https://en.wikipedia.org/wiki/Linear_extension
In order theory, the Szpilrajn extension theorem (also called the order-extension principle), proved by Edward Szpilrajn in 1930,[1] states that every strict partial order is contained in a total order. Intuitively, the theorem says that any method of comparing elements that leaves some pairs incomparable can be extended in such a way that every pair becomes comparable. The theorem is one of many examples of the use of the axiom of choice in the form of Zorn's lemma to find a maximal set with certain properties.
https://en.wikipedia.org/wiki/Szpilrajn_extension_theorem
Linear time[edit]
An algorithm is said to take linear time, or O(n) time, if its time complexity is O(n). Informally, this means that the running time increases at most linearly with the size of the input. More precisely, this means that there is a constant c such that the running time is at most cn for every input of size n. For example, a procedure that adds up all elements of a list requires time proportional to the length of the list, if the adding time is constant, or, at least, bounded by a constant.
Linear time is the best possible time complexity in situations where the algorithm has to sequentially read its entire input. Therefore, much research has been invested into discovering algorithms exhibiting linear time or, at least, nearly linear time. This research includes both software and hardware methods. There are several hardware technologies which exploit parallelism to provide this. An example is content-addressable memory. This concept of linear time is used in string matching algorithms such as the Boyer–Moore algorithm and Ukkonen's algorithm.
https://en.wikipedia.org/wiki/Time_complexity#Linear_time
Linear
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