There is a really cool course on Coursera regarding Union-Find. The course was quite refreshing because I was never exposed to this simple concept before.
I just wanted to share the link for those learning graph theory as I am.
Now comes the boring stuff (how I found out about it and what I did with it).
I ran into a problem solving a question, Maximal Tourism on HackerRank. The problem is about getting most connected node counts in a graph given sets of connected nodes per line.
It seemed like a very simple problem but I had trouble due to timeouts. I wanted to get some tips on how to solve the problem so I decided to check Discussion forum (I try to solve myself for hours or days before resorting to this usually).
Mikhail(@mikesmnx) posted a link to a Coursera course for those having a problem solving the problem. I was hesitant at first but decided to watch the video. After the first video in the course, I started digging it. After finishing the course, I screamed, "I know Kung-Fu".
Union-Find made me realize the flaw in my approach that I was just busy finding ways to build graphs. The better way was to caching or keeping track of connected nodes as I am building the graph. Using a tree structure never came into my mind during my attempts to solve it before watching the course.
Here is the C# version of Union-Find converted from Java (using Improved algorithm, which tracks sizes)
|internal class QuickUnionUF|
|private readonly int _id;|
|private readonly int _size;|
|public QuickUnionUF(int n)|
|_id = new int[n + 1];|
|_size = new int[n + 1];|
|for (int i = 0; i < n; i++)|
|_id[i] = i;|
|_size[i] = 1;|
|private int GetRoot(int i)|
|while (i != _id[i])|
|i = _id[i];|
|public bool IsConnected(int p, int q)|
|return GetRoot(p) == GetRoot(q);|
|public void Union(int p, int q)|
|int i = GetRoot(p);|
|int j = GetRoot(q);|
|if (i == j) return;|
|if (_size[i] < _size[j])|
|_id[i] = j;|
|_size[j] += _size[i];|
|_id[j] = i;|
|_size[i] += _size[j];|
|public int GetMaximumConnectedRoute()|
I was able to solve the problem with this code without any timeouts. Learning a new algorithm will make your day as well!
The full source for the Maximal Tourism answer is posted on GitHub.
Check out Union-Find and see how you can integrate it into your existing code base.
You can find Union-Find algorithm applications in the last video in the course.