Minidx

Minidx is a term used in programming and mathematics to denote the position of the smallest element in a sequence, such as an array or list. It refers to the index at which the minimum value occurs, rather than the value itself. In the presence of ties, a common convention is to select the first occurrence of the minimum value.

Formally, for a sequence a[1..n], the minidx is the index i such that a[i] is less than or equal to every other a[j] for all j. The exact index can depend on the chosen numbering system: many languages use 0-based indexing (minidx in an array would be the position i where a[i] is minimal), while others use 1-based indexing.

Computationally, minidx can be found by a simple linear scan: traverse the sequence, keeping track of the smallest value seen so far and its index. This approach runs in O(n) time and O(1) additional space. In languages with built-in functions, the operation is often expressed as finding the position of the minimum element, sometimes called argmin.

Common variants and related concepts include argmin, which is the value that minimizes a function rather than the index, and maxidx, the index of the maximum element. Minidx is frequently used in algorithms such as selection sort, where the smallest element’s index is repeatedly located and swapped into place, and in optimization contexts to identify the location of minimal values in data or objective functions.

Edge cases include an empty sequence, for which minidx is undefined and may raise an error or return a sentinel value depending on the implementation.