Unordered

Unordered is an adjective used to describe collections or sequences where the order of elements is not significant. In mathematics and computer science, an unordered collection treats different arrangements of the same elements as equivalent. For example, the sets {a, b} and {b, a} are the same unordered collection, because a set has no inherent order.

In mathematics, unordered collections include sets and multisets. The distinction between unordered and ordered objects is central in combinatorics: unordered selections (combinations) do not consider the sequence of chosen elements, whereas ordered objects (permutations) do. This helps distinguish problems where order matters from those where it does not.

In programming, many languages implement unordered containers using hash tables. These containers store elements without a meaningful iteration order, and they aim for fast average-case performance. For instance, C++ provides std::unordered_map and std::unordered_set, which offer average constant-time complexity for insertions and lookups, but the order of iteration is unspecified and can vary with rehashing and usage. Python uses hash-based structures for sets; those collections do not guarantee a stable iteration order. By contrast, ordered containers maintain a defined sequence or sort elements, which affects performance characteristics and semantics.

When order matters, explicit ordering or sorted structures should be used rather than unordered ones. Unordered collections are advantageous when fast access and unique membership are the primary requirements, and when the iteration order is irrelevant to the task.