How to merge two big Lists in one sorted List in Java?

Question

I had an interview today, and they gave me:

List A has:

f  
google   
gfk  
fat  
...

List B has:

hgt    
google  
koko  
fat  
ffta  
...

They asked me to merge these two list in one sorted List C.

What I said:

I added List B to List A, then I created a Set from List A, then create a List from the Set. The interviewer told me the lists are big, and this method will not be good for performance, he said it will be a nlog(n).

What would be a better approach to this problem?

Answer 1

Well your method would require O(3N) additional space (the concatenated List, the Set and the result List), which is its main inefficiency.

I would sort ListA and ListB with whatever sorting algorithm you choose (QuickSort is in-place requiring O(1) space; I believe Java's default sort strategy is MergeSort which typically requires O(N) additional space), then use a MergeSort-like algorithm to examine the "current" index of ListA to the current index of ListB, insert the element that should come first into ListC, and increment that list's "current" index count. Still NlogN but you avoid multiple rounds of converting from collection to collection; this strategy only uses O(N) additional space (for ListC; along the way you'll need N/2 space if you MergeSort the source lists).

IMO the lower bound for an algorithm to do what the interviewer wanted would be O (NlogN). While the best solution would have less additional space and be more efficient within that growth model, you simply can't sort two unsorted lists of strings in less than NlogN time.

EDIT: Java's not my forte (I'm a SeeSharper by trade), but the code would probably look something like:

Collections.sort(listA);
Collections.sort(listB);

ListIterator<String> aIter = listA.listIterator();
ListIterator<String> bIter = listB.listIterator();
List<String> listC = new List<String>();

while(aIter.hasNext() || bIter.hasNext())
{
   if(!bIter.hasNext())
      listC.add(aIter.next());
   else if(!aIter.hasNext())
      listC.add(bIter.next());
   else
   {
      //kinda smells from a C# background to mix the List and its Iterator, 
      //but this avoids "backtracking" the Iterators when their value isn't selected.
      String a = listA[aIter.nextIndex()];
      String b = listB[bIter.nextIndex()];

      if(a==b) 
      {
         listC.add(aIter.next());
         listC.add(bIter.next());
      }
      else if(a.CompareTo(b) < 0)
         listC.add(aIter.next());
      else
         listC.add(bIter.next());          
   }
}