For already sorted, quick sort performance degrades to O(N^{2}) . Here, all the elements are equal, means array is already sorted . So, it should degrade to O(N^{2}) .

But, quick sort is more improved now and it can be implemented by 2 partition methods - Hoare's and Lomuto's partition method .

A rigourous and detailed implementation is shown here =>

There is no such situation in which Lomuto can perform better than Hoare.

Hoare always gives optimal partitioning and gives O(N log N) whereas Lomuto observes the worst case partitioning, making the overall performance still degrading to O(N^{2}) .