Sorting Algorithms
Contents
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 (a_{1}, a_{2}, ... a_{n}) 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.
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
Sorting Algorithms
Key Comparison Sorting Algorithms
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. The worst-case running time of comparison sort algorithms is Ω(n lgn).
Non-Comparison Sorting Algorithms