Measuring performance is a difficult task. All the benchmarks on this page are synthetic in the sense that they test one function repeatedly. Measurements in live systems are much harder to produce reliably. So take the following data with a grain of salt. That being said, a stated feature of :doc:`Sorted Containers<index>` is performance so we would be remiss not to produce this page with comparisons.

The source for all benchmarks can be found under the "tests" directory in the files prefixed "benchmark." Measurements are made from the min, max, and median of 5 repetitions. In the graphs below, the line follows the median at each point. Note that the axes are log-log so properly reading two different lines would describe one metric as "X times" faster rather than "X seconds" faster. In all graphs, lower is better. Measurements are made by powers of ten: 100 through 10,000,000.

Measurements up to ten billion elements have been successfully tested and benchmarked. Read :doc:`performance-scale` for details. Only a couple implementations (including :doc:`Sorted Containers<index>`) are capable of handling so many elements. The major limiting factor at that size is memory. Consider the simple case of storing CPython's integers in a :doc:`sortedlist`. Each integer object requires ~24 bytes so one hundred million elements will require about three gigabytes of memory. If the implementation adds significant overhead then most systems will run out of memory. For all datasets which may be kept in memory, :doc:`Sorted Containers<index>` is an excellent choice.

A good effort has been made to find competing implementations. Seven in total were found with various list, set, and dict implementations.

1. blist -- Provides list, dict, and set containers based on the blist data-type. Uses a B-Tree data structure. Implemented in Python and C. BSD License. Last updated March, 2014. blist on PyPI
2. bintrees -- Provides several tree-based implementations for dict and set containers. Fastest were AVL-Tree and Red-Black-Tree data structures.. Extends the conventional API to provide set operations for the dict type. Now deprecated in favor of :doc:`Sorted Containers<index>` Implemented in C. MIT License. Last updated April, 2017. bintrees on PyPI
3. sortedmap -- Provides a fast, C++ implementation for dict data types. Uses the C++ standard library std::map data structure which is usually a red-black tree. Last updated February, 2016. sortedmap on PyPI
4. banyan -- Provides a fast, C++ implementation for dict and set data types. Offers some features also found in sortedcontainers like accessing the n-th item in a set or dict. Uses sources from the tree implementation in GNU libstdc++. GPLv3 License. Last updated April, 2013. banyan on PyPI
5. treap -- Uses Cython for improved performance and provides a dict container. Apache V2 License. Last updated June, 2017. treap on PyPI
6. skiplistcollections -- Pure-Python implementation based on skip-lists providing a limited API for dict and set types. MIT License. Last updated January, 2014. skiplistcollections on PyPI
7. sortedcollection -- Pure-Python implementation of sorted list based solely on a list. Feature-poor and inefficient for writes but included because it is written by Raymond Hettinger and linked from the official Python docs. MIT License. Last updated April, 2011. sortedcollection recipe

Several alternative implementations were omitted for reasons documented below:

1. rbtree -- C-implementation that only supports Python 2. Provides a fast, C-implementation for dict and set data types. GPLv3 License. Last updated March, 2012. rbtree on PyPI
2. ruamel.ordereddict.sorteddict -- C-implementation that only supports Python 2. Performance was measured in correspondence with the module author. Performance was generally very good except for __delitem__. At scale, deleting entries became exceedingly slow. MIT License. Last updated July, 2017. ruamel.ordereddict on PyPI
3. pyskiplist -- Pure-Python skip-list based implementation supporting a sorted-list-like interface. Now deprecated in favor of :doc:`Sorted Containers<index>`. MIT License. Last updated July, 2015. pyskiplist on PyPI
4. sorteddict -- Pure-Python lazily-computed sorted dict implementation. Now deprecated in favor of :doc:`Sorted Containers<index>`. GPLv3 License. Last updated September, 2007. sorteddict on PyPI
5. rbtree from NewCenturyComputers -- Pure-Python tree-based implementation. Not sure when this was last updated. Unlikely to be fast. Unknown license. Unknown last update. rbtree from NewCenturyComputers
6. python-avl-tree from GitHub user pgrafov -- Pure-Python tree-based implementation. Unlikely to be fast. MIT License. Last updated October, 2010. python-avl-tree from GitHub user pgrafov
7. pyavl -- C-implementation for AVL tree-based dict and set containers. Claims to be fast. Lacking documentation and failed to build. Public Domain License. Last updated December, 2008. pyavl on PyPI
8. skiplist -- C-implementation of sorted list based on skip-list data structure. Only supports Python 2. Zlib/libpng License. Last updated Septemeber, 2013. skiplist from Bitbucket user mojaves

The most similar module to :doc:`Sorted Containers<index>` is skiplistcollections given that each is implemented in Python. But as is displayed below, Sorted Containers is several times faster and provides a richer API. Often the pure-Python implementation in Sorted Containers is faster even than the C-implementation counterparts. Where it lacks, performance is generally on the same magnitude.

Because :doc:`Sorted Containers<index>` is implemented in pure-Python, its performance depends directly on the Python runtime. A :doc:`runtime performance comparison<performance-runtime>` is also included with data from popular runtimes.

:doc:`Sorted Containers<index>` uses a segmented-list data structure similar to a B-tree limited to two levels of nodes. As part of the implementation, a load factor is used to determine how many values should be stored in each node. This can have a significant impact on performance and a :doc:`load factor performance comparison<performance-load>` is also provided.

Though these benchmarks exercise only one API repeatedly, an effort has also been made to simulate real-world workloads. The :doc:`simulated workload performance comparison<performance-workload>` contains examples with comparisons to other implementations, load factors, and runtimes.

Some final notes about the graphs below. Missing data indicates the benchmark either took too long or failed. The set operations with tiny, small, medium, and large variations indicate the size of the container involved in the right-hand-side of the operation: tiny is exactly 10 elements; small is 10% of the size of the left-hand-side; medium is 50%; and large is 100%. :doc:`Sorted Containers<index>` uses a different algorithm based on the size of the right-hand-side of the operation for a dramatic improvement in performance.

The legends of the graphs below correlate the underlying data structure used the Python project. The correlation is as follows:

.. currentmodule:: sortedcontainers

Graphs comparing :doc:`sortedlist` performance.

Initializing with a list of random numbers using :func:`SortedList.__init__`.

Randomly adding values using :func:`SortedList.add`.

Randomly testing membership using :func:`SortedList.__contains__`.

Counting objects at random using :func:`SortedList.count`.

Deleting objects at random using :func:`SortedList.__delitem__`.

Retrieving objects by index using :func:`SortedList.__getitem__`.

Finding the index of an object using :func:`SortedList.index`.

Iterating a SortedList using :func:`SortedList.__iter__`.

Removing the last object using :func:`SortedList.pop`.

Remove an object at random using :func:`SortedList.remove`.

Updating a SortedList with a large iterable using :func:`SortedList.update`.

Updating a SortedList with a small iterable using :func:`SortedList.update`.

Graphs comparing :doc:`sorteddict` performance.

Initializing with a list of pairs of random numbers using :func:`SortedDict.__init__`.

Given a key at random, test whether the key is in the dictionary using :func:`SortedDict.__contains__`.

Given a key at random, retrieve the value using :func:`SortedDict.__getitem__`.

Given a key at random, set the value using :func:`SortedDict.__setitem__`.

Given a key at random, delete the value using :func:`SortedDict.__delitem__`.

Iterate the keys of a SortedDict using :func:`SortedDict.__iter__`.

Given an existing key at random, set the value using :func:`SortedDict.__setitem__`.

Graphs comparing :doc:`sortedset` performance.

Initializing with a list of random numbers using :func:`SortedSet.__init__`.

Randomly add values using :func:`SortedSet.add`.

Randomly test membership using :func:`SortedSet.__contains__`.

Set difference using :func:`SortedSet.difference`.

Set difference using :func:`SortedSet.difference`.

Set difference using :func:`SortedSet.difference`.

Set difference using :func:`SortedSet.difference`.

Set difference using :func:`SortedSet.difference_update`.

Set difference using :func:`SortedSet.difference_update`.

Set difference using :func:`SortedSet.difference_update`.

Set difference using :func:`SortedSet.difference_update`.

Set intersection using :func:`SortedSet.intersection`.

Set intersection using :func:`SortedSet.intersection`.

Set intersection using :func:`SortedSet.intersection`.

Set intersection using :func:`SortedSet.intersection`.

Set intersection using :func:`SortedSet.intersection_update`.

Set intersection using :func:`SortedSet.intersection_update`.

Set intersection using :func:`SortedSet.intersection_update`.

Set intersection using :func:`SortedSet.intersection_update`.

Iterating a set using :func:`SortedSet.__iter__`.

Remove the last item in a set using :func:`SortedSet.pop`.

Remove an item at random using :func:`SortedSet.remove`.

Set union using :func:`SortedSet.union`.

Set union using :func:`SortedSet.union`.

Set union using :func:`SortedSet.union`.

Set union using :func:`SortedSet.union`.

Set update using :func:`SortedSet.update`.

Set update using :func:`SortedSet.update`.

Set update using :func:`SortedSet.update`.

Set update using :func:`SortedSet.update`.

Set symmetric-difference using :func:`SortedSet.symmetric_difference`.

Set symmetric-difference using :func:`SortedSet.symmetric_difference`.

Set symmetric-difference using :func:`SortedSet.symmetric_difference`.

Set symmetric-difference using :func:`SortedSet.symmetric_difference`.

Set symmetric-difference using :func:`SortedSet.symmetric_difference_update`.

Set symmetric-difference using :func:`SortedSet.symmetric_difference_update`.

Set symmetric-difference using :func:`SortedSet.symmetric_difference_update`.

Set symmetric-difference using :func:`SortedSet.symmetric_difference_update`.