Final answer:
The Big-O notation for Quick Sort's running time with evenly split sub lists is O(n log n), which results from the recursive depth of log n and the n operations at each level.
Step-by-step explanation:
Quicksort is a divide-and-conquer algorithm. It works by selecting a 'pivot' element from the array and partitioning the other elements into two sub-arrays, according to whether they are less than or greater than the pivot. The Big-O notation for Quick Sort's running time, when the sublists are evenly split, is O(n log n). Quick Sort operates by selecting a 'pivot' element from the array and partitioning the other elements into two subarrays, according to whether they are less than or greater than the pivot.
The sublists are then sorted recursively. In the case where the partitioning is balanced, each level of recursion processes about half the number of elements as the previous level, therefore the recursive tree has a depth of log n, and each level of recursion involves O(n) operations across all the sub lists at that level. Consequently, the overall time complexity is given by multiplying these two factors, resulting in O(n log n).