# Sorting
# Stability in Sorting
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 (opens new window)
- Insertion sort (opens new window)
- Radix sort (opens new window)
- Tim sort
- Bubble Sort (opens new window)
Well-known unstable sorts:
# Parameters
| 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). |