What is the BigO complexity of intersection for TreeSet algorithm?

Question

What is the BigO complexity of following lgorithms:

boolean intersection(TreeSet<?> set1, TreeSet<?> set1){
   if(set1.size() > set2.size()){
      return intersection(set2, set1);
   }
   for (Object e: set1){
       if(set2.contains(e)) return true;
   }
   return false;

}

UPDATE:

 N:=set1.size()
  K:=set2.size()

The possible answers: O(N*K) or O(N*log(K)) or O(K*log(N)) or O(N+K)

It should be `O(n * log k)`, you could do in `O(n)` if you use a "two pointer" approach. Maybe you want to look up the intersection of two sorted sets. — Thomas Jungblut, Nov 28 '13 at 13:51
If you do a merge sort/intersection instead it will be `O(N+K)` — Peter Lawrey, Nov 28 '13 at 14:06
This question belongs on [cs.stackexchange.com](http://cs.stackexchange.com/) — CL., Nov 28 '13 at 21:08

score 1 · Accepted Answer · answered Nov 28 '13 at 13:51

1

O(N * log M)

N - size of set1, M - size of set2

Because we iterating on set1 elements (N) and for each iteration we call contains method which is logM complexity

TreeSet javadoc:

This implementation provides guaranteed log(n) time cost for the basic operations (add, remove and contains).

answered Nov 28 '13 at 13:51

mishadoff

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i think the performance is not `O(N log K)` – Sage Nov 28 '13 at 14:39
@Sage I would not agree that tree iteration is `O(n * log n)`. All that iterator does it's inorder traversal. That's definitely O(n). – mishadoff Nov 28 '13 at 16:37
Well, how are we supposed to do in-order traversal on a tree? What kind of relation among the node must exist ? is there any supporting evidence or implementation that tells that we can actually traverse all of the element of a balanced-binary search tree in `O(n)` ? – Sage Nov 28 '13 at 16:51
There is parent for each node. So we actually move up in the tree. Take a look http://stackoverflow.com/questions/5471731/in-order-successor-in-binary-search-tree – mishadoff Nov 28 '13 at 17:40
Thank you. I can't believe that i have overlooked this premature theoretical knowledge. Actually the `successor(e)` call made me confused in the `next()` call as i have pointed out in my answer :(. – Sage Nov 28 '13 at 17:58

What is the BigO complexity of intersection for TreeSet algorithm?

1 Answers1