Parameter | Description |
---|---|

Stability | A sorting algorithm is stable if it preserves the relative order of equal elements after sorting. |

In place | A sorting algorithm is in-place if it sorts using only O(1) auxiliary memory (not counting the array that needs to be sorted). |

Best case complexity | A sorting algorithm has a best case time complexity of O(T(n)) if its running time is at least T(n) for all possible inputs. |

Average case complexity | A sorting algorithm has an average case time complexity of O(T(n)) if its running time, averaged over all possible inputs, is T(n) . |

Worst case complexity | A sorting algorithm has a worst case time complexity of O(T(n)) if its running time is at most T(n) . |

Stability in sorting means whether a sort algorithm maintains the relative order of the equals keys of the original input in the result output.

So a sorting algorithm is said to be stable if two objects with equal keys appear in the same order in sorted output as they appear in the input unsorted array.

Consider a list of pairs:**(1, 2) (9, 7) (3, 4) (8, 6) (9, 3)**

Now we will sort the list using the ﬁrst element of each pair.

A stable sorting of this list will output the below list:**(1, 2) (3, 4) (8, 6) (9, 7) (9, 3)**

Because (9, 3) appears after (9, 7) in the original list as well.

An unstable sorting will output the below list:**(1, 2) (3, 4) (8, 6) (9, 3) (9, 7)**

Unstable sort may generate the same output as the stable sort but not always.

Well-known stable sorts.

**Merge sort****Insertion sort****Radix sort****Tim sort****Bubble Sort**

Well-known unstable sorts:

**Heap sort****Quick sort**