When to use a SortedList<TKey, TValue> over a SortedDictionary<TKey, TValue>?

This may appear to be a duplicate of this [question][1], which asks "What’s the difference between [SortedList][2] and [SortedDictionary][3]?" Unfortunately, the answers do nothing more than quote the MSDN documentation (which clearly states that there are performance and memory use differences between the two) but don't actually answer the question.

In fact (and so this question doesn't get the same answers), according to MSDN:

> The SortedList<TKey, TValue> generic > class is a binary search tree with > O(log n) retrieval, where n is the > number of elements in the dictionary. > In this, it is similar to the > SortedDictionary<TKey, TValue> generic > class. The two classes have similar > object models, and both have O(log n) > retrieval. Where the two classes > differ is in memory use and speed of > insertion and removal: > > * SortedList<TKey, TValue> uses less > memory than SortedDictionary<TKey, > TValue>. > > * SortedDictionary<TKey, TValue> has > faster insertion and removal > operations for unsorted data, O(log n) > as opposed to O(n) for > SortedList<TKey, TValue>. > > * If the list is populated all at once > from sorted data, SortedList<TKey, > TValue> is faster than > SortedDictionary<TKey, TValue>.

So, clearly this would indicated that SortedList<TKey, TValue> is the better choice unless you need faster insert and remove operations for unsorted data.

The question still remains, given the information above what are the practical (real-world, business case, etc.) reasons for using a SortedDictionary<TKey, TValue>? Based on the performance information, it would imply that there really is no need to have SortedDictionary<TKey, TValue> at all. [1]: https://stackoverflow.com/questions/935621/whats-the-difference-between-sortedlist-and-sorteddictionary [2]: http://msdn.microsoft.com/en-us/library/ms132319.aspx [3]: http://msdn.microsoft.com/es-mx/library/f7fta44c.aspx

I'm not sure how accurate the MSDN documentation is on SortedList and SortedDictionary. It seems to be saying both are implemented using a binary search tree. But if the SortedList uses a binary search tree, why would it be much slower on additions than SortedDictionary?

Anyway, here are some performance test results.

Each test operates on a SortedList / SortedDictionary containing 10,000 int32 keys. Each test is repeated 1,000 times (Release build, Start without Debugging).

The first group of tests add keys in sequence from 0 to 9,999. The second group of tests add random shuffled keys between 0 to 9,999 (every number is added exactly once).

***** Tests.PerformanceTests.SortedTest

SortedDictionary Add sorted: 4411 ms
SortedDictionary Get sorted: 2374 ms


SortedList Add sorted: 1422 ms
SortedList Get sorted: 1843 ms

***** Tests.PerformanceTests.UnsortedTest

SortedDictionary Add unsorted: 4640 ms
SortedDictionary Get unsorted: 2903 ms


SortedList Add unsorted: 36559 ms
SortedList Get unsorted: 2243 ms

As with any profiling, the important thing is the relative performance, not the actual numbers.

As you can see, on sorted data the sorted list is faster than the SortedDictionary. On unsorted data the SortedList is slightly quicker on retrieval, but about 9 times slower on adding.

If both are using binary trees internally, it is quite surprising that the Add operation on unsorted data is so much slower for SortedList. It is possible that sorted list may also be adding items to a sorted linear data structure at the same time, which would slow it down.

However, you would expect the memory usage of a SortedList to be equal or greater than or at least equal to a SortedDictionary. But this contradicts what the MSDN documentation says.

I don't know why MSDN says that SortedList<TKey, TValue> use a binary tree for its implementation because if you look at code with a decompiler like Reflector you realize its not true.

SortedList<TKey, TValue> is simply an array that grows over the time.

Every time you insert an element, it first check if the array has enough capacity, if not, a bigger array is recreated and old elements are copied into it (like List<T>)

After that, it searches where to insert the element, using a binary search (this is possible since the array is indexable and already sorted).

To keep the array sorted, it moves (or pushes) all the elements situated after position of element to be inserted by one position (using Array.Copy()).

Eg :

// we want to insert "3" 

2  
4  <= 3
5
8
9
.      
.      
.  

// we have to move some elements first

2
.  <= 3
4 
5  |
8  v
9
.
.

That explains why performance of SortedList is so bad when you insert unsorted elements. It has to re-copy some elements almost every insertion. The only case it has not to be done is when the element has to be inserted at the end of the array.

SortedDictionary<TKey, TValue> is different and use a binary tree to insert and retrieve elements. It also has some cost at insert because sometimes the tree need to be re-balanced (but not every insertion).

Performance is quite similar while searching an element with SortedList or SortedDictionary because they both use a binary search.

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In my opinion, you should never use SortedList to just sort an array. Unless you have very few elements, it will always be faster to insert values into a list (or array) and then call Sort() method.

SortedList is mostly useful when you have a list of values already sorted (eg: from database), you want to keep it sorted and perform some operations that would take advantage it is sorted (eg: Contains() method of SortedList performs a binary search instead of linear search)

SortedDictionary offers same advantages than SortedList but performs better if values to insert are not already sorted.

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EDIT : If you are using .NET Framework 4.5, an alternative to SortedDictionary<TKey, TValue> is SortedSet<T>. It works the same way as SortedDictionary, using a binary tree, but keys and values are the same here.

Are they meant for two different purposes?

There is not much semantic difference these two collection types in .NET make. They both offer keyed lookup as well as keep the entries in sort order of keys. In most cases you will be ok with either of them. Perhaps the only differentiator would be the indexed retrieval SortedList permits.

But performance?

However there is a performance difference which might be a stronger factor to choose between them. Here is a tabular view of their asymptotic complexity.

+------------------+---------+----------+--------+----------+----------+---------+
| Collection       | Indexed | Keyed    | Value  | Addition |  Removal | Memory  |
|                  | lookup  | lookup   | lookup |          |          |         |
+------------------+---------+----------+--------+----------+----------+---------+
| SortedList       | O(1)    | O(log n) | O(n)   | O(n)*    | O(n)     | Lesser  |
| SortedDictionary | n/a     | O(log n) | O(n)   | O(log n) | O(log n) | Greater |
+------------------+---------+----------+--------+----------+----------+---------+

* Insertion is O(1) for data that are already in sort order, so that each 
  element is added to the end of the list (assuming no resize is required).

Summary

To roughly summarize, you want a SortedList<K, V> when:

1. you require indexed look-up.
2. it's desirable to have lesser memory overhead.
3. your input data is already sorted (say you get it already ordered from db).

You would instead want to prefer a SortedDictionary<K, V> when:

1. relative overall performance matters (with respect to scaling).
2. your input data is unordered.

Writing code

Both SortedList<K, V> and SortedDictionary<K, V> implement IDictionary<K, V>, so in your code you can return IDictionary<K, V> from the method or declare variable as IDictionary<K, V>. Basically hide the implementation detail, and code against interface.

IDictionary<K, V> x = new SortedDictionary<K, V>(); //for eg. 

In future, its easier to switch from either in case you're not happy with performance characteristic of one collection.

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For more info on the two collection types see the original question linked.

Visual representation of performance differences.

That's all there is to it. Retrieval of keys is comparable, but addition is much faster with Dictionaries.

I try to use SortedList as much as possible because it allows me to iterate over the keys and value collections. This is not possible with SortedDictionary as far as I know.

I'm not sure about this, but as far as I know Dictionaries store data in Tree structures, whereas List store data in linear arrays. That explains why insertion and removal is much faster with dictionaries, since less memory has to be shifted around. It also explains why you can iterate over SortedLists but not SortedDictionary.

An important consideration for us is the fact that we often have small dictionaries (<100 elements), and current processessors much faster at accessing sequential memory while performing few difficult to predict branches. (i.e. iterating over a linear array rather than traversing a tree) So when you have less than about 60 elements in your dictionary, SortedList<> is often the fastest and most memory efficient dictionary in many use cases.