Iterate through 2 collections

Question

Hi,
I have two collections. One collection (A) has "Item" objects. Next collection (B) has Strings, these Strings are ids of Items.
class Item{
    String id;
    String ....
}All the ids in Collection B matches with Item object's id field in Collection A.
ie: Collection B does not have a single id where you can't find an item object in Collection A.
So Collection A is larger than Collection B.
I have to iterate through the Collections and I want to separate the Items in Collection A into separate collections depending on whether Item's id was found in Collection B or not.
My question is; which one is good in Big-O.
1. for(Item i: A){
   for(String id: B){
}2. for(String id: B){
   for(Item i: A){
}Could you explain pls?

Answer 1

So, do you want someone to agree on ejp's explanation? Shall I repeat?
|A| = N
|B| = M
1. f.a. a in A: (f.a. b in B: b.id = a => retain(b))
2. f.a. b in B: (f.a. a in A: b.id = a => retain(b))
Without any "optimization" you get O(N*M) in both cases.
In both cases, you could break the inner loop once you found a match. I'd say that WLOG one will have to scan half the inner collection in average to find a match, so we have:
1. O(A * B/2)
2. O(B * A/2)
Which, obviously, is the same.
If one of the collections is sorted, the sorted one should be the inner loop, as it only takes O(log2(X)) instead O(X/2) to search for a match.
If one of the collections is hashed, the hashed one should be the inner loop, as it takes O(1) to search for a match (depending on the distribution of hash values).