precmin

Precmin is a term that does not have a single, universally accepted definition in mathematics or computer science. In practice, it is often used as shorthand for concepts related to the minimum value encountered in a sequence up to a point, sometimes specifically referring to a prefix minimum or to a previous minimum. Because it is not standardized, its exact meaning depends on context and the accompanying notation.

Possible interpretations

- Prefix minimum: precmin[i] may represent the minimum of all elements from the start of a sequence up to index i, i.e., precmin[i] = min(A[0], A[1], ..., A[i]). This form supports rapid queries about the smallest value seen so far.

- Previous minimum: precmin[i] may denote the minimum of elements strictly before index i, i.e., precmin[i] = min(A[0], A[1], ..., A[i-1]). This emphasizes values encountered prior to the current position.

- Running minimum in algorithms: In various algorithms, precmin can be used as a variable or structure field that carries forward the smallest value found along a search, scan, or streaming process.

Relation to other ideas

Precmin is closely related to concepts such as the prefix minimum, running minimum, cumulative minimum, and sliding-window minimum. It is often implemented as an auxiliary array aligned with the input to support constant-time queries about the smallest value observed up to each point.

Usage and clarification

Because precmin is not uniformly defined, encountering it in code or literature should prompt checking the surrounding definitions. If used in formal work, precmin should be explicitly defined to avoid ambiguity.

See also: prefix minimum, running minimum, cumulative minimum, monotone queue, sliding window minimum. Examples depend on the chosen interpretation of precmin in a given context.