How can I quickly tell if a list contains only duplicates?

Question

There are multiple related questions, but I'm looking for a solution specific to my case. There is an array of (usually) 14 integers. How can I quickly tell if each int appears exactly twice (i.e. there are 7 pairs)? The value range is from 1 to 35. The main aspect here is performance.

For reference, this is my current solution. It was written to resemble the spec as closely as possible and without performance in mind, so I'm certain is can be improved vastly:

var pairs = Array
    .GroupBy (x => x)
    .Where (x => x.Count () == 2)
    .Select (x => x.ToList ())
    .ToList ();
IsSevenPairs = pairs.Count == 7;

Using Linq is optional. I don't care how, as long as it's fast :)

Edit: There is the special case that an int appears 2n times with n > 1. In this case the check should fail, i.e. there should be 7 distinct pairs.

Edit: Result I tested Ani's and Jon's solutions with tiny modifications and found during multiple benchmark runs in the target app that Ani's has about twice Jon's throughput on my machine (some Core 2 Duo on Win7-64). Generating the array of ints already takes about as long as the respective checks, so I'm happy with the result. Thanks, all!

Answer 1

Well, given your exact requirements, we can be a bit smarter. Something like this:

public bool CheckForPairs(int[] array)
{
    // Early out for odd arrays.
    // Using "& 1" is microscopically faster than "% 2" :)
    if ((array.Length & 1) == 1)
    {
        return false;
    }

    int[] counts = new int[32];
    int singleCounts = 0;
    foreach (int item in array)
    {
        int incrementedCount = ++counts[item];
        // TODO: Benchmark to see if a switch is actually the best approach here
        switch (incrementedCount)
        {
            case 1:
                singleCounts++;
                break;
            case 2:
                singleCounts--;
                break;
            case 3:
                return false;
            default:
                throw new InvalidOperationException("Shouldn't happen");
        }
    }
    return singleCounts == 0;
}

Basically this keeps track of how many unpaired values you still have, and has an "early out" if it ever finds three of a kind.

(I don't know offhand whether this will be faster or slower than Ani's approach of incrementing and then checking for unmatched pairs afterwards.)