What is recurrence for worst case of QuickSort and what is the time complexity in Worst case?
A. Recurrence is T(n) = T(n-2) + O(n) and time complexity is O(n²)
B. Recurrence is T(n) = T(n-1) + O(n) and time complexity is O(n²)
C. Recurrence is T(n) = 2T(n/2) + O(n) and time complexity is O(nLogn)
D. Recurrence is T(n) = T(n/10) + T(9n/10) + O(n) and time complexity is O(nLogn)
Solution :
B) is correct.
The worst case of QuickSort occurs when the picked pivot is always one of the corner elements in sorted array. In worst case, QuickSort recursively calls one subproblem with size 0 and other subproblem with size (n-1). So recurrence is
T(n) = T(n-1) + T(0) + O(n)
The above expression can be rewritten as
T(n) = T(n-1) + O(n)
Below we can see the implementation of QuickSort :
