A union-find disjoint sets data structure implemented in Python with the "Weighted Quick Union with Path Compression" algorithm.
Union-find is a data structure that maintains disjoint set (called connected components or components in short) membership, and makes it easier to merge (union) two components, and to find if two elements are connected (i.e., belong to the same component).
This implements the "weighted-quick-union-with-path-compression" union-find algorithm. Only works if elements are immutable objects.
Worst case for union and find :math:(N + M \log^* N)
, with :math:N
elements
and :math:M
union/find operations. The function :math:\log^*
is the number
of times needed to take :math:\log
(base 2) of a number until reaching 1. In
practice, the amortized cost of each operation is nearly linear [1]_.
Update: This has now been packaged into an instalable pip package by Hagai Helman Tov (@hagai-helman). See the fork at https://github.com/hagai-helman/unionfind).
Module unionfind
with the class UnionFind
An example notebook UnionFindExamples.ipynb
License: MIT.
numpy