Theoretical analysis In the theoretical analysis of algorithms, the normal practice is to estimate their complexity in the asymptotic sense. The most commonly used notation to describe resource consumption or "complexity" is Donald Knuth's Big O notation, representing the complexity of an algorithm as a function of the size of the input . Big O notation is an asymptotic measure of function complexity, where roughly means the time requirement for an algorithm is proportional to , omitting lower-order terms that contribute less than to the growth of the function as grows arbitrarily large. This estimate may be misleading when is small, but is generally sufficiently accurate when is large as the notation is asymptotic. For example, bubble sort may be faster than merge sort when only a few items are to be sorted; however either implementation is likely to meet performance requirements for a small list. Typically, programmers are interested in algorithms that scale efficiently to large input sizes, and merge sort is preferred over bubble sort for lists of length encountered in most data-intensive programs.
Theoretical analysis In the theoretical analysis of algorithms, the normal practice is to estimate their complexity in the asymptotic sense. The most commonly used notation to describe resource consumption or "complexity" is Donald Knuth's Big O notation, representing the complexity of an algorithm as a function of the size of the input . Big O notation is an asymptotic measure of function complexity, where roughly means the time requirement for an algorithm is proportional to , omitting lower-order terms that contribute less than to the growth of the function as grows arbitrarily large. This estimate may be misleading when is small, but is generally sufficiently accurate when is large as the notation is asymptotic For example, bubble sort may be faster than merge sort when only a few items are to be sorted; however either implementation is likely to meet performance requirements for a small list. Typically, programmers are interested in algorithms that scale efficiently to large input sizes, and merge sort is preferred over bubble sort for lists of length encountered in most data-intensive programs.