Sorting algorithm with quadratic and linear runtime

Question

Is it possible to make a sorting algorithm

That its running time at worst case is quadratic => n^2

But in most cases

(That is, on more than half of the n-size inputs)

the run time will be linear => n ??

I was thinking about Radix Sort and just make the worst case, worse

But I do not know if it is possible.

Answer 1

yes, the Bucket Sort

https://www.geeksforgeeks.org/bucket-sort-2/?ref=lbp

you can reed abut the algorithm in the link

In the worst case, we could have a bucket which contains all n values of the array. Since insertion sort has worst case running time O(n^2), so does Bucket sort. We can avoid this by using merge sort to sort each bucket instead, which has worst case running time O(n lg n).

Answer 2

Yes, it is possible.

Bucket sort analysis does reveal such behaviour (with reasonable number of buckets).