Nothing special here. It’s just a blog post for summarising my algorithm learning course.


The underlying data structure for Quick Union is similar to Quick Find. We need an array for all the items. The values are still the id, but it’s the id of the parent item. The connected component is organised using a tree structure like this

  • isConnected(p, q) check whether the 2 items have the same root
  • union(p, q) set the id of p’s root to the id of q’s root

Sample implementation

  private int[] id;

  public QuickUnionUF(int N)
    // set id of each object to itself
    // (N array accesses)
    id = new int[N];
    for (int i = 0; i < N; i++) id[i] = i;

  private int root(int i)
    // chase parent pointers until reach root
    // (depth of i array accesses)
    while (i != id[i]) i = id[i];
    return i;

  public boolean connected(int p, int q)
    // check if p and q have same root
    // (depth of p and q array accesses)
    return root(p) == root(q);

  public void union(int p, int q)
    // change root of p to point to root of q
    // (depth of p and q array accesses)
    int i = root(p);
    int j = root(q);
    id[i] = j;


Method Complexity  
isConnected(p, q) O(N) Worst case, have to traverse through all items
union(p, q) O(n) Only need to update 1 id but including the cost of finding roots

=> Quick Union is faster than Quick Find when performing isConnected command but still too slow for large data set.