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Sorting algorithm

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Sorting algorithm
In computer science, a sorting algorithm is an algorithm that puts elements of a list in a certain order. The most-used orders are numerical order and lexicographical order. Efficient sorting is important for optimizing the use of other algorithms (such as search and merge algorithms) that require sorted lists to work correctly; it is also often useful for canonicalizing data and for producing human-readable output. More formally, the output must satisfy two conditions: 1. The output is in nondecreasing order (each element is no smaller than the previous element according to the desired total order);
2. The output is a permutation, or reordering, of the input.
Since the dawn of computing, the sorting problem has attracted a great deal of research, perhaps due to the complexity of solving it efficiently despite its simple, familiar statement. For example, bubble sort was analyzed as early as 1956.[1] Although many consider it a solved problem, useful new sorting algorithms are still being invented
(for example, library sort was first published in 2004). Sorting algorithms are prevalent in introductory computer science classes, where the abundance of algorithms for the problem provides a gentle introduction to a variety of core algorithm concepts, such as big O notation, divide and conquer algorithms, data structures, randomized algorithms, best, worst and average case analysis, time-space tradeoffs, and lower bounds.

Classification
Sorting algorithms used in computer science are often classified by:
• Computational complexity (worst, average and best behaviour) of element comparisons in terms of the size of the list . For typical sorting algorithms good behavior is and bad behavior is
. (See Big
O notation.) Ideal behavior for a sort is

, but this is not possible in the average case. Comparison-based

sorting algorithms, which evaluate the elements of the list via an abstract key comparison