A Python API for the Rust backend of `reunion`, i.e. a Union-Find w/ Rank data structure for Python.
Project description
A Disjoint-Set data structure (aka Union-Find w/ Rank)
What is Union-Find?
Suppose you have a collection S
of elements e1
, e2
, ...
, en
, and wish to group them into different collections using operations:
- "put
ei
andej
into the same group" (union), - "give me a representative of the group
ei
belongs to" (find).
Then a Union-Find data structure helps to store the underlying groups very efficiently and implements this API.
Note: The variant implemented uses Path Compression to further improve the performance.
(Some) Applications
-
Detect Cycles in Graph: Given a graph
G
, we can put the endpoints of edges into the same group (same connected component) unless there is a pair of endpoints(ei, ej)
that share a group representative. If that happens, there was already a path existing between them, and adding this edge will add multiple paths, which cannot be the case for acyclic graphs. -
Number of connected components in Graph: Given a graph
G
, put the endpoints of edges into the same group (same connected component). Once all nodes are exhausted, the number of groups formed is the number of connected components inG
.
Some interesting lecture notes regarding Union-Find.
Usage
Setup
Using any of the package installers, install pyreunion
from the PyPi.
For example, pip install pyreunion
.
API
Example 1
Task: Create a UnionFind data structure of arbitrary size that contains usize
at its elements.
Then, union a few elements and capture the state of the data structure after that.
Solution:
import pyreunion
def main():
# Create an empty UnionFind data structure.
uf = pyreunion.UnionFind()
print("Initial state:", uf.str())
print("All elements form their own group (singletons).")
print(uf.subsets())
uf.union(2, 1)
print("After combining the groups that contains 2 and 1:", uf.str())
uf.union(4, 3)
print("After combining the groups that contains 4 and 3:", uf.str())
uf.union(6, 5)
print("After combining the groups that contains 6 and 5:", uf.str())
hs1 = {1, 2}
hs2 = {3, 4}
hs3 = {5, 6}
subsets = uf.subsets()
assert (len(subsets) == 3)
assert (hs1 in subsets)
assert (hs2 in subsets)
assert (hs3 in subsets)
uf.union(1, 5)
print("After combining the groups that contains 1 and 5", uf.str())
subsets = uf.subsets()
assert (len(subsets) == 2)
for x in hs1:
hs3.add(x)
assert (hs3 in subsets)
assert (hs2 in subsets)
# It is possible to iterate over the subsets.
for partition in uf.subsets():
print(partition)
if __name__ == '__main__':
main()
Performance
The underlying implementation uses Path Compression and is written in Rust. The implementation and some performance statistics are available here.
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