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| 1 | +# Union Find (Disjoint Set Union) - Implementation and Use |
| 2 | + |
| 3 | +## Table of Contents |
| 4 | +- [Why Union Find?](#why-union-find) |
| 5 | +- [Functions and Examples](#functions-and-examples) |
| 6 | +- [Setup](#setup) |
| 7 | +- [Additional Resources](#additional-resources) |
| 8 | +- [Leetcode Questions](#leetcode-questions) |
| 9 | + |
| 10 | +## Why Union Find? |
| 11 | +Union Find is a popular data structure that allows us to solve many different types of graph |
| 12 | +problems. It works best with undirected graphs, and it allows us to figure out whether a node |
| 13 | +is connected to another node. |
| 14 | + |
| 15 | +Some problems it can be used to solve: |
| 16 | +- Find the minimum spanning tree in a graph (Kruskal's) |
| 17 | +- Check if there is a path between two nodes |
| 18 | +- Finding redundant edges |
| 19 | +- Representing networks |
| 20 | + |
| 21 | + |
| 22 | +## Functions and Examples |
| 23 | +Union Find seems complex at first, but it is actually a lot easier when you understand that there are |
| 24 | +only two functions. |
| 25 | +- Find(n) : returns the parent of a node n |
| 26 | +- Union(n1, n2) : connects n1 and n2 if they are not previously connected |
| 27 | + |
| 28 | +Let's look at an example! |
| 29 | +```python |
| 30 | +u = UnionFind(7) # create a UnionFind object with 7 nodes (numbered 0 to 6) |
| 31 | + |
| 32 | +u.union(0, 1) # connects 0 and 1 together |
| 33 | +u.union(5, 6) # connects 5 and 6 together |
| 34 | + |
| 35 | +u.find(1) # returns 0, since 0 is parent of 1 |
| 36 | +u.find(5) # returns 5, since 5 is its own parent |
| 37 | + |
| 38 | +u.union(1, 2) # connects 2 to the component 0-1 |
| 39 | +u.find(2) # 2s parent is now 0 |
| 40 | + |
| 41 | +# Now our structure looks like this |
| 42 | + |
| 43 | +# 0-1-2 3 4 5-6 |
| 44 | + |
| 45 | +u.union(1, 6) # first we find the parents of 1 and 6 |
| 46 | + # parents are 0, and 5 |
| 47 | + # connect the smaller component to the bigger |
| 48 | + # now 5's parent is 0 |
| 49 | + |
| 50 | +u.find(6) # now this goes: |
| 51 | + # 6 parent is 5 -> 5 parent is 0 -> 0 is its own parent |
| 52 | +``` |
| 53 | + |
| 54 | +And that's it! You can use the sample code to test different examples with Union Find. |
| 55 | +In the code, par keeps track of the parent of each node and rank keeps track of the size of |
| 56 | +each component. |
| 57 | + |
| 58 | +## Setup |
| 59 | + |
| 60 | +First clone the repo |
| 61 | + > `cd union_find` to get into this folder. |
| 62 | + > call the verify function anywhere, consider adding ``` if __name__ == '__main__'``` |
| 63 | + > `python union_find.py` to run the demo |
| 64 | + |
| 65 | + You can modify the structure in the verify function and play around with it. |
| 66 | + |
| 67 | + ## Additional Resources |
| 68 | + |
| 69 | + Here are some resources I found useful when learning: |
| 70 | + - Neetcode Graph Videos on YouTube |
| 71 | + - William Fiset - Union Find Video on YouTube |
| 72 | + - Union Find Medium Article by Claire Lee |
| 73 | + - Union Find Visualizer - Visualgo |
| 74 | + |
| 75 | + ## Leetcode Questions |
| 76 | + - 200 - Number of Islands |
| 77 | + - 684 - Redundant Connection |
| 78 | + - 695 - Max Area of an Island |
| 79 | + - 827 - Making a Large Island |
| 80 | + - 2316 - Count Unreachable Pairs of Nodes in an Undirected Graph |
| 81 | + - 2421 - Maximum Score of a Good Path |
| 82 | + - 2709 - Greatest Common Divisor Traversal |
| 83 | + |
| 84 | + I hope this was helpful. If there are any mistakes or issues or if you want to contribute to union find, feel free to contact me at rawateshaan0 [at] gmail [dot] com |
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