Sorting Algorithms: Difference between revisions
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Many programs use sorting as an intermediate step, and that is why sorting is considered a fundamental operation in computer science. | 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 (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'''. | ||
Revision as of 04:20, 5 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.
Comparison sort. Cannot do better than n lg n. Proof in a separate article.
Non-comparison sort.
Sorting algorithms characteristics:
- in-place
- stability