TRUE FALSE TRUE FALSE Mergesort must complete approximately N passes before a list is sorted TRUE FALSE TRUE FALSE TRUE Mergesort runs in O(NlogN) FALSE Mergesort is somewhat faster than selection sort, but in the same Big O function family On each pass, mergesort will need to perform approximately logN comparisons There is no comparison sorting algorithm in a faster function family than mergesort (assuming no prior knowledge about the unsorted items

How to solve this question

ALGORITHM Quicksort(A[l..r])//Sorts a subarray by quicksort//Input: Subarray of array A[0..n − 1], defined by its left and right// indices l and r//Output: Subarray A[l..r] sorted in nondecreasing order  if l < r    s = Partition(A[l..r]) //s is a split position    Quicksort(A[l..s − 1])    Quicksort(A[s + 1..r]) The above code is the quicksort algorithm.Perform a time complexity analysis for quicksort. You need to explain 1) what makes a worst case, what makes a best case, 2) the time complexity for both the worst case and the best case, 3) how to avoid the worst case in practice.

Create and test assumptions regarding the running times of insertion sort and selection sort for arrays with just two key values, assuming the values are equally likely to occur.

Note that this is also a Data Structure question.