Final answer:
Repeated elements in an array can severely decrease the efficiency of quicksort to O(n^2), especially if the list consists solely of identical items. The solution to handle repeated elements more efficiently in quicksort is to use a 3-way partition quicksort.
Step-by-step explanation:
The performance of the quicksort algorithm can be affected by the presence of repeated elements. When quicksort recursively divides the array, if elements are mostly identical, this division is not efficient because it does not split the list into two substantially equal parts. In the extreme case where the entire list consists of the same element, quicksort's running time would degrade to O(n^2), as it does not partition the list effectively (each partition step results in one less element for the next step, leading to quadratic time complexity).
To address the issue with repeated elements, a modified version of quicksort, known as 3-way partition quicksort, can be used. This version of quicksort divides the list into three parts: elements less than the pivot, elements equal to the pivot, and elements greater than the pivot. By doing this, it improves the partitioning step and thus the efficiency on lists with many repeated elements.