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Union-Find Algorithm

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 Featured Image - "Union St. Street Sign in Bodie" by m01229, used under CC BY-NC 2.0 (Medium sized image)

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];
return 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];
}
else
{
_id[j] = i;
_size[i] += _size[j];
}
}
public int GetMaximumConnectedRoute()
{
return _size.Max();
}
}
view raw QuickUnionUF.cs hosted with ❤ by GitHub

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.

Conclusion

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.