Question

Here is a common interview question i came across, however i failed to improve it in the way it demands.

assume we have an int array int[] A, we want to find the first duplicate entry. 

1. almost everyone can think of using a HashSet, and add to it while parsing.this will lead to O(n) time and O(n) space. After this I was asked to solve it without other data structures. I said the dumbest idea will be comparing each one in O(n^2) time. And then I was asked to improve the O(n^2) time.

2. And to improve it, i thought of using a fixed size array(assuming the maximum number is n), boolean[] b = new boolean[n]; however I was not allowed to use this method.

3. Then I thought of using an int variable, using bit manipulation, if the maximum number is smaller than 32, then for n we can push 1 to n bits left and | to a checker, then & the checker to the next entry in the array to check if it’s > 0.
   e.g.:

   int c = A[i];
   if(check & (1 << c) > 0) return false;
   check |= 1 << c;
   

however this is not allowed either.

So there was an hint that I can use the array itself as hashset/hashtable, and “linear hashing”?

any help ? thanks

Answer 1

Linear hashing as defined by Wikipedia has the advantage that resizing occurs incrementally, because buckets are split one-by-one in round-robin fashion, retaining constant amortized time complexity for insertion with resize. Their idea therefore is to iterate over the array, reusing the elements already iterated over as storage for linear hashing.

While I am far from an expert on linear hashing, I don’t see any way to fit the hash table in the array. Granted, to store n elements with linear hashing, you might get by with using n buckets. However, the number of elements in a bucket being unbounded, you’d need something like a linked list to implement each bucket, which costs an additional O(n) memory for pointers.

As such, this algorithm does not yield a better asymptotic space complexity than an ordinary HashSet. It does reduce memory consumption by a constant factor, though.

Its time complexity is on par with the ordinary HashSet.

Edit: It appears to me this answer is being ignored (no votes, no comments). Is it not useful? Please comment so I know what to improve.