Sorting Algorithms: Difference between revisions
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The '''sorting problem''' if formally defined as follows: given a sequence of n numbers (a<sub>1</sub>, a<sub>2</sub>, ... a<sub>n</sub>) provided as input, the algorithm must produce as output a permutation (reordering) (a<sup>'</sup><sub>1</sub>, a<sup>'</sup><sub>2</sub>, ... a<sup>'</sup><sub>n</sub>) of the input sequence such that a<sup>'</sup><sub>1</sub> ≤ a<sup>'</sup><sub>2</sub> ≤ ... ≤ a<sup>'</sup><sub>n</sub>. A specific input sequence is called an '''[[Data Structures and Algorithms#Instance_of_the_problem|instance]]''' of the sorting problem. Although conceptually we are sorting a '''sequence''', the input comes to the sorting function as an '''[[Array#Overview|array]]''' with n elements. | The '''sorting problem''' if formally defined as follows: given a sequence of n numbers (a<sub>1</sub>, a<sub>2</sub>, ... a<sub>n</sub>) provided as input, the algorithm must produce as output a permutation (reordering) (a<sup>'</sup><sub>1</sub>, a<sup>'</sup><sub>2</sub>, ... a<sup>'</sup><sub>n</sub>) of the input sequence such that a<sup>'</sup><sub>1</sub> ≤ a<sup>'</sup><sub>2</sub> ≤ ... ≤ a<sup>'</sup><sub>n</sub>. A specific input sequence is called an '''[[Data Structures and Algorithms#Instance_of_the_problem|instance]]''' of the sorting problem. Although conceptually we are sorting a '''sequence''', the input comes to the sorting function as an '''[[Array#Overview|array]]''' with n elements. | ||
The numbers we wish to sort are also known as '''keys'''. | The numbers we wish to sort are also known as '''keys'''. In practice, it is rarely the case when the keys exist in isolation. Usually they are part of a larger structure called '''record''', which also contains '''satellite data'''. | ||
<span id='Comparison_Sort'></span>A sorting algorithm may compare keys, and in this case it is said to be a '''key comparison algorithm'''. It can be demonstrated that a key comparison algorithm [[Comparison_Sorting_Algorithms_Complexity|cannot perform better than n lg n]]. | <span id='Comparison_Sort'></span>A sorting algorithm may compare keys, and in this case it is said to be a '''key comparison algorithm'''. It can be demonstrated that a key comparison algorithm [[Comparison_Sorting_Algorithms_Complexity|cannot perform better than n lg n]]. | ||
Revision as of 00:13, 10 August 2018
Internal
Overview
Many programs use sorting as an intermediate step, and that is why sorting is considered a fundamental operation in computer science.
The sorting problem if formally defined as follows: given a sequence of n numbers (a1, a2, ... an) provided as input, the algorithm must produce as output a permutation (reordering) (a'1, a'2, ... a'n) of the input sequence such that a'1 ≤ a'2 ≤ ... ≤ a'n. A specific input sequence is called an instance of the sorting problem. Although conceptually we are sorting a sequence, the input comes to the sorting function as an array with n elements.
The numbers we wish to sort are also known as keys. In practice, it is rarely the case when the keys exist in isolation. Usually they are part of a larger structure called record, which also contains satellite data.
A sorting algorithm may compare keys, and in this case it is said to be a key comparison algorithm. It can be demonstrated that a key comparison algorithm cannot perform better than n lg n.
Non-comparison sort.
Sorting algorithms characteristics:
- in place: a sorting algorithm is said to sort the input numbers "in place" if it rearranges the numbers within the input array, while at most a constant number of elements are stored outside the array at any time.
- stability