What is recurrence for worst case of QuickSort and what is the time complexity in Worst case?
Question
What is recurrence for worst case of QuickSort and what is the time complexity in Worst case?
Solution
The worst case of QuickSort occurs when the partition process always picks greatest or smallest element as pivot. If we consider a large array with n elements, the partition process will divide the array into two sub-arrays with 0 and n-1 elements. So, the recurrence for the worst case is:
T(n) = T(n-1) + Θ(n)
The above recurrence represents time complexity in the worst case and solving it we get the time complexity as Θ(n^2).
The Θ(n) is the time required to process the partition. Since in worst case, the partition process is performed n times (recursively), the time complexity in worst case becomes Θ(n^2).
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