> For the complete documentation index, see [llms.txt](https://blog.sunilgudivada.dev/notebook/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://blog.sunilgudivada.dev/notebook/data-structures-and-algorithms/topics/union-find-data-structure/quick-union-+-path-comparison.md).

# Quick Union + path comparison

## Quick Union + path comparison

![](https://1133441777-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MP3gpNOfmHBf90k26iY%2Fuploads%2Fgit-blob-70d162ac9a8233952bcacab128e601b097136620%2Fimage%20\(12\).png?alt=media)

![](https://1133441777-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MP3gpNOfmHBf90k26iY%2Fuploads%2Fgit-blob-1d8fce1f33daa4711a5a13f593a30ea26f504adb%2Fimage%20\(10\).png?alt=media)

![](https://1133441777-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MP3gpNOfmHBf90k26iY%2Fuploads%2Fgit-blob-61a429691942861e8837fc1192140e0309b04dc4%2Fimage%20\(15\).png?alt=media)

![](https://1133441777-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MP3gpNOfmHBf90k26iY%2Fuploads%2Fgit-blob-29bc4168af46b42ce895653c2a1f49fc0755e8c9%2Fimage%20\(18\).png?alt=media)

### Java Implementation

```java
public class QuickUnionPathComparisonUF 
{
   private int[] id;
   
   // set id of each object to itself (N array accesses)
   public QuickUnionUF(int N)
   {
      id = new int[N];
      for (int i = 0; i < N; i++) id[i] = i;
   }
   
   // chase parent pointers until reach root (depth of i array accesses)
   private int root(int i)
   {
      while (i != id[i])
      { 
         id[i] = id[id[i]]; // only change with quick union
         i = id[i];
      }
      return i; 
   }
   
   // check if p and q have same root (depth of p and q array accesses)
   public boolean connected(int p, int q)
   {
      return root(p) == root(q);
   }
   
   // change root of p to point to root of q (depth of p and q array accesses)
   public void union(int p, int q)
   {
      int i = root(p);
      int j = root(q);
      id[i] = j;
   }
}
```

##