Why is Dictionary.First() so slow?

Question

Not a real question because I already found out the answer, but still interesting thing.

I always thought that hash table is the fastest associative container if you hash properly.

However, the following code is terribly slow. It executes only about 1 million iterations and takes more than 2 minutes of time on a Core 2 CPU.

The code does the following: it maintains the collection todo of items it needs to process. At each iteration it takes an item from this collection (doesn't matter which item), deletes it, processes it if it wasn't processed (possibly adding more items to process), and repeats this until there are no items to process.

The culprit seems to be the Dictionary.Keys.First() operation.

The question is why is it slow?

Stopwatch watch = new Stopwatch();
watch.Start();

HashSet<int> processed = new HashSet<int>();
Dictionary<int, int> todo = new Dictionary<int, int>();

todo.Add(1, 1);
int iterations = 0;

int limit = 500000;
while (todo.Count > 0)
{
    iterations++;
    var key = todo.Keys.First();
    var value = todo[key];
    todo.Remove(key);
    if (!processed.Contains(key))
    {
        processed.Add(key);
        // process item here
        if (key < limit) { todo[key + 13] = value + 1; todo[key + 7] = value + 1; }
        // doesn't matter much how
    }
}
Console.WriteLine("Iterations: {0}; Time: {1}.", iterations, watch.Elapsed);

This results in:

Iterations: 923007; Time: 00:02:09.8414388.

Simply changing Dictionary to SortedDictionary yields:

Iterations: 499976; Time: 00:00:00.4451514.

300 times faster while having only 2 times less iterations.

The same happens in java. Used HashMap instead of Dictionary and keySet().iterator().next() instead of Keys.First().

Answer 1

Dictionary<TKey, TValue> maintains a hash table.

Its enumerator will loop through the buckets in the hash table until it finds a non-empty bucket, then return the value in that bucket.
Once the dictionary grows large, this operation becomes expensive.
In addition, removing an item from the dictionary doesn't shrink the buckets array, so the First() call gets slower as you remove items. (Because it has to loop further to find a non-empty bucket)

Therefore, repeatedly calling First() and removing is O(n²).

---

By the way, you can avoid the value lookup like this: (This will not make it noticeably faster)

var kvp = todo.First();

//Use kvp.Key and kcp.Value

Answer 2

Dictionary makes no effort to keep track of a list of keys. So the iterator needs to walk the buckets. Many of these buckets, particularly for a large dictionary, many not have anything in them.

It may be helpful to compare OpenJDK's HashIterator.nextEntry and PrivateEntryIterator.nextEntry (which uses TreeMap.successor). The hash version walks an unknown number of entries looking for one that's non-null. This could be particularly slow if the hash table has had many elements removed (which it has in your case). In TreeMap, the only walking we do is our in-order traversal. There are no nulls in the way (only at the leaves).

Answer 3

Well, Hash Tables aren't sorted, my guess is it it has to do some sort of sort before it can do an iteration, or some sort of scan, if its already sorted, it can just loop through.

Answer 4

Reflector shows that Dictionary<TKey, TValue> maintains a Entry<TKey, TValue> array that it's KeyCollection<TKey, TValue>.Enumerator<TKey, TValue> uses. Normally, the lookup should be relatively fast, as it can just index into the array (assuming you don't want a sorted First):

// Dictionary<TKey. TValue>
private Entry<TKey, TValue>[] entries;

However, if you're removing the first elements of that array, then you end up walking the array until you find a non-empty one:

// Dictionary<TKey, TValue>.KeyCollection<TKey, TValue>.Enumerator<TKey, TValue>
while (this.index < this.dictionary.count) {
    if (this.dictionary.entries[this.index].hashCode >= 0) {
        this.currentKey = this.dictionary.entries[this.index].key;
        this.index++;
        return true;
    }
    this.index++;
}

As you remove your entries, you start getting more and more empties at the front of the entries array, and it becomes slower to retrieve First next time.

Answer 5

Without looking, the simplest implementation of a sorted dictionary is a sorted list (like TreeSet) of keys and a hash combined; the list gives you the ordering, the dictionary gives you values. Thus the keys are already available. Hashtable does not have keys readily available, thus the culprit is not first, it's keys (all without any shred of evidence, feel free to test the hypothesis ;D )