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August 5, 2018 08:08
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Union-Find in Python
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class UnionFind: | |
"""Weighted quick-union with path compression. | |
The original Java implementation is introduced at | |
https://www.cs.princeton.edu/~rs/AlgsDS07/01UnionFind.pdf | |
>>> uf = UnionFind(10) | |
>>> for (p, q) in [(3, 4), (4, 9), (8, 0), (2, 3), (5, 6), (5, 9), | |
... (7, 3), (4, 8), (6, 1)]: | |
... uf.union(p, q) | |
>>> uf._id | |
[8, 3, 3, 3, 3, 3, 3, 3, 3, 3] | |
>>> uf.find(0, 1) | |
True | |
>>> uf._id | |
[3, 3, 3, 3, 3, 3, 3, 3, 3, 3] | |
""" | |
def __init__(self, n): | |
self._id = list(range(n)) | |
self._sz = [1] * n | |
def _root(self, i): | |
j = i | |
while (j != self._id[j]): | |
self._id[j] = self._id[self._id[j]] | |
j = self._id[j] | |
return j | |
def find(self, p, q): | |
return self._root(p) == self._root(q) | |
def union(self, p, q): | |
i = self._root(p) | |
j = self._root(q) | |
if i == j: | |
return | |
if (self._sz[i] < self._sz[j]): | |
self._id[i] = j | |
self._sz[j] += self._sz[i] | |
else: | |
self._id[j] = i | |
self._sz[i] += self._sz[j] |
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