Distinguishing extra element from two arrays?

Question

One of my friend was asked this question in an interview -

• You have given two integer arrays each of size 10.
• Both contains 9 equal elements (say 1 t

Answer 1

Technically, you can do it in constant time, since the arrays (and values within them) are limited. For the generalized problem, we have to make out something trickier.

Here's a linear-time solution.

First, we should build a hash based on one array. Value lookup in a hash table takes O(1 + k/n) comparisons [1], where k is the length of hash table. Thus iteration over the first array (that contains n elements) and lookups for each value takes O(n+k).

Then we iterate the other one, looking up for each element in the hash. When an element is not found -- that's unique one from the other array. (O(n+k) again). Then we iterate hash to look for the second unique element (O(k)).

Total time is O(n+k). Since it doesn't make sense to let k be more than n, it's the linear solution.

Perl code for that:

sub unique
{
  my ($arr, $brr) = @_;
  my %hash = map{$_ => 1} @$arr;
  %hash{$_}-- for @$brr;
  return grep {$_} keys %hash;
}