version, and a version that has the more computationally-intensive portion in cython. The two are automatically derived from a single m4-preprocessed file.

Here's a table comparing the asymptotic running time of various python
datastructures across a variety of operations. As you can see, like any
datastructure it's not stellar at *everything*, but it does have a nice set of
tradeoffs:

unsorted list (array) | sorted list (array) | dictionary (hash) | minheap | treap | |

insert lowest value | O(1) | O(n) | O(1) | O(log_{2}(n)) |
O(log_{2}(n)) |

insert highest value | O(1) | O(1) | O(1) | O(log_{2}(n)) |
O(log_{2}(n)) |

insert arbitrary value | O(1) | O(n) | O(1) | O(log_{2}(n)) |
O(log_{2}(n)) |

remove lowest value | O(n) | O(n) | O(n) | O(log_{2}(n)) |
O(log_{2}(n)) |

remove highest value | O(n) | O(1) | O(n) | O(n) | O(log_{2}(n)) |

remove arbitrary | O(n) | O(n) | O(1) | O(n) | O(log_{2}(n)) |

lookup lowest value | O(n) | O(1) | O(n) | O(1) | O(log_{2}(n)) |

lookup highest value | O(n) | O(1) | O(n) | O(n) | O(log_{2}(n)) |

lookup arbitrary value | O(n) | O(log_{2}(n)) |
O(1) | O(n) | O(log_{2}(n)) |

sort all values | O(n*log_{2}(n)) |
O(1) (it's already sorted) | O(n*log_{2}(n)) |
O(n*log_{2}(n)) |
O(n) (requires a tree traversal) |

If asymtoptic running time is something you don't want to think about,
you might just consider that running times can be sorted like the
following, for large inputs, where O(1) is fastest and
O(n*log_{2}(n)) is slowest:

- O(1)
- O(log
_{2}(n)) - O(n)
- O(n*log
_{2}(n))

The download also comes with a "nest.py" module, that's intended to make it easy to keep the lowest (or highest) p objects (objects having a __cmp__ method) out of a collection of q objects.

Looking for duptreaps? Check out dupdict_mod.

See also this list of datastructures I've worked on.

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