# Sorting

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Parameter Descrip;tion
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

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:

Well-known unstable sorts: