Sortedcontainers

Sortedcontainers is a Python library that provides highly optimized implementations of sorted list, dictionary, and set data structures. These data structures are designed to be more performant than Python's built-in counterparts for certain operations, particularly those involving insertions and deletions in sorted order. The library aims to offer a balance between memory usage and speed, making it suitable for applications that require efficient management of ordered collections.

The core components of sortedcontainers include SortedList, SortedDict, and SortedSet. SortedList maintains its elements in sorted order, allowing for efficient searching, insertion, and deletion. Unlike a standard Python list, adding or removing an element from a SortedList preserves the sorted order without requiring a full re-sort. SortedDict functions similarly to a standard dictionary but keeps its items sorted by key. This enables efficient iteration over keys in sorted order and fast lookups based on key proximity. SortedSet provides the functionality of a set with the added benefit of maintaining elements in sorted order, offering fast membership testing, insertion, and deletion while ensuring order.

The library is implemented using a balanced tree structure, which allows for logarithmic time complexity for many operations. This makes sortedcontainers a valuable tool for tasks such as data analysis, scientific computing, and any application where maintaining and querying sorted data efficiently is crucial. It can be particularly useful when dealing with large datasets where the overhead of repeated sorting or inefficient data structure operations becomes a bottleneck. The library is freely available under a permissive license and can be installed using pip.